Abstract
The study of black hole perturbations is an indispensable means of understanding the processes that give rise to gravitational and electromagnetic radiation. The observation of sources of gravitational radiation is an ongoing endeavour worldwide.
Perturbations of the most general black hole states have been first investigated by Chrzanowski and Misner [1, 2], Detweiler [3] and Chandrasekhar [5]. Among these pioneering studies, Chandrasekhar’s is most detailed. He uses a Newman-Penrose (NP) approach both to the unperturbed Kerr metric and to the perturbed space-time.
In this talk we present the full set of black-hole perturbations in the ingoing radiation gauge. Space-time is treated here as a Kerr-metric background on which NP formalism is featured plus a perturbative part hab in the metric. In the spirit of the weak-field approximation, we take all perturbations as fields being defined on the background manifold of the Kerr metric.
In treatments of black-hole perturbations, it is a common practice to seek a suitable gauge fixing. A convenient choice, promoted by Chrzanowski, is the incoming (or outgoing) radiation gauge for the normal modes. This choice does not uniquely fix the coordinate gauge, however. In fact, the present work has been launched with the intent to take a second look at the remaining gauge freedom.
In this paper, the following picture emerges for the classical electrovacuum perturbations. There exists a subset of the field equations, consisting of two gravitational equations and two Maxwell equations not containing any mode mixing. (This is because the complex conjugate electromagnetic stresses are absent). From these relations alone, using the definition of the Weyl tensor perturbation ψ0, it is possible to obtain a pair of coupled equations for ψ0 and the electromagnetic perturbation φ0. Thus a normal mode expansion for this doublet of fields is available. Mode mixing occurs only in the further gravitational and electromagnetic perturbation components derived from the fundamental doublet. This picture fully agrees with the results obtained in an entirely different gauge [10].
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Bibliography
P.L. Chrzanowski and C.W. Misner, Phys. Rev. D10, 1701 (1974)
P.L. Chrzanowski, Phys. Rev. D11, 2042 (1975)
S. Detweiler, Proc. Roy. Soc. Lond. A 352, 381
E.T. Newman and R. Penrose, J. Math. Phys. 3, 566 (1962)
S. Chandrasekhar: The mathematical theory of black holes, Clarendon Press, Oxford, 1983
E.T. Newman et al., J. Math. Phys. 6, 918 (1965)
S. Mano and E. Takasugi, Prog. Theor. Phys. 97, 213 (1997), gr-qc/9611014
S.A. Teukolsky, Astrophys. J. 185, 635 (1973)
D.M. Chitre, Phys.Rev. D13, 2713 (1976)
Z. Perjés, Fundamental equations for the gravitational and electromagnetic perturbations of a charged black hole, gr-qc/0206088
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer Science+Business Media, Inc.
About this chapter
Cite this chapter
Perjés, Z. (2006). Black Hole Perturbations. In: Prékopa, A., Molnár, E. (eds) Non-Euclidean Geometries. Mathematics and Its Applications, vol 581. Springer, Boston, MA. https://doi.org/10.1007/0-387-29555-0_23
Download citation
DOI: https://doi.org/10.1007/0-387-29555-0_23
Publisher Name: Springer, Boston, MA
Print ISBN: 978-0-387-29554-1
Online ISBN: 978-0-387-29555-8
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)