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.

arXiv comment37 pages, no figures; final extended and improved version accepted for publication in Phys. Rev. D

References in corpus (19)

• The Black Hole in Three Dimensional Space Time
• Geometry of the 2+1 Black Hole
• Charged Rotating Black Hole in Three Spacetime Dimensions
• Algebraic classification of higher dimensional spacetimes based on null alignment
• Robinson-Trautman spacetimes in higher dimensions
• Kundt spacetimes as solutions of topologically massive gravity
• Quantum Gravity in 2+1 Dimensions
• General Kundt spacetimes in higher dimensions
• Energy conditions in arbitrary dimensions
• Unification of Gravity and Yang-Mills Theory in (2+1)-Dimensions
• Robinson-Trautman spacetimes with an electromagnetic field in higher dimensions
• Three dimensional stationary cyclic symmetric Einstein-Maxwell solutions; black holes
• Static and radiating p-form black holes in the higher dimensional Robinson-Trautman class
• All solutions of Einstein's equations in 2+1 dimensions: $\Lambda$-vacuum, pure radiation, or gyratons
• Explicit algebraic classification of Kundt geometries in any dimension
• Algebraic classification of Robinson-Trautman spacetimes
• Algebraic structure of Robinson-Trautman and Kundt geometries in arbitrary dimension
• Rainich Conditions in (2+1)-Dimensional Gravity
• Three dimensional stationary cyclic symmetric Einstein-Maxwell solutions; energy, mass, momentum, and algebraic tensors characteristics

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• 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