Late-time decay of coupled electromagnetic and gravitational perturbations outside an extremal charged black hole

Abstract

In this paper we employ the results of a previous paper on the late-time decay of scalar-field perturbations of an extreme Reissner-Nordstrom black hole, in order to find the late-time decay of coupled electromagnetic and gravitational perturbations of this black hole. We explicitly write the late-time tails of Moncrief's gauge invariant variables and of the perturbations of the metric tensor and the electromagnetic field tensor in the Regge-Wheeler gauge. We discuss some of the consequences of the results and relations to previous works.

Late-time asymptotics for the wave equation on extremal Reissner–Nordström backgrounds

“…We remark that an extension of the above instabilities to linearized electromagnetic and gravitational perturbations of ERN was presented in [30] and [39]. Nonlinear extensions have been presented in [121,123,125,131,132].…”

“…Sela [39] subsequently used the decay rates obtained in [37,38] in order to obtain decay rates for the coupled electromagnetic and gravitational system for ERN.…”

“…The above results do not provide an insight into the precise asymptotic behavior for ψ. There is extensive work in the physics literature regarding late-time asymptotics for scalar fields on extremal Reissner-Nordström via heuristic or numerical methods, see for instance [30,[34][35][36][37][38][39][40] and Section 1.5 for more details. However, there has been no mathematically rigorous proof or derivation of these asymptotics.…”

On late time tails in an extreme Reissner–Nordström black hole: frequency domain analysis

“…Andersson [34] has presented a very clear computation of the branch cut of the Green's function in the low-frequency asymptotic expansion using some results from [36]. Instead of reviewing those details here, we simply write equation (40) of that reference (which has a typo of an overall minus sign) [34]: The late time solution using this Green's function is simply (see e.g., equation (7.3.5) of [37] or [35])…”

Exact gravitational wave signatures from colliding extreme black holes

“…( 20) shows the gravity/EM wave's decay at late times for a merger. It is known that for t → ∞, a massless scalar field around a single ERN BH decays as t −(2 +2) [29] (and see [30] for a discussion of massless tensor fields). The field's decay in eq.…”