Correlation between the Peak Spectral Energy of Gamma-Ray Bursts and the Peak Luminosity of the Underlying Supernovae: Implication for the Nature of GRB-SN Connection: In this paper we present a correlation between the peak spectral energy of gamma-ray bursts (GRBs) and the peak bolometric luminosity of the underlying supernovae (SNe), based on a sample of four pairs of GRBs-SNe with spectroscopically confirmed connection. Combining it with the well-known relation between the peak spectral energy and the isotropic equivalent energy of GRBs, we obtain an upper limit on the isotropic energy of GRBs, which is \approx 10^{52} erg (L_{SN,peak}/10^{43} erg s^{-1})^{10}, where L_{SN,peak} is the peak bolometric luminosity of the SNe. Our results suggest that the critical parameter determining the GRB-SN connection is the peak luminosity of SNe, rather than the feature of the SN spectra and/or the SN explosion energy as commonly hypothesized. Since it is generally believed that the peak luminosity of SNe powered by radioactive decays is related to the amount of 56Ni produced in the SN explosion, the mass of 56Ni may be a key physical factor for understanding the nature of GRBs and their connection with SNe. Application of our relation to Type Ibc SNe with normal peak luminosities indicates that if those normal SNe have GRBs accompanying them, the GRBs would be extremely soft and sub-energetic in gamma-rays, and hence easier to detect with X-ray or UV detectors than with gamma-ray detectors. [Mon. Not. R. Astron. Soc. 372, 1357 (2006)]
Improved Correlation between the Variability and Peak Luminosity of Gamma-Ray Bursts: A new procedure for smoothing a gamma-ray burst (GRB) lightcurve and calculating its variability is presented. Applying the procedure to a sample of 25 long GRBs, we have obtained a very tight correlation between the variability and the peak luminosity. The only significant outlier in the sample is GRB 030329. With this outlier excluded, the data scatter is reduced by a factor of ~3 compared to that of Guidorzi et al. (2005), measured by the deviation of fit. Possible causes for the outlier are discussed. [Mon. Not. R. Astron. Soc. 366, 219 (2006)]
Estimating the Spin of Stellar-Mass Black Holes via Spectral Fitting of the X-ray Continuum: We fit X-ray spectral data in the thermal dominant or high soft state of two dynamically confirmed black holes, GRO J1655-40 and 4U1543-47, and estimate the dimensionless spin parameters a* = a/M of the two holes. Our spectral model consists of one principal component, a multitemperature blackbody disk model that includes all general relativistic effects, plus standard low-energy absorption and Gaussian line components. For GRO J1655-40, using a luminosity-dependent spectral hardening factor computed for a non-LTE relativistic accretion disk, we estimate a* ~ 0.8 and ~ 0.7-0.75, respectively, from ASCA and RXTE data. For 4U 1543-47, we estimate a* ~ 0.85-0.9 from RXTE data. We conclude that neither black hole is likely to have a spin approaching the theoretical maximum a* = 1. On the other hand, the spin of 4U1543-47 appears to be too large to be explained by disk accretion over the lifetime of the system, which suggests that our measurements are sensitive to the natal spins of these black holes. [Astrophys. J. Lett. 636, L113 (2006)]
Vacuum Polarization in an Anti-de Sitter Space as an Origin for a Cosmological Constant in a Brane World: In this Letter we show that the vacuum polarization of quantum fields in an anti-de Sitter space naturally gives rise to a small but nonzero cosmological constant in a brane world living in it. To explain the extremely small ratio of mass density in the cosmological constant to the Planck mass density in our universe (\approx 10^{-123}) as suggested by cosmological observations, all we need is a four-dimensional brane world (our universe) living in a five-dimensional anti-de Sitter space with a curvature radius r_0 \sim 10^{-3}cm and a fundamental Planck energy M_P \sim 10^9 GeV, and a scalar field with a mass m \sim r_0^{-1}\sim 10^{-2}eV. Probing gravity down to a scale \sim 10^{-3}cm, which is attainable in the near future, will provide a test of the model. [Mod. Phys. Lett. A20, 733 (2005)]
Multi-Temperature Blackbody Spectrum of a Thin Accretion Disk around a Kerr Black Hole: Model Computations and Comparison with Observations: We use a ray-tracing technique to compute the observed spectrum of a thin accretion disk around a Kerr black hole. We include all relativistic effects such as frame-dragging, Doppler boost, gravitational redshift, and bending of light by the gravity of the black hole. We also include self-irradiation of the disk as a result of light deflection. Assuming that the disk emission is locally blackbody, we show how the observed spectrum depends on the spin of the black hole, the inclination of the disk, and the torque at the inner edge of the disk. We find that the effect of a nonzero torque on the spectrum can, to a good approximation, be absorbed into a zero-torque model by adjusting the mass accretion rate and the normalization. We describe a computer model, called KERRBB, which we have developed for fitting the spectra of black hole X-ray binaries. Using KERRBB within the X-ray data reduction package XSPEC, and assuming a spectral hardening factor f_col = 1.7, we analyze the spectra of three black hole X-ray binaries: 4U1543-47, XTE J1550-564, and GRO J1655-40. We estimate the spin parameters of the black holes in 4U1543-47 and GRO J1655-40 to be a/M ~ 0.6 and ~ 0.6-0.7, respectively. If f_col ~ 1.5-1.6, as in a recent study, then we find a/M ~ 0.7-0.8 and ~ 0.8-0.9, respectively. These estimates are subject to additional uncertainties in the assumed black hole masses, distances and disk inclinations. [Astrophys. J. Suppl. 157, 335 (2005)]
