Black Holes in Modified Gravity (MOG)

TL;DR

This paper explores black hole solutions in Scalar-Tensor-Vector-Gravity (MOG), deriving new metrics, analyzing particle orbits and shadows, and constructing a traversable wormhole, thereby expanding understanding of modified gravity's implications.

Contribution

It provides new static, spherically symmetric and rotating black hole solutions in MOG, including a regular, singularity-free solution and a traversable wormhole model.

Findings

Derived the MOG black hole metrics and horizons.

Calculated black hole shadows for Schwarzschild-MOG and Kerr-MOG.

Constructed a stable traversable wormhole solution.

Abstract

The field equations for Scalar-Tensor-Vector-Gravity (STVG) or modified gravity (MOG) have a static, spherically symmetric black hole solution determined by the mass $M$ with two horizons. The strength of the gravitational constant is $G=G_N(1+\alpha)$ where $\alpha$ is a parameter. A regular singularity-free MOG solution is derived using a nonlinear field dynamics for the repulsive gravitational field component and a reasonable physical energy-momentum tensor. The Kruskal-Szekeres completion of the MOG black hole solution is obtained. The Kerr-MOG black hole solution is determined by the mass $M$, the parameter $\alpha$ and the spin angular momentum $J=Ma$. The equations of motion and the stability condition of a test particle orbiting the MOG black hole are derived, and the radius of the black hole photosphere and the shadows cast by the Schwarzschild-MOG and Kerr-MOG black holes are calculated. A traversable wormhole solution is constructed with a throat stabilized by the repulsive component of the gravitational field.