Numerical investigation of the late-time Kerr tails

TL;DR

This paper numerically studies the late-time decay of scalar fields on Kerr black holes, revealing how decay rates vary with initial data and location, and analyzing energy and angular momentum transfer during evolution.

Contribution

It introduces a numerical framework combining conformal compactification and spectral methods to analyze late-time Kerr tails in detail.

Findings

Decay rates differ for stationary and non-stationary initial data.

Decay exponents at null infinity are smaller than at the horizon.

Energy and angular momentum fluxes show distinct behaviors over time.

Abstract

The late-time behavior of a scalar field on fixed Kerr background is examined in a numerical framework incorporating the techniques of conformal compactification and hyperbolic initial value formulation. The applied code is 1+(1+2) as it is based on the use of the spectral method in the angular directions while in the time-radial section fourth order finite differencing, along with the method of lines, is applied. The evolution of various types of stationary and non-stationary pure multipole initial states are investigated. The asymptotic decay rates are determined not only in the domain of outer communication but along the event horizon and at future null infinity as well. The decay rates are found to be different for stationary and non-stationary initial data, and they also depend on the fall off properties of the initial data toward future null infinity. The energy and angular momentum transfers are found to show significantly different behavior in the initial phase of the time evolution. The quasinormal ringing phase and the tail phase are also investigated. In the tail phase, the decay exponents for the energy and angular momentum losses at future null infinity are found to be smaller than at the horizon which is in accordance with the behavior of the field itself and it means that at late times the energy and angular momentum falling into the black hole become negligible in comparison with the energy and angular momentum radiated toward future null infinity. The energy and angular momentum balances are used as additional verifications of the reliability of our numerical method.