Energetics of a Black Hole-Accretion Disk System with Magnetic Connection: Limit of Low Accretion Rate: We study the energetics of a black hole-accretion disk system with magnetic connection: a Keplerian disk is connected to a Kerr black hole by a large-scale magnetic field going through the transition region. We assume that the magnetic field is locked to the inner boundary of the disk and corotates with the inner boundary, the accretion rate is low but the accretion from the disk can still provide enough amount of cold plasma particles in the transition region so that the magnetohydrodynamics approximation is valid. Then, the magnetic field is dynamically important in the transition region and affects the transportation of energy and angular momentum. Close to the equatorial plane, the motion of particles is governed by a one-dimensional radial momentum equation, which contains a fast critical point as the only intrinsic singularity. By finding solutions that smoothly pass the fast critical point, we find that a system with a fast rotating black hole and that with a slow rotating black hole behave very differently. For a black hole with $a > a_{\rm cr}\equiv 0.3594 M$, where $M$ is the mass, $a$ the specific angular momentum of the black hole, the spinning energy of the black hole is efficiently extracted by the magnetic field and transported to the disk, increasing the radiation efficiency of the disk by many orders of magnitude. For a black hole with $0\leq a < a_{\rm cr}$, the inner region of the disk is disrupted by the magnetic field and the inner boundary of the disk moves out to a radius where the Keplerian angular velocity of the disk is equal to the spinning angular velocity of the black hole (which is at infinity if the black hole is nonrotating). As a result, the disk may have an extremely low radiation efficiency if $0\leq a/M \ll 1$. [Publ. Astron. Soc. Jap. 56, 685 (2004)]
Quasi-periodic Oscillations from Rayleigh-Taylor and Kelvin-Helmholtz Instability at a Disk-Magnetosphere Interface: We consider the interface between an accretion disk and a magnetosphere surrounding the accreting mass. We argue that such an interface can occur not only with a magnetized neutron star but also sometimes with an unmagnetized neutron star or a black hole. The gas at the magnetospheric interface is generally Rayleigh-Taylor unstable and may also be Kelvin-Helmholtz unstable. Because of these instabilities, modes with low azimuthal wavenumbers m are expected to grow to large amplitude. It is proposed that the resulting nonaxisymmetric structures contribute to the high frequency quasi-periodic oscillations that have been seen in neutron-star and black-hole X-ray binaries. The mode oscillation frequencies are calculated to be approximately equal to m \Omega_m, where \Omega_m is the angular velocity of the accreting gas at the magnetospheric radius. Thus, mode frequencies should often be in the approximate ratio 1:2:3, etc. If the pressure of the gas in the disk is not large, then the m = 1 mode will be stable. In this case, the mode frequencies should be in the approximate ratio 2:3, etc. There is some observational evidence for such simple frequency ratios. [Astrophys.J. 601, 414 (2004)]
Double-Peaked Low-Ionization Emission Lines in Active Galactic Nuclei: We present a new sample of 116 double-peaked Balmer line Active Galactic Nuclei (AGN) selected from the Sloan Digital Sky Survey. Double-peaked emission lines are believed to originate in the accretion disks of AGN, a few hundred gravitational radii (Rg) from the supermassive black hole. We investigate the properties of the candidate disk emitters with respect to the full sample of AGN over the same redshifts, focusing on optical, radio and X-ray flux, broad line shapes and narrow line equivalent widths and line flux-ratios. We find that the disk-emitters have medium luminosities (~10^44erg/s) and FWHM on average six times broader than the AGN in the parent sample. The double-peaked AGN are 1.6 times more likely to be radio-sources and are predominantly (76%) radio quiet, with about 12% of the objects classified as LINERs. Statistical comparison of the observed double-peaked line profiles with those produced by axisymmetric and non-axisymmetric accretion disk models allows us to impose constraints on accretion disk parameters. The observed Halpha line profiles are consistent with accretion disks with inclinations smaller than 50 deg, surface emissivity slopes of 1.0-2.5, outer radii larger than ~2000 Rg, inner radii between 200-800Rg, and local turbulent broadening of 780-1800 km/s. The comparison suggests that 60% of accretion disks require some form of asymmetry (e.g., elliptical disks, warps, spiral shocks or hot spots). [Astron.J. 126, 1720 (2003); Erratum: Astron. J. 130, 1961 (2005)]
