Linear perturbations of a Schwarzschild black hole by thin disc - convergence

Conference paper

Linear perturbations of a Schwarzschild black hole by thin disc - convergence

Čížek, P.; Semerák, O.

In: Proceedings of the Spanish Relativity Meeting 2011 (AIP Conference Proceedings Vol. 1458), ed. J. Beltrán Jiménez, J. A. Ruiz Cembranos, A. Dobado, A. López Maroto, A. De la Cruz Dombriz, AIP, pp. 351-354 (2012)

doi ↗

Abstract

In order to find the perturbation of a Schwarzschild space-time due to a rotating thin
disc, we try to adjust the method used by [4] in the case of perturbation by a one-dimensional
ring. This involves solution of stationary axisymmetric Einstein’s equations in terms of sphericalharmonic
expansions whose convergence however turned out questionable in numerical examples.
Here we show, analytically, that the series are almost everywhere convergent, but in some regions
the convergence is not absolute.

Note

ISBN: 978-0-7354-1060-2

Institute authors

Semerák, Oldřich

Supported by

GACR 202/09/0772 — Current problems of gravitation, general relativity and relativistic astrophysics
GACR 205/09/H033 — General relativity and its applications in astrophysics and cosmology
GAUK 428011 — Studium astrofyzikálních důsledků obecné teorie relativity
MSM0021620860 — Fyzikální studium objektů a procesů ve sluneční soustavě a v astro-fyzikálních systémech
SVV-265301 — Aktuální problémy teoretické fyziky, astronomie a astrofyziky

BibTeX

@inproceedings{UTF494,
  author        = {Čížek, P. and Semerák, O.},
  title         = {{Linear perturbations of a Schwarzschild black hole by thin disc - convergence}},
  booktitle     = {Proceedings of the Spanish Relativity Meeting 2011 (AIP Conference Proceedings Vol. 1458)},
  editor        = {J. Beltrán Jiménez, J. A. Ruiz Cembranos, A. Dobado, A. López Maroto, A. De la Cruz Dombriz},
  publisher     = {AIP},
  volume        = {1458},
  pages         = {351-354},
  year          = {2012},
  month         = {7},
  doi           = {10.1063/1.4734432},
  note          = {ISBN: 978-0-7354-1060-2},
}