On the Chen-Teo family of stationary asymptotically locally Minkowskian black holes

TL;DR

This paper analyzes a family of five-dimensional stationary black hole solutions with unique topological and asymptotic properties, demonstrating their physical consistency and stability, and confirming key thermodynamic relations.

Contribution

The paper proves the smooth extendability of the Chen-Teo black hole metrics through the horizon and verifies the validity of the Smarr relation and first law for these solutions.

Findings

Solutions can be smoothly extended through the event horizon.

The exterior spacetime is stably causal.

The Smarr relation and first law hold for these black holes.

Abstract

Chen and Teo have constructed a two-parameter family of five dimensional, stationary vacuum black hole solutions whose spatial hypersurfaces are asymptotically locally Euclidean with boundary at infinity is $L(2,1)$. Spatial cross sections of the event horizon have topology $S^3$ equipped with inhomogeneous metrics. When the mass is zero, the solution reduces to the trivial product of time with the Eguchi-Hanson gravitational instanton. We show that the spacetime metric can be smoothly extended through an event horizon and that the exterior region is stably causal. We also investigate their geometric and physical properties. In particular, we show that the Smarr relation and first law of black hole mechanics hold and compute the renormalized gravitational action.