Gravitational Lensing by a Compound Population of Halos: Standard Models: Based on observed rotation curves of galaxies and theoretical simulations of dark matter halos, there are reasons for believing that at least three different types of dark matter halos exist in the Universe classified by their masses M and the inner slope of mass density -\alpha: Population A (galaxies): 10^{10} h^{-1} M_\odot < M < 2 \times 10^{13} h^{-1} M_\odot, \alpha = 2; Population B (cluster halos): M > 2 \times 10^{13} h^{-1} M_\odot, \alpha = 1.3; and Population C (dwarf halos): M < 10^{10} h^{-1} M_\odot, \alpha = 1.3. In this paper we calculate the lensing probability produced by such a compound population of dark halos, for both image separation and time delay, assuming that the mass function of halos is given by the Press-Schechter function and the Universe is described by an LCDM, OCDM, or SCDM model. The LCDM model is normalized to the WMAP observations, OCDM and SCDM models are normalized to the abundance of rich clusters. We compare the predictions of the different cosmological models with observational data and show that, both LCDM and OCDM models are marginally consistent with the current available data, but the SCDM model is ruled out. The fit of the compound model to the observed correlation between splitting angle and time delay is excellent but the fit to the number vs splitting angle relation is only adequate using the small number of sources in the objective JVAS/CLASS survey. A larger survey of the same type would have great power in discriminating among cosmological models. Furthermore, population C in an LCDM model has a unique signature in the time domain, an additional peak at ~3 seconds potentially observable in GRBs, which makes it distinguishable from variants of CDM scenarios, such as warm dark matter, repulsive dark matter, or collisional dark matter. [Astrophys. J. 595, 603 (2003)]
Nonaxisymmetric g-Mode and p-Mode Instability in a Hydrodynamic Thin Accretion Disk: It has been suggested that quasi-periodic oscillations of accreting X-ray sources may relate to the modes named in the title. We consider non-axisymmetric linear perturbations to an isentropic, isothermal, unmagnetized thin accretion disk. The radial wave equation, in which the number of vertical nodes (n) appears as a separation constant, admits a wave-action current that is conserved except, in some cases, at corotation. Waves without vertical nodes amplify when reflected by a barrier near corotation. Their action is conserved. As was previously known, this amplification allows the n=0 modes to be unstable under appropriate boundary conditions. In contrast, we find that waves with n >0 are strongly absorbed at corotation rather than amplified; their action is not conserved. Therefore, non-axisymmetric p-modes and g-modes with n>0 are damped and stable even in an inviscid disk. This eliminates a promising explanation for quasi-periodic oscillations in neutron-star and black-hole X-ray binaries. [Astrophys.J. 593, 980 (2003)]
Disk Accretion Flow Driven by Large-Scale Magnetic Fields: Solutions with Constant Specific Energy: (Abridged) We study the dynamical evolution of a stationary, axisymmetric, and perfectly conducting cold accretion disk containing a large-scale magnetic field around a Kerr black hole, trying to understand the relation between accretion and the transportation of angular momentum and energy. We solve the radial momentum equation for solutions corresponding to an accretion flow that starts from a subsonic state at infinity, smoothly passes the fast critical point, then supersonically falls into the horizon of the black hole. The solutions always have the following features: 1) The specific energy of fluid particles remains constant but the specific angular momentum is effectively removed by the magnetic field. 2) At large radii, where the disk motion is dominantly rotational, the energy density of the magnetic field is equipartitioned with the rotational energy density of the disk. 3) Inside the fast critical point, where radial motion becomes important, the ratio of the electromagnetic energy density to the kinetic energy density drops quickly. The results indicate that: 1) Disk accretion does not necessarily imply energy dissipation since magnetic fields do not have to transport or dissipate a lot of energy as they effectively transport angular momentum. 2) When resistivity is small, the large-scale magnetic field is amplified by the shearing rotation of the disk until the magnetic energy density is equipartitioned with the rotational energy density, ending up with a geometrically thick disk. This is in contrast with the evolution of small-scale magnetic fields where if the resistivity is nonzero the magnetic energy density is likely to be equipartitioned with the kinetic energy density associated with local random motions (e.g., turbulence), making a thin Keplerian disk possible. [Phys. Rev. D68, 024022 (2003)]
