Density-metric unimodular gravity:vacuum spherical symmetry

TL;DR

This paper explores an alternative gravity theory using tensor density metrics, deriving vacuum solutions with spherical symmetry, revealing regular solutions without horizons and discussing geodesics and perihelion shifts.

Contribution

It introduces a novel tensor density metric-based gravity theory and derives explicit vacuum solutions with spherical symmetry, highlighting differences from general relativity.

Findings

Solutions are regular for r>0 with no event horizon.

Singularity exists at r=0.

Null geodesics and perihelion shifts are analyzed.

Abstract

We analyze an alternative theory of gravity characterized by metrics that are tensor density of rank(0,2)and weight-1/2.The metric compatibility condition is supposed to hold. The simplest expression for the action of gravitational field is used.Taking the metric and trace of connections as dynamical variables,the field equations in the absence of matter and other kinds of sources are derived.The solutions of these equations are obtained for the case of vacuum static spherical symmetric spacetime.The null geodesics and advance of perihelion of ellipes are discussed.We confirm a subclass of solutions is regular for r>0 and there is no event horizon while it is singular at r=0.