Late-time tails in the Reissner-Nordström spacetime revisited

Abstract

We propose that the late-time tail problem in the Reissner-Nordström (RN) spacetime is dual to a tail problem in the Schwarzschild spacetime with a different initial data set: at a fixed observation point the asymptotic decay rate of the fields are equal. This duality is used to find the decay rate for tails in RN. This decay rate is exactly as in Schwarzschild, including the case of the extremelycharged RN spacetime (ERN). The only case where any deviation from the Schwarzschild decay rate is found is the case of the tails along the event horizon of an ERN spacetime, where the decay rate is the same as at future null infinity. As observed at a fixed location, the decay rate in ERN is the same as in Schwarzschild. We verify these expectations with numerical simulations.

Horizon Hair of Extremal Black Holes and Measurements at Null Infinity

“…We present below the precise late-time asymptotics away from the horizon: (1) , yield (5). The asymptotic term for ψ| r=R for outgoing perturbations in the strong field region {r = R} is consistent with the results presented in [26,29,35,39,43,52,62].…”

Late-time decay of perturbations outside extremal charged black hole

“…This symmetry of the potential was later employed by Blaksley and Burko [4], who considered two special classes of initial data: (i) compact initial support which does not extend up to the horizon, and (ii) initially-static multipoles that extend up to the horizon (and up to future null infinity). Using the aforementioned symmetry of V l (r * ), Blaksley and Burko obtained decay rates t −2l−3 and t −2l−2 , respectively.…”

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

“…In particular, we have explicitly shown that the coupled perturbations do decay (except l = 1 odd perturbations that might correspond to a slowly rotating Kerr-Newman black hole) and found the decay rate in a way that is consistent with Refs. [11,13,17]. In addition , we can notice some nontrivial features of the decay of coupled perturbations that do not appear in the scalar case.…”

“…See Refs. [17][18][19][12][13][14] for further details. Note that this tail is also formed if the initial data have a generic regular behavior across the horizon or FNI (corresponds to types A, B, and C); However, in the scalar case, the tails that result from the centrifugal part of the potential [∼ t −(2l+2) ] dominates these curvature-induced tails [∼ t −(2l+3) ].…”