Evolution of Magnetic Fields around a Kerr Black Hole: The evolution of magnetic fields frozen to a perfectly conducting plasma fluid around a Kerr black hole is investigated. We focus on the plunging region between the black hole horizon and the marginally stable circular orbit in the equatorial plane. Adopting the kinematic approximation where the dynamical effects of magnetic fields are ignored, we exactly solve Maxwell's equations with the assumptions that the geodesic motion of the fluid is stationary and axisymmetric, the magnetic field has only radial and azimuthal components and depends only on time and radial coordinates. We show that the stationary state of the magnetic field in the plunging region is uniquely determined by the boundary conditions at the marginally stable circular orbit. If the magnetic field at the marginally stable circular orbit is in a stationary state, the magnetic field in the plunging region will quickly settle into a stationary state if it is not so initially, in a time determined by the dynamical time scale. The radial component of the magnetic field at the marginally stable circular orbit is more important than the toroidal component in determining the structure and evolution of the magnetic field in the plunging region. Even if at the marginally stable circular orbit the toroidal component is zero, in the plunging region a toroidal component is quickly generated from the radial component by the shear motion of the fluid. Finally, we show that the dynamical effects of magnetic fields are unimportant in the plunging region if they are negligible on the marginally stable circular orbit. This supports the ``no-torque inner boundary condition'' of thin disks, contrary to the claim in the recent literature. [Phys. Rev. D67, 044007 (2003)]
The Giant X-Ray Flare of NGC 5905: Tidal Disruption of a Star, a Brown Dwarf, or a Planet?: We model the 1990 giant X-ray flare of the quiescent galaxy NGC 5905 as the tidal disruption of a star by a supermassive black hole. From the observed rapid decline of the luminosity, over a timescale of a few years, we argue that the flare was powered by the fallback of debris rather than subsequent accretion via a thin disk. The fallback model allows constraints to be set on the black hole mass and the mass of debris. The latter must be very much less than a solar mass to explain the very low luminosity of the flare. The observations can be explained either as the partial stripping of the outer layers of a low-mass main sequence star or as the disruption of a brown dwarf or a giant planet. We find that the X-ray emission in the flare must have originated within a small patch rather than over the entire torus of circularized material surrounding the black hole. We suggest that the patch corresponds to the ``bright spot'' where the stream of returning debris impacts the torus. Interestingly, although the peak luminosity of the flare was highly sub-Eddington, the peak flux from the bright spot was close to the Eddington limit. We speculate on the implications of this result for observations of other flare events. [Astrophys. J. 576, 753 (2002)]
Observational Signatures of the Magnetic Connection between a Black Hole and a Disk: In this Letter we use a simple model to demonstrate the observational signatures of the magnetic connection between a black hole and a disk: (1) With the magnetic connection more energy is dissipated in and radiated away from regions close to the center of the disk; (2) The magnetic connection can produce a very steep emissivity compared to the standard accretion; (3) The observational spectral signature of the magnetic connection can be robust. These signatures may be identified with the observations of Chandra and XMM-Newton. In fact, the steep emissivity index for the Seyfert 1 galaxy MCG--6-30-15 inferred from the recent XMM-Newton observation is very difficult to be explained with a standard accretion disk but can be easily explained with the magnetic connection between a black hole and a disk. [Astron. Astrophys. 392, 469 (2002)]
