The late-time tails in the Reissner-Nordstr\"{o}m spacetime revisited

TL;DR

This paper establishes a duality between tail decay problems in Reissner-Nordström and Schwarzschild spacetimes, allowing the prediction of decay rates in RN, confirmed by numerical simulations, with unique behavior along the ERN horizon.

Contribution

It introduces a duality approach to determine late-time tail decay rates in RN spacetime based on Schwarzschild results, including the extremal case, verified through simulations.

Findings

Decay rates in RN match Schwarzschild for most cases.

Along the ERN horizon, decay rates differ from Schwarzschild.

Numerical simulations confirm the theoretical predictions.

Abstract

We propose that the late-time tail problem in the Reissner-Nordstr\"{o}m (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 extremely-charged 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.