All solutions of Einstein-Maxwell equations with a cosmological constant in 2+1 dimensions

Abstract

We present a general solution of the coupled Einstein-Maxwell field equations (without the source charges and currents) in three spacetime dimensions. We also admit any value of the cosmological constant. The whole family of such $\Lambda$-electrovacuum local solutions splits into two distinct subclasses, namely the non-expanding Kundt class and the expanding Robinson-Trautman class. While the Kundt class only admits electromagnetic fields which are aligned along the geometrically privileged null congruence, the Robinson-Trautman class admits both aligned and also more complex non-aligned Maxwell fields. We derive all the metric and Maxwell field components, together with explicit constraints imposed by the field equations. We also identify the most important special spacetimes of this type, namely the coupled gravitational-electromagnetic waves and charged black holes.

37 pages, no figures; final extended and improved version accepted for publication in Phys. Rev. D

References in corpus (8)

• Robinson-Trautman spacetimes in higher dimensions
• Algebraic classification of higher dimensional spacetimes based on null alignment
• Quantum Gravity in 2+1 Dimensions
• General Kundt spacetimes in higher dimensions
• Robinson-Trautman spacetimes with an electromagnetic field in higher dimensions
• Static and radiating p-form black holes in the higher dimensional Robinson-Trautman class
• Algebraic structure of Robinson-Trautman and Kundt geometries in arbitrary dimension
• Rainich Conditions in (2+1)-Dimensional Gravity

Cited by in corpus (8)

• Charging Kerr-Schild spacetimes in higher dimensions
• Scalar field instabilities in charged BTZ black holes
• Algebraic classification of 2+1 geometries: a new approach
• Quasinormal modes of charged BTZ black holes
• A novel classification method of 2+1 spacetimes based on the Cotton scalars
• Charged rotating BTZ solution revisited: New coordinates and algebraic classifications
• Interpreting gravitational fields of Topologically Massive Gravity using geodesic deviation
• Extremal rotating BTZ black holes cannot be dressed in (anti-)self-dual Maxwell field