A Toy Model for the Magnetic Connection between a Black Hole and a Disk: A magnetic field connecting a Kerr black hole to a disk rotating around it can extract energy and angular momentum from the black hole and transfer them to the disk if the black hole rotates faster than the disk. The energy can be dissipated and radiated away by the disk, which makes the disk shine without the need of accretion. In this paper we present a toy model for the magnetic connection: a single electric current flowing around a Kerr black hole in the equatorial plane generates a poloidal magnetic field which connects the black hole to the disk. The rotation of the black hole relative to the disk generates an electromotive force which in turn generates a poloidal electric current flowing through the black hole and the disk and produces a power on the disk. We will consider two cases: (1) The toroidal current flows on the inner boundary of the disk, which generates a poloidal magnetic field connecting the horizon of the black hole to a region of the disk {\it beyond} the inner boundary; (2) The toroidal current flows on a circle inside the inner boundary of the disk but outside the horizon of the black hole, which generates a poloidal magnetic field connecting a portion of the horizon of the black hole to the {\it whole} disk. We will calculate the power produced by the magnetic connection and the resulting radiation flux of the disk in the absence of accretion, and compare them with that produced by accretion. [Phys. Rev. D65, 084047 (2002)]
Accretion Disk Torqued by a Black Hole: If a Kerr black hole is connected to a disk rotating around it by a magnetic field, the rotational energy of the Kerr black hole provides an energy source for the radiation of the disk in addition to disk accretion. The black hole exerts a torque on the disk, which transfers energy and angular momentum between the black hole and the disk. If the black hole rotates faster than the disk, energy and angular momentum are extracted from the black hole and transfered to the disk. The energy deposited into the disk is eventually radiated away by the disk, which will increase the efficiency of the disk. If the black hole rotates slower than the disk, energy and angular momentum are transfered from the disk to the black hole, which will lower the efficiency of the disk. With suitable boundary conditions, quasi-steady state solutions are obtained for a thin Keplerian disk magnetically coupled to a Kerr black hole. By ``quasi-steady state'' we mean that any macroscopic quantity at a given radius in the disk slowly changes with time: the integrated change within one rotation period of the disk is much smaller than the quantity itself. We find that, the torque produced by the magnetic coupling propagates only outward in the disk, the total radiation flux of the disk is a superposition of the radiation flux produced by the magnetic coupling and that produced by accretion. Most interestingly, a disk magnetically coupled to a rapidly rotating black hole can radiate without accretion. Such a disk has an infinite efficiency. For a specific example that the magnetic field touches the disk at the inner boundary, the radial radiation profile is very different from that of a standard accretion disk: the emissivity index is significantly bigger, most radiation comes from a region which is closer to the center of the disk. [Astrophys. J. 567, 463 (2002)]
Semi-Analytical Models for Lensing by Dark Halos: I. Splitting Angles: We use the semi-analytical approach to analyze gravitational lensing of quasars by dark halos in various cold dark matter (CDM) cosmologies, in order to determine the sensitivity of the prediction probabilities of images separations to the input assumptions regarding halos and cosmologies. The mass function of dark halos is assumed to be given by the Press-Schechter function. The mass density profile of dark halos is alternatively taken to be the singular isothermal sphere (SIS), the Navarro-Frenk-White (NFW) profile, or the generalized NFW profile. The cosmologies include: the Einstein-de Sitter model (SCDM), the open model (OCDM), and the flat \Lambda-model (LCDM). As expected, we find that the lensing probability is extremely sensitive to the mass density profile of dark halos, and somewhat less so to the mean mass density in the universe, and the amplitude of primordial fluctuations. NFW halos are very much less effective in producing multiple images than SIS halos. However, none of these models can completely explain the current observations: the SIS models predict too many large splitting lenses, while the NFW models predict too few small splitting lenses. This indicates that there must be at least two populations of halos in the universe. A combination of SIS and NFW halos can reasonably reproduce the current observations if we choose the mass for the transition from SIS to NFW to be ~ 10^{13} solar masses. Additionally, there is a tendency for CDM models to have too much power on small scales, i.e. too much mass concentration; and it appears that the cures proposed for other apparent difficulties of CDM would help here as well, an example being the warm dark matter (WDM) variant which is shown to produce large splitting lenses fewer than the corresponding CDM model by one order of magnitude. [Astrophys. J. 566, 652 (2002)]
