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arXiv · 2309.02900

Charging Kerr-Schild spacetimes in higher dimensions

Marcello Ortaggio·Aravindhan Srinivasan
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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.

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Marcello Ortaggio, Aravindhan Srinivasan. 2023-09-06. Charging Kerr-Schild spacetimes in higher dimensions. https://doi.org/10.1103/physrevd.110.044035

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