Gravitational Perturbations of Rotating Black Holes in Lorenz Gauge
Abstract
Perturbations of Kerr spacetime are typically studied with the Teukolsky formalism, in which a pair of gauge invariant components of the perturbed Weyl tensor are expressed in terms of separable modes that satisfy ordinary differential equations. However, for certain applications it is desirable to construct the full metric perturbation in the Lorenz gauge, in which the linearized Einstein field equations take a manifestly hyperbolic form. Here we obtain a set of Lorenzgauge solutions to the linearized vacuum field equations on KerrNewmanUntiTamburino spacetimes in terms of homogeneous solutions to the spin2, spin1, and spin0 Teukolsky equations. We also derive Lorenzgauge completion pieces representing mass and angular momentum perturbations of Kerr spacetime.
 Publication:

Physical Review Letters
 Pub Date:
 April 2022
 DOI:
 10.1103/PhysRevLett.128.151101
 arXiv:
 arXiv:2108.06344
 Bibcode:
 2022PhRvL.128o1101D
 Keywords:

 General Relativity and Quantum Cosmology;
 High Energy Physics  Theory
 EPrint:
 6 pages, no figures. Version accepted by PRL