Jet Collimation by Small-Scale Magnetic Fields: A popular model for jet collimation is associated with the presence of a large-scale and predominantly toroidal magnetic field originating from the central engine (a star, a black hole, or an accretion disk). Besides the problem of how such a large-scale magnetic field is generated, in this model the jet suffers from the fatal long-wave mode kink magnetohydrodynamic instability. In this paper we explore an alternative model: jet collimation by small-scale magnetic fields. These magnetic fields are assumed to be local, chaotic, tangled, but are dominated by toroidal components. Just as in the case of a large-scale toroidal magnetic field, we show that the ``hoop stress'' of the tangled toroidal magnetic fields exerts an inward force which confines and collimates the jet. The magnetic ``hoop stress'' is balanced either by the gas pressure of the jet, or by the centrifugal force if the jet is spinning. Since the length-scale of the magnetic field is small (< the cross-sectional radius of the jet << the length of the jet), in this model the jet does not suffer from the long-wave mode kink instability. Many other problems associated with the large-scale magnetic field are also eliminated or alleviated for small-scale magnetic fields. Though it remains an open question how to generate and maintain the required small-scale magnetic fields in a jet, the scenario of jet collimation by small-scale magnetic fields is favored by the current study on disk dynamo which indicates that small-scale magnetic fields are much easier to generate than large-scale magnetic fields. [Astrophys. J. 564, 108 (2002)]
Two Open Universes Connected by a Wormhole: Exact Solutions: In this paper I present a spacetime of two open universes connected by a Lorentzian wormhole. The spacetime has the following features: (1) It can exactly solve the Einstein equations; (2) The weak energy condition is satisfied everywhere; (3) It has a topology of R^2\times T_g (g\ge 2); (4) It has no event horizons. [J. Geom. Phys. 40, 154 (2001)]
Making Clean Energy with a Kerr Black Hole: a Tokamak Model for Gamma-Ray Bursts: In this paper we present a model for making clean energy with a Kerr black hole. Consider a Kerr black hole with a dense plasma torus spinning around it. A toroidal electric current flows on the surface of the torus, which generates a poloidal magnetic field outside the torus. On the surface of the tours the magnetic field is parallel to the surface. The closed magnetic field lines winding around the torus compress and confine the plasma in the torus, as in the case of tokamaks. Though it is unclear if such a model is stable, we look into the consequences if the model is stable. If the magnetic field is strong enough, the baryonic contamination from the plasma in the torus is greatly suppressed by the magnetic confinement and a clean magnetosphere of electron-positron pairs is built up around the black hole. Since there are no open magnetic field lines threading the torus and no accretion, the power of the torus is zero. If some magnetic field lines threading the black hole are open and connect with loads, clean energy can be extracted from the Kerr black hole by the Blandford-Znajek mechanism. The model may be relevant to gamma-ray bursts. The energy in the Poynting flux produced by the Blandford-Znajek mechanism is converted into the kinetic energy of the electron-positron pairs in the magnetosphere around the black hole, which generates two oppositely directed jets of electron-positron pairs with super-high bulk Lorentz factors. The jets collide and interact with the interstellar medium, which may produce gamma-ray bursts and the afterglows. [Astrophys. J. 544, 375 (2000)]
Extracting Energy from a Black Hole through the Transition Region: A new scenario for extracting energy from a Kerr black hole is proposed. With magnetic field lines connecting plasma particles inside the ergosphere with remote loads, the frame dragging twists the field lines so that energy and angular momentum are extracted from the plasma particles. If the magnetic field is strong enough, the energy extracted from the particles can be so large that the particles have negative energy as they fall into the black hole. So effectively the energy is extracted from the black hole. The particles inside the ergosphere can be continuously replenished with accretion from a disk surrounding the black hole, so a transition region with sufficient amount of plasma is formed between the black hole's horizon and the inner edge of the disk. Thus the energy can be continuously extracted from the black hole through the transition region. This may be the most efficient way for extracting energy from a Kerr black hole: in principle almost all of the rotational energy (up to $\approx 29%$ of the total energy of the black hole) can be extracted. [Astrophys. J. 540, L17 (2000)]
Extracting Energy from Accretion into a Kerr Black Hole: The highest efficiency of converting rest mass into energy by accreting matter into a Kerr black hole is ~ 31% (Thorne 1974). We propose a new process in which periods of accretion from a thin disk, and the associated spin-up of the black hole, alternate with the periods of no accretion and magnetic transfer of energy from the black hole to the disk. These cycles can repeat indefinitely, at least in principle, with the black hole mass increasing by ~ 66% per cycle, and up to ~ 43% of accreted rest mass radiated away by the disk. [Astrophys. J. 534, L197 (2000)]
