The Jeans theorem and the "Tolman-Oppenheimer-Volkov equation" in an exact wave solution of R^2 gravity

TL;DR

This paper extends previous models of galaxy-like states in R^2 gravity by proving a Jeans theorem and deriving an analog of the TOV equation, providing insights into dark matter modeling.

Contribution

It demonstrates that star density depends only on energy and angular momentum, and derives a TOV-like equation in an R^2 gravity context, advancing galaxy modeling theories.

Findings

Star density is a functional of energy and angular momentum.

Derived an analog of the TOV equation for R^2 gravity.

Provided models suggesting dark matter may not be essential.

Abstract

Corda, Mosquera Cuesta and Lorduy Gomez have shown that spherically symmetric stationary states can be used as a model for galaxies in the framework of the linearized R^2 gravity. Those states could represent a partial solution to the Dark Matter Problem. Here we discuss an improvement of this work. In fact, as the star density is a functional of the invariants of the associated Vlasov equation, we show that any of these invariants is in its turn a functional of the local energy and the angular momentum. As a consequence, the star density depends only on these two integrals of the Vlasov system. This result is known as the "Jeans theorem". In addition, we find an analogous of the historical Tolman- Oppenheimer-Volkov equation for the system considered in this paper. For the sake of completeness, in the final Section of the paper we consider two additional models which argue that Dark Matter could not be an essential element.