Luis Lehner

Incorporation of matter into characteristic numerical relativity

A code that implements Einstein equations in the characteristic formulation in 3D has been developed and thoroughly tested for the vacuum case. Here, we describe how to incorporate matter, in the form of a perfect fluid, into the code. The extended code has been written and validated in a number of cases. It is stable and capable of contributing towards an understanding of a number of problems in black hole astrophysics.

Approximate analytical solutions to the initial data problem of black hole binary systems

We present approximate analytical solutions to the Hamiltonian and momentum constraint equations, corresponding to systems composed of two black holes with arbitrary linear and angular momentum. The analytical nature of these initial data solutions makes them easier to implement in numerical evolutions than the traditional numerical approach of solving the elliptic equations derived from the Einstein constraints. Although in general the problem of setting up initial conditions for black hole binary simulations is complicated by the presence of singularities, we show that the methods presented in this work provide initial data with l 1 and l ‘ norms of violation of the constraint equations falling below those of the truncation error ~residual error due to discretization! present in finite difference codes for the range of grid resolutions currently used. Thus, these data sets are suitable for use in evolution codes. Detailed results are presented for the case of a head-on collision of two equal-mass M black holes with specific angular momentum 0.5M at an initial separation of 10M. A straightforward superposition method yields data adequate for resolutions of h5M/4, and an ‘‘attenuated’’ superposition yields data usable to resolutions at least as fine as h5M/8. In addition, the attenuated approximate data may be more tractable in a full ~computational! exact solution to the initial value problem.

Gravitational radiation, black holes and the characteristic formulation of G.R.

The characteristic formulation of General Relativity constitutes a useful and important tool in analytical and numerical investigations. We review its main accomplishments in regards to numerical models of Einstein equations and discuss some of its main present and future applications.