Extracting Energy from a Black Hole through Its Disk: When some magnetic field lines connect a Kerr black hole with a disk rotating around it, energy and angular momentum are transferred between them. If the black hole rotates faster than the disk, $ca/GM_H>0.36$ for a thin Keplerian disk, then energy and angular momentum are extracted from the black hole and transferred to the disk ($M_H$ is the mass and $a M_H$ is the angular momentum of the black hole). This way the energy originating in the black hole may be radiated away by the disk. The total amount of energy that can be extracted from the black hole spun down from $ca/GM_H = 0.998$ to $ca/GM_H = 0.36$ by a thin Keplerian disk is $\approx 0.15 M_Hc^2$. This is larger than $\approx 0.09 M_Hc^2$ which can be extracted by the Blandford-Znajek mechanism. [Astrophys. J. 533, L115 (2000)]
Electromagnetic Energy for a Charged Kerr Black Hole in a Uniform Magnetic Field: With the Komar mass formula we calculate the electromagnetic energy for a charged Kerr black hole in a uniform magnetic field. We find that the total electromagnetic energy takes the minimum when the Kerr black hole possesses a non-zero net charge $Q = 2\xi B_0 J_H$ where $B_0$ is the strength of the magnetic field, $J_H$ is the angular momentum of the black hole, $\xi$ is a dimensionless parameter determined by the spin of the black hole. [Phys. Rev. D61, 084033 (2000)]
Screw Instability and the Blandford-Znajek Mechanism: When magnetic field lines thread a rotating black hole's horizon and connect with remote astrophysical loads, the rotational energy of the black hole can be extracted through the Blandford-Znajek mechanism. Due to the rotation of the black hole, the magnetic field lines are twisted and toroidal components are generated. So poloidal electric currents are induced and the black hole's rotational energy is transported to the astrophysical loads through Poynting flux. The Blandford-Znajek mechanism has been considered to be a possible process for powering extragalactic jets. In this paper we show that due to the screw instability of magnetic field, the toroidal components of the magnetic field, and thus the poloidal currents, cannot exceed the limits given by the Kruskal-Shafranov criterion. This significantly lowers the power of the Blandford-Znajek mechanism when the loads are far from the black hole. So the Blandford-Znajek mechanism can only work efficiently within the neighborhood of the black hole. The implications of the results for the scenario of extragalactic jets powered by the Blandford-Znajek mechanism are discussed. [Astrophys. J. 531, L111 (2000)]
Toy Model for the Blandford-Znajek Mechanism: A toy model for the Blandford-Znajek mechanism is investigated: a Kerr black hole with a toroidal electric current residing in a thin disk around the black hole. The toroidal electric current generates a poloidal magnetic field threading the black hole and disk. Due to the interaction of the magnetic field with remote charged particles, the rotation of the black hole and disk induces an electromotive force, which can power an astrophysical load at remote distance. The power of the black hole and disk is calculated. It is found that, for a wide range of parameters specifying the rotation of the black hole and the distribution of the electric current in the disk, the power of the disk exceeds the power of the black hole. The torque provided by the black hole and disk is also calculated. The torque of the disk is comparable to the torque of the black hole. As the disk loses its angular momentum, the mass of the disk gradually drifts towards the black hole and gets accreted. Ultimately the power comes from the gravitational binding energy between the disk and the black hole, as in the standard theory of accretion disk, instead of the rotational energy of the black hole. This suggests that the Blandford-Znajek mechanism may be less efficient in extracting energy from a rotating black hole with a thin disk. The limitations of our simple model and possible improvements deserved for future work are also discussed. [Phys. Rev. D61, 084016 (2000)]
Time Machines Constructed from Anti-de Sitter Space: n this paper time machines are constructed from anti-de Sitter space. One is constructed by identifying points related via boost transformations in the covering space of anti-de Sitter space and it is shown that this Misner-like anti-de Sitter space is just the Lorentzian section of the complex space constructed by Li, Xu, and Liu in 1993. The others are constructed by gluing an anti-de Sitter space to a de Sitter space, which could describe an anti-de Sitter phase bubble living in a de Sitter phase universe. Self-consistent vacua for a massless conformally coupled scalar field are found for these time machines, whose renormalized stress-energy tensors are finite and solve the semi-classical Einstein equations. The extensions to electromagnetic fields and massless neutrinos are discussed. It is argued that, in order to make the results consistent with Euclidean quantization, a new renormalization procedure for quantum fields in Misner-type spaces (Misner space, Misner-like de Sitter space, and Misner-like anti-de Sitter space) is required. Such a "self-consistent" renormalization procedure is proposed. With this renormalization procedure, self-consistent vacua exist for massless conformally coupling scalar fields, electromagnetic fields, and massless neutrinos in these Misner-type spaces. [Phys. Rev. D59, 084016 (1999)]
