# Black holes in multi-fractional and Lorentz-violating models

## TL;DR

This paper investigates black hole solutions in multi-fractional gravity models with varying spacetime dimensions, revealing unique horizon shifts, singularities, and thermodynamic properties, and compares these with other Lorentz-violating theories.

## Contribution

It provides the first detailed analysis of static, spherically symmetric black holes in multi-fractional theories with $q$- and weighted derivatives, highlighting novel geometric features and thermodynamic behaviors.

## Key findings

- Tiny horizon shifts in $q$-derivative models.
- Additional ring singularities proportional to $\,ell_*$.
- De Sitter-like solutions with geometric cosmological constant.

## Abstract

We study static and radially symmetric black holes in the multi-fractional theories of gravity with $q$-derivatives and with weighted derivatives, frameworks where the spacetime dimension varies with the probed scale and geometry is characterized by at least one fundamental length $\ell_*$. In the $q$-derivatives scenario, one finds a tiny shift of the event horizon. Schwarzschild black holes can present an additional ring singularity, not present in general relativity, whose radius is proportional to $\ell_*$. In the multi-fractional theory with weighted derivatives, there is no such deformation, but non-trivial geometric features generate a cosmological-constant term, leading to a de Sitter--Schwarzschild black hole. For both scenarios, we compute the Hawking temperature and comment on the resulting black hole thermodynamics. In the case with $q$-derivatives, black holes can be hotter than usual and possess an additional ring singularity, while in the case with weighted derivatives they have a de Sitter hair of purely geometric origin, which may lead to a solution of the cosmological constant problem similar to that in unimodular gravity. Finally, we compare our findings with other Lorentz-violating models.