# Black hole solutions correspondence between conformal and massive theories of gravity

## TL;DR

This paper establishes a correspondence between black hole solutions in conformal and massive gravity theories, revealing parameter constraints and relationships between black hole mass and gravity parameters.

## Contribution

It introduces a novel correspondence between solutions of conformal and massive gravity theories and determines acceptable parameter ranges based on black hole mass.

## Key findings

- Constraints on parameters of gravity theories are derived.
- A relation between black hole mass and massive gravity parameters is established.
- Acceptable parameter ranges depend on black hole mass positivity.

## Abstract

In this work, a correspondence between black hole solutions of conformal and massive theories of gravity is found. It is seen that this correspondence imposes some constraints on parameters of these theories. What is more, a relation between the mass of black holes and the parameters of massive gravity is found. Indeed, the acceptable ranges of massive gravity parameters ($c_{1}$\ and $c_{2}$) are found. It is shown that by considering the positive mass of black holes, some ranges of $c_{1}$\ and $c_{2}$ are acceptable.