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<p>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 <i>L</i>(2,&#xa0;1). Spatial cross sections of the event horizon have topology <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(S^3\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>S</mi> <mn>3</mn> </msup> </math></EquationSource> </InlineEquation> 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.</p>

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

  • 期刊论文

  • 发表日期：

    2026年4月15日

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  • Federico Elizondo Lopez,
  • Hari K. Kunduri,
  • Hakim Temacini

摘要

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 L(2, 1). Spatial cross sections of the event horizon have topology \(S^3\) 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.