Galactic space-times in modified theories of gravity

TL;DR

This paper investigates Bertrand space-times as models for galactic dark matter in modified gravity theories, analyzing their properties and fitting observational data in $f(R)$ and Brans-Dicke frameworks.

Contribution

It demonstrates the viability of Bertrand space-times in modified gravity theories and explores their potential to explain galactic rotation curves.

Findings

BSTs can fit galactic rotation curve data.

Effective equations of state in $f(R)$ gravity align with observations.

Constraints on Brans-Dicke parameters are derived.

Abstract

We study Bertrand space-times (BSTs), which have been proposed as viable models of space-times seeded by galactic dark matter, in modified theories of gravity. We first critically examine the issue of galactic rotation curves in General Relativity, and establish the usefulness of BSTs to fit experimental data in this context. We then study BSTs in metric $f(R)$ gravity and in Brans-Dicke theories. For the former, the nature of the Newtonian potential is established, and we also compute the effective equation of state and show that it can provide good fits to some recent experimental results. For the latter, we calculate the Brans-Dicke scalar analytically in some limits and numerically in general, and find interesting constraints on the parameters of the theory. Our results provide evidence for the physical nature of Bertrand space-times in modified theories of gravity.