Gravitational wave recoil in Robinson-Trautman spacetimes

TL;DR

This paper investigates gravitational recoil effects in Robinson-Trautman spacetimes, demonstrating how initial data influence black hole velocities and providing analytical and numerical insights into the recoil phenomenon.

Contribution

It offers analytical expressions for recoil velocities and radiated energy, and applies spectral methods to estimate recoil from initial data asymmetries.

Findings

Recoil velocity correlates with initial data asymmetries.

Final black hole states are Schwarzschild with constant velocity.

Analytical and numerical methods agree on recoil estimates.

Abstract

We consider the gravitational recoil due to non-reflection-symmetric gravitational wave emission in the context of axisymmetric Robinson-Trautman spacetimes. We show that regular initial data evolve generically into a final configuration corresponding to a Schwarzschild black-hole moving with constant speed. For the case of (reflection-)symmetric initial configurations, the mass of the remnant black-hole and the total energy radiated away are completely determined by the initial data, allowing us to obtain analytical expressions for some recent numerical results that have been appeared in the literature. Moreover, by using the Galerkin spectral method to analyze the non-linear regime of the Robinson-Trautman equations, we show that the recoil velocity can be estimated with good accuracy from some asymmetry measures (namely the first odd moments) of the initial data. The extension for the non-axisymmetric case and the implications of our results for realistic situations involving head-on collision of two black holes are also discussed.