Simulation of axisymmetric, relativistic flows using null foliations of spacetime

Purpose:

The goal of this project is to study axisymmetric, non-rotating stellar core collapse in full general relativity and to extract gravitational waves. We use the characteristic formulation of general relativity [1]. This approach allows us to calculate the whole asymptotically flat spacetime of an aspherical stellar core on a finite grid and to extract gravitational waves at null infinity. Our approach is based on the Bondi-metric [2], we generalize the results obtained in reference [3] and take into account a perfect fluid matter field. We use relativistic high-resolution-shock-capturing schemes to solve the fluid equations [4,5].
 
 

References:

1. J. Winicour, Characteristic Evolution and Matching, Living Reviews in Relativity 1 (1998).
2. H. Bondi, M.G.J. van der Burg, A.W.K. Metzner, Gravitational waves in general relativity, VII. Waves from axi-symmetric isolated systems, Proc. Roy. Soc A,  269 (1962).
3. R. Gomez, P. Papadopoulos, J. Winicour, Null cone evolution of axisymmetric vacuum space-times, J. Math. Phys. 35 (8) (1994).
4. P. Papadopoulos, J.A. Font, Relativistic hydrodynamics on spacelike and null surfaces: Formalism and computations of spherically symmetric spacetimes, Phys. Rev. D 62 (2000) (gr-qc/9902018).
5. P. Papadopoulos, J.A. Font, Analysis of relativistic hydrodynamics in conservation form, submitted to Class. Quantum Grav.