Novel classification method of 2 + 1 spacetimes based on the Cotton scalars

Article

Novel classification method of 2 + 1 spacetimes based on the Cotton scalars

Podolský J.; Papajčík M.

Phys. Rev. D 108 (2023)

Abstract

A new effective approach to the algebraic classification of geometries in 2 þ 1 gravity is presented. It uses five real Cotton scalars ΨA of distinct boost weights, which are 3D analogs of the Newman-Penrose scalars representing the Weyl tensor in 4D. The classification into types I, II, D, III, N, O is directly related to the multiplicity of the four Cotton-aligned null directions (CANDs). We derive a synoptic algorithm based on the invariants constructed from ΨA, and we show its agreement with the Petrov scheme based on eigenvalues and canonical Jordan form of the Cotton-York tensor. Our method is simpler and also general because it can be used in any 2 þ 1 theory, such as Einstein’s gravity or topologically massive gravity. As an example we analyze the algebraic structure of Robinson-Trautman spacetimes which include charged black holes with a cosmological constant.

Institute authors

Podolský, Jiří

Supported by

GACR 23-05914S — Pokročilé techniky aplikované na přesné prostoročasy s černými dírami a gravitačními vlnami

BibTeX

@article{UTF910,
  author        = {Podolský J. and Papajčík M.},
  title         = {{Novel classification method of 2 + 1 spacetimes based on the Cotton scalars}},
  journal       = {Phys. Rev. D},
  volume        = {108},
  year          = {2023},
  month         = {12},
  doi           = {10.1103/PhysRevD.108.L121504},
}