Perturbations of the almost Killing equation and their implications

Sumanta Chakraborty and Justin C. Feng
Phys. Rev. D 103, 084020 – Published 12 April 2021

Abstract

Killing vectors play a crucial role in characterizing the symmetries of a given spacetime. However, realistic astrophysical systems are in most cases only approximately symmetric. Even in the case of an astrophysical black hole, one might expect Killing symmetries to exist only in an approximate sense due to perturbations from external matter fields. In this work, we consider the generalized notion of Killing vectors provided by the almost Killing equation, and study the perturbations induced by a perturbation of a background spacetime satisfying exact Killing symmetry. To first order, we demonstrate that for nonradiative metric perturbations (that is, metric perturbations with nonvanishing trace) of symmetric vacuum spacetimes, the perturbed almost Killing equation avoids the problem of an unbounded Hamiltonian for hyperbolic parameter choices. For traceless metric perturbations, we obtain similar results for the second-order perturbation of the almost Killing equation, with some additional caveats. Thermodynamical implications are also explored.

  • Received 7 December 2020
  • Accepted 12 March 2021

DOI:https://doi.org/10.1103/PhysRevD.103.084020

© 2021 American Physical Society

Physics Subject Headings (PhySH)

Gravitation, Cosmology & Astrophysics

Authors & Affiliations

Sumanta Chakraborty1,2 and Justin C. Feng3

  • 1School of Mathematical and Computational Sciences, Indian Association for the Cultivation of Science, Kolkata-700032, India
  • 2School of Physical Sciences, Indian Association for the Cultivation of Science, Kolkata-700032, India
  • 3CENTRA, Departamento de Física, Instituto Superior Técnico IST, Universidade de Lisboa UL, Avenida Rovisco Pais 1, 1049 Lisboa, Portugal

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Issue

Vol. 103, Iss. 8 — 15 April 2021

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