A spherically symmetric gravitational solution of nearly conformally flat metric~measure~space

TL;DR

This paper explores a nearly flat conformally invariant gravitational theory within metric measure space, deriving vacuum solutions and showing how it can mimic dark matter effects through a density function related to observed rotation curves.

Contribution

It introduces a vacuum solution in MMS that can simulate dark matter effects by employing a density function, linking conformal invariance with astrophysical observations.

Findings

Derived vacuum solution in MMS that mimics dark matter

Provided density functions for PSS and NFW profiles

Connected conformal invariance with galaxy rotation curves

Abstract

In this manuscript, we study the nearly flat approximation of a conformally invariant gravitational theory in metric measure space (MMS). In addition, we investigate the transformation of the energy-momentum tensor in this context and obtain the vacuum solution of MMS and its weak field limit in the spherically symmetric coordinates. We show that while it is already a vacuum solution, it can simulate dark matter when restricted to the framework of general relativity, i.e., a symmetry-broken conformal frame. This is done by employing a density function which is an essential part of MMS. We derive an equation for the density function for a general profile of a rotation curve obtained from observations. Specifically, the density function corresponding to two well-known profiles PSS and NFW are provided.