Einstein-Vlasov system in spherical symmetry. II. Spherical perturbations of static solutions - INSPIRE

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Einstein-Vlasov system in spherical symmetry. II. Spherical perturbations of static solutions

Carsten Gundlach

Aug 23, 2017

13 pages

Published in:

Phys.Rev.D 96 (2017) 8, 084008

Published: Oct 4, 2017

e-Print:

1708.07191 [gr-qc]

DOI:

10.1103/PhysRevD.96.084008

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Abstract: (APS)

We reduce the equations governing the spherically symmetric perturbations of static spherically symmetric solutions of the Einstein-Vlasov system (with either massive or massless particles) to a single stratified wave equation -ψ,tt=Hψ, with H containing second derivatives in radius, and integrals over energy and angular momentum. We identify an inner product with respect to which H is symmetric, and use the Ritz method to approximate the lowest eigenvalues of H numerically. For two representative background solutions with massless particles we find a single unstable mode with a growth rate consistent with the universal one found by Akbarian and Choptuik in nonlinear numerical time evolutions.

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