Late-time decay of perturbations outside extremal charged black hole

Abstract

We analyze the late-time decay of scalar perturbations in extremal Reissner-Nordstrom spacetime. We consider individual spherical-harmonic modes l of a test massless scalar field, restricting our attention to initial data of compact support, with generic regular behavior across the horizon. We obtain a decay rate ∝ t −(2l+3) (just like in Schwarzschild) for incident waves scattered by the black hole. However, for waves originating at the horizon's neighborhood we obtain a slightly slower decay, ∝ t −(2l+2) . We discuss relations to previous works.

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].…”

“…The ingoing asymptotics are new and have not appeared before in the literature. The outgoing asymptotics are consistent with [26,35,43].…”

Linear Waves in the Interior of Extremal Black Holes I

“…Heuristics and numerics regarding latetime tails for extremal Reissner-Nordström in [33,44,47] suggest an extremal variant of "Price's law" that in particular predicts:…”

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

“…For compactly supported initial data the solution at late times decays as t −2l−3 and for initial data with initial static moment it decays asd l t −2l−2 [1]. For the function ψ u (u), following [12,14,15], we use the Couch-Torrence symmetry to map the problem from near the horizon to near infinity. The problem near infinity can be analysed again using the well developed techniques mentioned above.…”

“…Using the Couch-Torrence symmetry, an initial data with regular behaviour across the horizon on the v := t + r * = 0 surface can be mapped to an initial data on the u := t − r * = 0 surface. Analysing this inverted initial data, Sela [15] has argued that there is a contribution to the late time tail in an extreme Reissner-Nordström background that is not due to the curvature of the spacetime. This contribution can be obtained from a flat space analysis of the inverted initial data.…”