arXiv subjects

Olivier Sarbach

Publications and source records attributed to Olivier Sarbach.

95 records · Page 6Linked to original sources

arXiv2002

Hyperbolicity of the BSSN system of Einstein evolution equations

We discuss an equivalence between the Baumgarte-Shapiro-Shibata-Nakamura (BSSN) formulation of the Einstein evolution equations, a subfamiliy of the Kidder--Scheel--Teukolsky formulation, and other strongly or symmetric hyperbolic first order systems with fixed shift and densitized lapse. This allows us to show under which conditions the BSSN system is, in a sense to be discussed, hyperbolic. This desirable property may account in part for the empirically observed better behavior of the BSSN formulation in numerical evolutions involving black holes.

gr-qc↗

arXiv2001

Close limit evolution of Kerr-Schild type initial data for binary black holes

We evolve the binary black hole initial data family proposed by Bishop {\em et al.} in the limit in which the black holes are close to each other. We present an exact solution of the linearized initial value problem based on their proposal and make use of a recently introduced generalized formalism for studying perturbations of Schwarzschild black holes in arbitrary coordinates to perform the evolution. We clarify the meaning of the free parameters of the initial data family through the results for the radiated energy and waveforms from the black hole collision.

gr-qc↗

arXiv2001

Gauge invariant perturbations of Schwarzschild black holes in horizon-penetrating coordinates

We derive a geometrical version of the Regge-Wheeler and Zerilli equations, which allows us to study gravitational perturbations on an arbitrary spherically symmetric slicing of a Schwarzschild black hole. We explain how to obtain the gauge-invariant part of the metric perturbations from the amplitudes obeying our generalized Regge-Wheeler and Zerilli equations and vice-versa. We also give a general expression for the radiated energy at infinity, and establish the relation between our geometrical equations and the Teukolsky formalism. The results presented in this paper are expected to be useful for the close-limit approximation to black hole collisions, for the Cauchy perturbative matching problem, and for the study of isolated horizons.

gr-qc↗

arXiv1999

Perturbation theory for self-gravitating gauge fields I: The odd-parity sector

A gauge and coordinate invariant perturbation theory for self-gravitating non-Abelian gauge fields is developed and used to analyze local uniqueness and linear stability properties of non-Abelian equilibrium configurations. It is shown that all admissible stationary odd-parity excitations of the static and spherically symmetric Einstein-Yang-Mills soliton and black hole solutions have total angular momentum number $\ell = 1$, and are characterized by non-vanishing asymptotic flux integrals. Local uniqueness results with respect to non-Abelian perturbations are also established for the Schwarzschild and the Reissner-Nordström solutions, which, in addition, are shown to be linearly stable under dynamical Einstein-Yang-Mills perturbations. Finally, unstable modes with $\ell = 1$ are also excluded for the static and spherically symmetric non-Abelian solitons and black holes.

gr-qc↗

arXiv1999

The generalization of the Regge-Wheeler equation for self-gravitating matter fields

It is shown that the dynamical evolution of perturbations on a static spacetime is governed by a standard pulsation equation for the extrinsic curvature tensor. The centerpiece of the pulsation equation is a wave operator whose spatial part is manifestly self-adjoint. In contrast to metric formulations, the curvature-based approach to gravitational perturbation theory generalizes in a natural way to self-gravitating matter fields. For a certain relevant subspace of perturbations the pulsation operator is symmetric with respect to a positive inner product and therefore allows spectral theory to be applied. In particular, this is the case for odd-parity perturbations of spherically symmetric background configurations. As an example, the pulsation equations for self-gravitating, non-Abelian gauge fields are explicitly shown to be symmetric in the gravitational, the Yang Mills, and the off-diagonal sector.

gr-qc↗