Gravitational Wave Generation via the Einstein-Langevin Equation

TL;DR

This paper explores a stochastic gravity approach to gravitational wave generation using the Einstein-Langevin equation, modeling graviton fluctuations as a Brownian process to simulate GW waveforms during binary coalescence.

Contribution

It introduces a novel stochastic framework linking graviton fluctuations to GW formation, employing the Einstein-Langevin equation and a Brownian motion analogy for the first time.

Findings

Simulated graviton fluctuations resemble GW waveforms.

Established a scaling relation for graviton dissipation during coalescence.

Provided a computational heuristic for graviton-scale perturbations in GW signals.

Abstract

Detections of gravitational waves (GWs) since GW150914 has gained a contemporary interest in a potential quantum-classical correspondence between GWs and hypothetical gravitons. One such correspondence theory is stochastic gravity, whereby graviton fluctuations are treated as the stochastic noise embedded in globally-flat manifolds and local gravitational interactions. Utilizing the Einstein-Langevin equation that describes graviton fluctuations, in attempt to form a correlation with GW generation, we utilize the hollow mass-shell model of coalescing compact binaries. This is to explore the second Newtonian postulate of neutralized internal gravitational fields, i.e. the stochastic noise of an enclosed, internal Minkowski manifold. This stochatic picture of GW formation implies the treatment of the enclosed gravitons as a Brownian bath. From the Einstein-Langevin equation, we establish a scaling relation where quanta dissipation depends inversely with the contracting volume (i.e., emission increases during coalescence). Using an Euler iteration scheme, we simulate the graviton fluctuations from inspiral to merger as a Wiener process, revealing a signal that qualitatively resembles macroscopic GW waveforms. While inherently heuristic and phenomenological, this approach provides a computational framework for exploring graviton-scale perturbations in GW formation. We discuss furthermore analytical waveform matching with the iteration scheme, as well as the justification of a Brownian analogy amidst current and state-of-the-art effective field theory frameworks.