Gravitational Waves beyond the Linear Approximation and Gravitational Wave Reflection

TL;DR

This paper develops a relativistic equation for gravitational waves beyond the linear approximation, predicts wave scattering by black holes, and explores implications for gravitational wave reflection and dark matter.

Contribution

It introduces a massive Klein-Gordon equation for metric perturbations, analyzes wave scattering by black holes, and discusses potential gravitational wave reflection and dark matter quanta.

Findings

Black holes scatter gravitational waves, providing a testable prediction.

The equation predicts gravitational wave reflection at density interfaces.

Implications for gravitational wave propulsion and dark matter are discussed.

Abstract

We derive a relativistic field equation for the trace of the metric perturbation beyond the weak field approximation to the Einstein field equations. The dynamics is governed by a massive Klein-Gordon equation on curved space-time, where the effective mass of the field is associated with the material and the dark energy content via the cosmological term. We solve the equation in the case of a Schwarzschild black hole and show that it can be cast into an effective Schr\"odinger form with an effective geometric potential which binds the zero angular momentum states. The non-zero angular momentum states experience a positive potential peak before the event horizon pointing to gravitational waves scattering. Black holes scatter gravitational waves and thus we provide an unambiguous testable prediction of black hole existence. The Newtonian limit for this equation points to the possibility of reflecting gravitational waves at interfaces with sharp density boundary, thus opening up gravitational wave propulsion physics. We discuss this type of propulsion in the light of Newton's third law of Mechanics. Compelling questions such as the existence of quanta of this field which may account for the dark matter content are also addressed.