New identities for linearized gravity on the Kerr spacetime
Artikel i vetenskaplig tidskrift, 2019

In this paper we derive a differential identity for linearized gravity on the Kerr spacetime and more generally on vacuum spacetimes of Petrov type D. We show that a linear combination of second derivatives of the linearized Weyl tensor can be formed into a complex symmetric 2-tensor Mab which solves the linearized Einstein equations. The identity makes this manifest by relating Mab to two terms solving the linearized Einstein equations by construction. The self-dual Weyl curvature of Mab gives a covariant version of the Teukolsky-Starobinsky identities for linearized gravity which, in addition to the two classical identities for linearized Weyl scalars with extreme spin weights, includes three additional equations. In particular, they are not consequences of the classical Teukolsky-Starobinsky identities, but are additional integrability conditions for linearized gravity. The result has direct application in the construction of symmetry operators and also yields a set of nontrivial gauge invariants for linearized gravity.

Författare

Steffen Aksteiner

Max Planck-institutet

Lars Andersson

Max Planck-institutet

Thomas Bäckdahl

University of Edinburgh

Örebro universitet

Chalmers, Matematiska vetenskaper, Analys och sannolikhetsteori

Physical Review D

2470-0010 (ISSN) 2470-0029 (eISSN)

Vol. 99 4 044043

Ämneskategorier

Beräkningsmatematik

Geometri

Matematisk analys

DOI

10.1103/PhysRevD.99.044043

Mer information

Senast uppdaterat

2019-03-27