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

Abstract

A new effective approach to the algebraic classification of geometries in 2+1 gravity is presented. It uses five real Cotton scalars ${\Psi }_A$ of distinct boost weights, which are 3D analogues 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 ${\Psi }_A$, 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+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.

6 pages, 1 figure, 4 tables

References in corpus (5)

• Classification of the Weyl Tensor in Higher Dimensions and Applications
• Algebraic classification of higher dimensional spacetimes based on null alignment
• Quantum Gravity in 2+1 Dimensions
• Asymptotic structure of radiation in higher dimensions
• All solutions of Einstein-Maxwell equations with a cosmological constant in 2+1 dimensions

Cited by in corpus (4)

• Charged rotating BTZ solution revisited: New coordinates and algebraic classifications
• Robinson-Trautman spacetimes in (2+1) dimensions
• Interpreting gravitational fields of Topologically Massive Gravity using geodesic deviation
• Extremal rotating BTZ black holes cannot be dressed in (anti-)self-dual Maxwell field