Charging Kerr-Schild spacetimes in higher dimensions

Abstract

We study higher dimensional charged Kerr-Schild (KS) spacetimes that can be constructed by a KS transformation of a vacuum solution with an arbitrary cosmological constant, and for which the vector potential is aligned with the KS vector $\mathbf{k}$. Focusing on the case of an expanding $\mathbf{k}$, we first characterize the presence of shear as an obstruction to non-null fields (thereby extending an early no-go result of Myers and Perry). We next obtain the complete family of shearfree solutions. In the twistfree case, they coincide with charged Schwarzschild-Tangherlini-like black holes. Solutions with a twisting $\mathbf{k}$ consist of a four-parameter family of higher dimensional charged Taub-NUT metrics with a base space of constant holomorphic sectional curvature. In passing, we identify the configurations for which the test-field limit gives rise to instances of the KS double copy. Finally, it is shown that null fields define a branch of twistfree but shearing solutions, exemplified by the product of a Vaidya-like radiating spacetime with an extra dimension.

30 pages. v2: typos fixed, new footnote 6, appendix A extended to the 4D hyperbolic and planar cases, example of an odd-dimensional vacuuum NUT (with non-Einstein base) added in appendix C, removed an incorrect statement about the 4D case in appendix D, refs. added (main results unchanged)

References in corpus (18)

• Black holes and the double copy
• The Kerr-Schild double copy in curved spacetime
• Robinson-Trautman spacetimes in higher dimensions
• Algebraic classification of higher dimensional spacetimes based on null alignment
• Generalization of the Geroch-Held-Penrose formalism to higher dimensions
• Type D Einstein spacetimes in higher dimensions
• Electromagnetic Properties of Kerr-Anti-de Sitter Black Holes
• Charged Rotating Black Holes in Odd Dimensions
• Higher dimensional Kerr-Schild spacetimes
• Kerr-Schild spacetimes with (A)dS background
• Robinson-Trautman spacetimes with an electromagnetic field in higher dimensions
• New Taub-NUT-Reissner-Nordström spaces in higher dimensions
• Thermodynamics of Taub-NUT Black Holes in Einstein-Maxwell Gravity
• On higher dimensional Einstein spacetimes with a warped extra dimension
• Static and radiating p-form black holes in the higher dimensional Robinson-Trautman class
• Asymptotic behaviour of Maxwell fields in higher dimensions
• Black hole formation by incoming electromagnetic radiation
• On the Goldberg-Sachs theorem in higher dimensions in the non-twisting case

Cited by in corpus (9)

• Gravito-electromagnetism, Kerr-Schild and Weyl double copies; a unified perspective
• Weyl double copy in type D spacetime in four and five dimensions
• Five dimensional Weyl double copy
• New framework for classical double copies
• The dyonic Kerr-Schild ansatz
• On the uniqueness of the Kerr-(A)dS metric as a type II(D) solution in six dimensions
• Einstein manifolds with optical geometries of Kerr type
• Kerr-Schild transformation of the Benenti-Francaviglia metric
• Novel five-dimensional rotating Lifshitz black holes with electric and axionic charges