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We compute the tidal Love numbers for a particular axially symmetric configuration of extremal Reissner-Nordstrom geometry. By exactly solving the non-linear Einstein equations, we investigate the tidal response of extremal Reissner-Nordstrom black holes in four-dimensional spacetimes under external gravitational fields. We show that, for the specific geometry considered, the static tidal Love number remains finite and non-vanishing to all orders in the external tidal field. By contrast, we verify that the Love number of an isolated extremal Reissner-Nordstrom black hole remains zero, in agreement with previous expectations. Furthermore, we explicitly calculate the Zerilli-Moncrief master functions and match them with the effective field theory description.
We derive the phase acquired by a neutral scalar particle propagating along Reissner-Nordstrom geodesics. Considering two flavours propagating on different trajectories which intersect, we plot the interference pattern induced by gravitational lensing from the charged compact object. Although the effect of the charge is subdominant in the metric, it proves to be significant in the phase, and shifts the interference pattern, compared to the Schwarzschild case. This pattern is characterised by two oscillation lengths which, if known, would allow the determination of both eigen masses independently.
We study spherically symmetric spacetime perturbations induced by a neutral scalar in the near-horizon region of extreme Reissner-Nordstrom black holes. For the unperturbed black hole, the near-horizon region is given by another exact solution of the Einstein-Maxwell equations, namely the Bertotti-Robinson spacetime. Our aim is to extend this connection beyond the background level and identify perturbations of a Bertotti-Robinson spacetime as near-horizon perturbations of an extreme Reissner-Nordstrom black hole. We explain that explicit identification of the perturbative solutions to the two different backgrounds can only work in appropriate gauges. For this reason, we first solve the two perturbation problems in the most general spherically symmetric gauges and then find the necessary gauge conditions for matching the Reissner-Nordstrom and Bertotti-Robinson perturbative solutions in the near-horizon limit.
The superradiant stability of higher dimensional non-extremal Reissner-Nordstrom black hole under charged massive scalar perturbation is analytically studied. We extend our previous studies of four- and five-dimensional non-extremal Reissner-Nordstrom black hole cases to six-dimensional case. By analyzing the derivative of the effective potential with an analytical method, we find that no potential well exists outside the outer horizon of the black hole for the superradiant scalar modes. This means that there is no black hole bomb for the system consisting of six-dimensional Reissner-Nordstrom black hole and charged massive scalar perturbation and the system is superradiantly stable.
The superradiant stability of asymptotically flat D-dimensional extremal Reissner-Nordstrom black holes under charged massive scalar perturbation is analytically studied. Recently, an analytical method has been proposed by the author and used to prove that five and six-dimensional extremal Reissner-Nordstrom black holes are superradiantly stable under charged massive scalar perturbation. We apply this analytical method in the D-dimensional extremal Reissner-Nordstrom black hole cases and prove that the D-dimensional Reissner-Nordstrom black holes are all superradiantly stable under charged massive scalar perturbation. Our result is consistent with the previous numerical observation in the literature and provides a rigorous analytical proof.
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