Charging Kerr-Schild spacetimes in higher dimensions
arXiv:2309.02900 · doi:10.1103/PhysRevD.110.044035
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 . Focusing on the case of an expanding , 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 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.
arXiv comment30 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)
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