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The European Physical Journal C

, 77:335

First Online: 20 May 2017Received: 29 March 2017Accepted: 28 April 2017DOI: 10.1140-epjc-s10052-017-4879-5

Cite this article as: Calcagni, G., Rodríguez Fernández, D. & Ronco, M. Eur. Phys. J. C 2017 77: 335. doi:10.1140-epjc-s10052-017-4879-5


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.

Autor: Gianluca Calcagni - David Rodríguez Fernández - Michele Ronco


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