Transient Events from Neutron Star Mergers: Mergers of neutron stars (NS+NS) or neutron stars and stellar mass black holes (NS+BS) eject a small fraction of matter with a sub-relativistic velocity. Upon rapid decompression nuclear density medium condenses into neutron rich nuclei, most of them radioactive. Radioactivity provides a long term heat source for the expanding envelope. A brief transient has the peak luminosity in the supernova range, and the bulk of radiation in the UV -- Optical domain. We present a very crude model of the phenomenon, and simple analytical formulae which may be used to estimate the parameters of a transient as a function of poorly known input parameters. The mergers may be detected with high redshift supernova searches as rapid transients, many of them far away from the parent galaxies. It is possible that the mysterious optical transients detected by Schmidt et al. (1998) are related to neutron star mergers as they typically have no visible host galaxy. [Astrophys. J. 507, L59 (1998)]
Inflation in Kaluza-Klein Theory: Relation between the Fine-Structure Constant and the Cosmological Constant: In this paper we investigate a model of an inflationary universe in Kaluza-Klein theory, which is a four-dimensional de Sitter space plus a one-dimensional compactified internal space. We find that the energy scale for inflation can be predicted from the fine-structure constant in a self-consistent solution of the semi-classical Einstein equations including the Casimir effect. From the observed value of the fine-structure constant, we obtain an energy scale for inflation of $\epsilon=1.84\times 10^{16}g_*^{1/4}$ Gev, where $g_*$ is a dimensionless number depending on the spin and number of matter fields existing in the universe. This value is consistent with the values often discussed for inflation and grand unification. The wave function for this model predicts a high probability for forming such universes, independent of the value of the cosmological constant. The tunneling probability favors the creation of inflationary universes with a compactified dimension, over those with all macroscopic dimensions. [Phys. Rev. D58, 103513 (1998)]
Can the Universe Create Itself? The question of first-cause has troubled philosophers and cosmologists alike. Now that it is apparent that our universe began in a Big Bang explosion, the question of what happened before the Big Bang arises. Inflation seems like a very promising answer, but as Borde and Vilenkin have shown, the inflationary state preceding the Big Bang must have had a beginning also. Ultimately, the difficult question seems to be how to make something out of nothing. This paper explores the idea that this is the wrong question --- that that is not how the Universe got here. Instead, we explore the idea of whether there is anything in the laws of physics that would prevent the Universe from creating itself. Because spacetimes can be curved and multiply connected, general relativity allows for the possibility of closed timelike curves (CTCs). Thus, tracing backwards in time through the original inflationary state we may eventually encounter a region of CTCs giving no first-cause. This region of CTCs, may well be over by now (being bounded toward the future by a Cauchy horizon). We illustrate that such models --- with CTCs --- are not necessarily inconsistent by demonstrating self-consistent vacuums for Misner space and a multiply connected de Sitter space in which the renormalized energy-momentum tensor does not diverge as one approaches the Cauchy horizon and solves Einstein's equations. We show such a Universe can be classically stable and self-consistent if and only if the potentials are retarded, giving a natural explanation of the arrow of time. Some specific scenarios (out of many possible ones) for this type of model are described. For example: an inflationary universe gives rise to baby universes, one of which turns out to be itself. Interestingly, the laws of physics may allow the Universe to be its own mother. [Phys. Rev. D58, 023501 (1998)]
Self-Consistent Vacuum for Misner Space and the Chronology Protection Conjecture: In this paper we find a self-consistent vacuum for Misner space. For this "adapted" Rindler vacuum the renormalized stress-energy tensor is zero throughout the Misner space. A point-like particle detector traveling on a timelike geodesic in a Misner space with this vacuum detects nothing. Misner space with this vacuum thus creates no problems for time travel in and of itself but a time traveler may pose a danger to himself and to the spacetime. [Phys. Rev. Lett. 80, 2980 (1998)]
Back to Professional Page