Three-dimensional Chern-Simons black holes
K. Ait Moussa, G. Clement, H. Guennoune, C. Leygnac
TL;DR
The paper constructs intrinsically rotating black hole solutions in three-dimensional Einstein–Maxwell theory augmented by gravitational and electromagnetic Chern–Simons terms using a two-Killing-vector reduction and a quadratic X-ansatz. It presents two explicit metric forms supporting horizons and analyzes global structure, causal properties, and ergoregions, showing the spacetimes are geodesically complete and thermodynamically consistent with the first law and a Smarr relation. The black holes exhibit a four-parameter local isometry algebra, generically sl(2,R)×R, and can be generated from vacuum solutions via local coordinate transformations, linking to TMG and BBCG limits. The work lays groundwork for exploring asymptotic symmetries, separability, and extensions to dilaton-augmented CS theories in three dimensions.
Abstract
We construct black hole solutions to three-dimensional Einstein-Maxwell theory with both gravitational and electromagnetic Chern-Simons terms. These intrinsically rotating solutions are geodesically complete, and causally regular within a certain parameter range. Their mass, angular momentum and entropy are found to satisfy the first law of black hole thermodynamics. These Chern-Simons black holes admit a four-parameter local isometry algebra, which generically is $sl(2,R)\times R$, and may be generated from the corresponding vacua by local coordinate transformations.