https://doi.org/10.1140/epjc/s10052-017-4879-5
Regular Article - Theoretical Physics
Black holes in multi-fractional and Lorentz-violating models
1
Instituto de Estructura de la Materia, CSIC, Serrano 121, 28006, Madrid, Spain
2
Department of Physics, Universidad de Oviedo, Avda. Calvo Sotelo 18, 33007, Oviedo, Spain
3
Dipartimento di Fisica, Università di Roma “La Sapienza”, P.le A. Moro 2, 00185, Rome, Italy
4
INFN, Sez. Roma1, P.le A. Moro 2, 00185, Rome, Italy
* e-mail: calcagni@iem.cfmac.csic.es
Received:
29
March
2017
Accepted:
28
April
2017
Published online:
20
May
2017
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 
. 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 . 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.
© The Author(s), 2017
