Black Hole Thermodynamics in MOdified Gravity (MOG)

TL;DR

This paper explores the thermodynamics of black holes within a modified gravity theory, revealing how the theory alters black hole properties, introduces a new gravitational charge, and may eliminate horizons under certain conditions.

Contribution

It provides a detailed analysis of black hole thermodynamics in MOG, highlighting the effects of a mass-dependent gravitational charge and the possibility of horizonless solutions.

Findings

Modified gravity changes black hole thermodynamics.

A new gravitational charge replaces electric charge in solutions.

Possible existence of horizonless black hole solutions.

Abstract

We analyze the thermodynamical properties of black holes in a modified theory of gravity, which was initially proposed to obtain correct dynamics of galaxies and galaxy clusters without dark matter. The thermodynamics of non-rotating and rotating black hole solutions resembles similar solutions in Einstein-Maxwell theory with the electric charge being replaced by a new mass dependent gravitational charge $Q = \sqrt{\alpha G_N}M$. This new mass dependent charge modifies the effective Newtonian constant from $G_N$ to $G = G_N(1+\alpha)$, and this in turn critically affects the thermodynamics of the black holes. We also investigate the thermodynamics of regular solutions, and explore the limiting case when no horizons forms. So, it is possible that the modified gravity can lead to the absence of black hole horizons in our universe. Finally, we analyze corrections to the thermodynamics of a non-rotating black hole and obtain the usual logarithmic correction term.