Spherically symmetric vacuum solutions arising from trace dynamics modifications to gravitation

TL;DR

This paper investigates static, spherically symmetric vacuum solutions in modified gravity theories derived from trace dynamics, revealing unique features such as the absence of horizons and the presence of singularities.

Contribution

It provides analytic and numerical solutions for modified Einstein equations incorporating trace dynamics effects, highlighting novel properties of these solutions.

Findings

No horizons in static solutions due to non-vanishing g_{00}

Ricci scalar R vanishes identically

Existence of a physical singularity at cosmological distances

Abstract

We derive the equations governing static, spherically symmetric vacuum solutions to the Einstein equations, as modified by the frame-dependent effective action arising from trace dynamics. We give analytic and numerical results for the solutions of these equations, first in polar coordinates, and then in isotropic coordinates. General features of the static case are that (i) there is no horizon, since $g_{00}$ is non-vanishing for finite values of the polar radius, and only vanishes (in isotropic coordinates) at the internal singularity, (ii) the Ricci scalar $R$ vanishes identically, and (iii) there is a physical singularity at cosmological distances. The large distance singularity may be an artifact of the static restriction, since we find that the behavior at large distances is altered in a time-dependent solution using the Mc Vittie Ansatz.