Gravitational Radiation in D-dimensional Spacetimes

TL;DR

This paper explores gravitational wave solutions and their generation in D-dimensional flat spacetimes, deriving formulas for energy emission, analyzing special cases like black hole collisions, and considering implications for extra dimensions and black hole creation.

Contribution

It provides new analytical results for gravitational radiation in higher dimensions, including a quadrupole formula, quasinormal frequencies, and energy estimates for black hole collisions and pair creation.

Findings

Derived the D-dimensional quadrupole formula for gravitational radiation.

Calculated scalar quasinormal frequencies of higher-dimensional Schwarzschild black holes.

Estimated gravitational energy emitted during black hole collisions and pair creation.

Abstract

Gravitational wave solutions to Einstein's equations and their generation are examined in D-dimensional flat spacetimes. First the plane wave solutions are analyzed; then the wave generation is studied with the solution for the metric tensor being obtained with the help of retarded D-dimensional Green's function. Due to the difficulties in handling the wave tails in odd dimensions we concentrate our study in even dimensions. We compute the metric quantities in the wave zone in terms of the energy momentum tensor at retarded time. Some special cases of interest are studied: first the slow motion approximation, where the $D$-dimensional quadrupole formula is deduced. Within the quadrupole approximation, we consider two cases of interest, a particle in circular orbit and a particle falling radially into a higher dimensional Schwarzschild black hole. Then we turn our attention to the gravitational radiation emitted during collisions lasting zero seconds, i.e., hard collisions. We compute the gravitational energy radiated during the collision of two point particles, in terms of a cutoff frequency. In the case in which at least one of the particles is a black hole, we argue this cutoff frequency should be close to the lowest gravitational quasinormal frequency. In this context, we compute the scalar quasinormal frequencies of higher dimensional Schwarzschild black holes. Finally, as an interesting new application of this formalism, we compute the gravitational energy release during the quantum process of black hole pair creation. These results might be important in light of the recent proposal that there may exist extra dimensions in the Universe, one consequence of which may be black hole creation at the Large Hadron Collider at CERN.