Dissipative systems in metric theories of gravity. Foundations and applications of the energy formalism

TL;DR

This paper introduces an energy formalism for analyzing dissipative systems in metric theories of gravity, providing a new method to derive the Rayleigh dissipation function and applying it to the relativistic Poynting-Robertson effect.

Contribution

The paper presents a novel energy formalism approach for dissipative systems in gravity theories, including a detailed method and an application to the relativistic Poynting-Robertson effect.

Findings

Derived the Rayleigh dissipation function analytically.

Applied the formalism to the relativistic Poynting-Robertson effect.

Discussed implications for gravitational theories.

Abstract

In this paper we introduce a new procedure, termed by us \emph{energy formalism}, to deal with dissipative systems in metric theories of gravity. This approach aims at determining the analytic expression of Rayleigh dissipation function in the context of the inverse problem in the calculus of variations. We describe our method in detail, presenting a simple example. After, we consider as first extensive application the general relativistic Poynting-Robertson effect. The obtained results and future implications are discussed.