Three dimensional origin of Godel spacetimes and black holes

TL;DR

The work constructs and analyzes Gödel-type spacetimes in 2+1 dimensions within Einstein-Maxwell-Chern-Simons theory with a negative cosmological constant. By leveraging identifications along isometries and a constant topological mass, the authors generate Gödel particles (cosmons) and Gödel black holes, unifying particle and black hole sectors through a single general solution valid for all $\alpha^2 l^2$. The paper derives the conserved charges (mass, angular momentum, electric charge) via a Noether-based formalism and establishes a first law for the Gödel black holes, including a frame transformation that connects to standard BTZ AdS black holes. The results illuminate how the Chern-Simons term reshapes the effective cosmological constant and the stress-energy content, yielding rich causal structures (CTCs, horizons) in a controlled 3D setting with potential links to higher-dimensional Gödel backgrounds. Overall, the work provides a coherent 3D mechanism for Gödel-type spacetimes, their particle/black-hole realizations, and their thermodynamic properties, with implications for holography and lower-dimensional gravity models.

Abstract

We construct Godel-type black hole and particle solutions to Einstein-Maxwell theory in 2+1 dimensions with a negative cosmological constant and a Chern-Simons term. On-shell, the electromagnetic stress-energy tensor effectively replaces the cosmological constant by minus the square of the topological mass and produces the stress-energy of a pressure-free perfect fluid. We show how a particular solution is related to the original Godel universe and analyze the solutions from the point of view of identifications. Finally, we compute the conserved charges and work out the thermodynamics.

Figures (5)

• Figure 1: Gödel cosmons
• Figure 2: Gödel black holes
• Figure 3: Carter-Penrose diagram of Gödel black hole
• Figure 4: Sectors of the general solution.
• Figure 5: Sectors of the $\alpha^2l^2 = 1$ solution. The BTZ mass axis $M=\mu-\alpha J$ and the extremal solutions are explicitly indicated.