General Wahlquist Metrics in All Dimensions

Abstract

It is shown that the Wahlquist metric, which is a stationary, axially symmetric perfect fluid solution with $\rho +3p=\text{const.}$, admits a rank-2 generalized closed conformal Killing-Yano tensor with a skew-symmetric torsion. Taking advantage of the presence of such a tensor, we obtain a higher-dimensional generalization of the Wahlquist metric in arbitrary dimensions, including a family of vacuum black hole solutions with spherical horizon topology such as Schwarzschild-Tangherlini, Myers-Perry and higher-dimensional Kerr-NUT-(A)dS metrics and a family of static, spherically symmetric perfect fluid solutions in higher dimensions.

14 pages, no figures, v2: references added, version to appear in Phys. Rev. D

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Cited by in corpus (11)

• Black holes, hidden symmetries, and complete integrability
• Schwarzschild and Kerr Solutions of Einstein's Field Equation -- an introduction
• A simple test for spacetime symmetry
• Spacetimes with a separable Klein-Gordon equation in higher dimensions
• Hidden symmetry and the separability of the Maxwell equation on the Wahlquist spacetime
• Existence and absence of Killing horizons in static solutions with symmetries
• An alternative to the Simon tensor
• A massless scalar particle coupled to the Wahlquist metric
• Higher-dimensional lifts of Killing-Yano forms with torsion
• Fake Schwarzschild and Kerr black holes
• Wahlquist Metric Revisited