8 research outputs found
A constrained scheme for Einstein equations based on Dirac gauge and spherical coordinates
We propose a new formulation for 3+1 numerical relativity, based on a
constrained scheme and a generalization of Dirac gauge to spherical
coordinates. This is made possible thanks to the introduction of a flat
3-metric on the spatial hypersurfaces t=const, which corresponds to the
asymptotic structure of the physical 3-metric induced by the spacetime metric.
Thanks to the joint use of Dirac gauge, maximal slicing and spherical
components of tensor fields, the ten Einstein equations are reduced to a system
of five quasi-linear elliptic equations (including the Hamiltonian and momentum
constraints) coupled to two quasi-linear scalar wave equations. The remaining
three degrees of freedom are fixed by the Dirac gauge. Indeed this gauge allows
a direct computation of the spherical components of the conformal metric from
the two scalar potentials which obey the wave equations. We present some
numerical evolution of 3-D gravitational wave spacetimes which demonstrates the
stability of the proposed scheme.Comment: Difference w.r.t. v1: Major revision: improved presentation of the
tensor wave equation and addition of the first results from a numerical
implementation; w.r.t. v2: Minor changes: improved conclusion and figures;
w.r.t. v3: Minors changes, 1 figure added; 25 pages, 13 figures, REVTeX,
accepted for publication in Phys. Rev.
Numerical Evolution of axisymmetric vacuum spacetimes: a code based on the Galerkin method
We present the first numerical code based on the Galerkin and Collocation
methods to integrate the field equations of the Bondi problem. The Galerkin
method like all spectral methods provide high accuracy with moderate
computational effort. Several numerical tests were performed to verify the
issues of convergence, stability and accuracy with promising results. This code
opens up several possibilities of applications in more general scenarios for
studying the evolution of spacetimes with gravitational waves.Comment: 11 pages, 6 figures. To appear in Classical and Quantum Gravit
Excised black hole spacetimes: quasi-local horizon formalism applied to the Kerr example
We present a numerical work aiming at the computation of excised initial data
for black hole spacetimes in full general relativity, using Dirac gauge in the
context of a constrained formalism for the Einstein equations. Introducing the
isolated horizon formalism for black hole excision, we especially solve the
non-conformally flat part of the equations, and assess the boundary condition
problem for this part. In the stationary single black hole case, we present and
justify a no-boundary treatment on the black hole horizon. We compare the data
obtained with the well-known analytic Kerr solution in Kerr-Schild coordinates,
and assess the widely used conformally flat approximation for simulating
axisymmetric black hole spacetimes. Our method shows good concordance on
physical and geometrical issues, with the particular application of the
isolated horizon multipolar analysis to confirm that the solution obtained is
indeed the Kerr spacetime. Finally, we discuss a previous suggestion in the
literature for the boundary conditions for the conformal geometry on the
horizon.Comment: 15 pages, 5 figures. Part IV significantly expanded, and additional
appendix included. Version coherent with the published pape
GYOTO: a new general relativistic ray-tracing code
GYOTO, a general relativistic ray-tracing code, is presented. It aims at
computing images of astronomical bodies in the vicinity of compact objects, as
well as trajectories of massive bodies in relativistic environments. This code
is capable of integrating the null and timelike geodesic equations not only in
the Kerr metric, but also in any metric computed numerically within the 3+1
formalism of general relativity. Simulated images and spectra have been
computed for a variety of astronomical targets, such as a moving star or a
toroidal accretion structure. The underlying code is open source and freely
available. It is user-friendly, quickly handled and very modular so that
extensions are easy to integrate. Custom analytical metrics and astronomical
targets can be implemented in C++ plug-in extensions independent from the main
code.Comment: 20 pages, 11 figure