Second order perturbation theory in general relativity: Taub charges as integral constraints

Altas E., TEKİN B.

PHYSICAL REVIEW D, vol.99, no.10, 2019 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume: 99 Issue: 10
  • Publication Date: 2019
  • Doi Number: 10.1103/physrevd.99.104078
  • Journal Name: PHYSICAL REVIEW D
  • Journal Indexes: Science Citation Index Expanded, Scopus


In a nonlinear theory, such as general relativity, linearized field equations around an exact solution are necessary but not sufficient conditions for linearized solutions. Therefore, the linearized field equations can have some solutions which do not come from the linearization of possible exact solutions. This fact can make the perturbation theory ill defined, which would be a problem both at the classical and semiclassical quantization level. Here we study the first and second order perturbation theory in cosmological Einstein gravity and give the explicit form of the integral constraint, which is called the Taub charge, on the first order solutions for spacetimes with a Killing symmetry and a compact hypersurface without a boundary.