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2017

Black holes in multi-fractional and Lorentz-violating models

Calcagni, Gianluca, Fernández, David Rodríguez, Ronco, Michele

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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.