# Relativistic Hydrodynamics & Numerical Relativity

If the typical velocity in an astrophysical system is small and gravity is weak, it is sufficient to use the Newtonian approximation of the laws of motion and gravity to model such a system. However, these approximations do not always hold.

Supermassive black holes in quasars and solar-mass-sized black holes with accretion discs power jets made of particles which move at velocities close to the speed of light. Here, special relativistic hydrodynamics is needed for numerical simulations. Our group has developed and successfully applied computer codes for such simulations for many years.

To describe compact objects one must resort to general relativity, a generalization of Newton's theory of gravity. Such a situation is encountered near black holes (the prospective driving engines of astrophysical jets), during the formation of a neutron star or a black hole in a core collapse supernova, in collapsars (one possible source of gamma-ray bursts), or during the merger of two neutron stars. (another possible source of gamma-ray bursts).

Some of these sources are thought to emit detectable amounts of gravitational radiation. While light or sound waves propagate through spacetime, gravitational waves are ripples of spacetime itself. Such spacetime distortions have been predicted by Einstein in his General Theory of Relativity hundred years ago. They are planned to be measured soon by laser interferometers (GEO 600, LIGO, VIRGO).

In order to accomplish a successful detection of gravitational waves, very efficient electronic filters have to be employed to extract a possible signal from the very noisy detector data. It is therefore of great importance to predict as precise as possible the signals from theoretical models of various astrophysical sources of gravitational radiation. As part of the German research network SFB Transregio 7 "Gravitational Wave Astronomy", our group has taken part in this international interdisciplinary scientific effort.

## Further Information:

Below we provide further information about our projects to develop numerical codes for simulations of both special and general relativistic hydrodynamics, and for applications involving dynamical spacetimes.

A simulation tool that resulted from our efforts is CoCONuT, a general relativistic hydrodynamics code with approximate dynamical space-time evolution

As a service to the scientific community, we also provide a catalog of gravitational waveforms of general relativistic numerical simulations of rotational core collapse and a literature catalog of publications about gravitational wave from core collapse supernovae.

Self-consistent and stable simulations of general relativistic hydrodynamics

Pedro Montero, T.W. Baumgarte, and Ewald Müller

We have developed and implemented a new approach that applies in spherical polar coordinates the numerical methods that have previously proven to be extremely successful in Cartesian coordinates. This approach relies on a reference-metric formulation of the BSSN equations, factoring out appropriate geometrical factors from tensor components, and using a ''partially implicit" Runge-Kutta (PIRK) method.

A Solution for the Nonuniqueness Problem of the Spacetime Constraint Equations

I. Cordero-Carrión, P. Cerdá-Durán, H. Dimmelmeier, J.L. Jaramillo, J. Novak, E. Gourgoulhon

The otherwise very successful CFC scheme for approximating the Einstein equations in simulations of compact astrophysical objects fail at very high densities. We have found a reformulation which solves this problem and extends the applicability of CFC to e.g. black hole formation.

C.D. Ott, H. Dimmelmeier

For models of rotating stellar cores collapsing to a neutron star to a with both microphysics and a simple equation of state we have demonstrated that the often used CFC approach is an excellent approximation of full general relativity.

H. Dimmelmeier, C.D. Ott, A. Marek, H.-T. Janka

In order to investigate the influence of various stellar progenitor models and the role of different prescriptions for the properties of matter at high densities in rotating stellar core collapse to a neutron star, we have significantly extended the parameter range in our simulations of this scenario. Again, as previously we find a generic gravitational wave burst signal.

General Relativistic Rotational Core Collapse with Improved Dynamics and Waveforms in CFC+

P. Cerdá-Durán, G. Faye, H. Dimmelmeier, J.A. Font, J.M. Ibáñez, E. Müller, G. Schäfer

We have improved the collapse dynamics and gravitational waveforms from the our previous simulations of general relativistic rotational core collapse by extending the mathematical approximation used in that approach to higher orders.

Gravitational Radiation from General Relativistic Rotational Core Collapse

H. Dimmelmeier, J.A. Font, E. Müller

We have succeeded for the first time to simulate the collapse of a rotating stellar core to a neutron star including the effects of general relativity, making a major step forward towards realistic predictions of gravitational wave signals.

Simulations of Magnetorotational Supernova Core Collapse in Newtonian and Relativistic Gravity

M.A. Aloy, P. Cerdá-Durán, H. Dimmelmeier, J.A. Font, E. Müller, M. Obergaulinger

Neutron stars have intense or (in the case of magnetars) even extremely strong magnetic fields. We have performed simulations which can explain what role magnetic field play during the birth of these compact objects as proto-neutron stars in a supernova core collapse event.

B. Müller, A. Marek, H. Dimmelmeier, H.-T. Janka, E. Müller, R. Buras

We have approximated relativistic effects in simulations of supernova core collapse by using an effective relativistic potential in an otherwise standard Newtonian code. With a simple modification of the potential, such codes can be extended into the moderately relativistic regime.

H. Dimmelmeier, J. Novak, J.A. Font, J.M. Ibáñez, E. Müller

Based on an axisymmetric code used for our previous simulations of general relativistic rotational core collapse we have combined spectral methods and finite difference grid methods in a 3D general relativistic hydrodynamics code.

Synthetic Light Curves of BL Lac Objects

P. Mimica, M.A. Aloy, E. Müller, W. Brinkmann

For the first time we have performed a two-dimensional simulation of the internal shocks in a blazar jet under realistic conditions and have computed the light curve resulting from the collision of two dense shells moving with different velocities within a jet.