A spherically symmetric gravitational solution of nearly conformally flat metric measure space
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.
- Publication:
-
Physics of the Dark Universe
- Pub Date:
- May 2023
- DOI:
- 10.1016/j.dark.2023.101196
- arXiv:
- arXiv:2209.00719
- Bibcode:
- 2023PDU....4001196O
- Keywords:
-
- Metric measure space;
- Conformal gravity;
- Linearized gravity;
- Flat rotation curve;
- General Relativity and Quantum Cosmology
- E-Print:
- 12 pages