Search

Thermodynamics of rotating black holes described by the R��nyi formula as equilibrium and zeroth law compatible entropy function is investigated. We show that similarly to the standard Boltzmann approach, isolated Kerr black holes are stable with respect to axisymmetric perturbations in the R��nyi model. On the other hand, when the black holes are surrounded by a bath of thermal radiation, slowly rotating black holes can also be in stable equilibrium with the heat bath at a fixed temperature, in contrast to the Boltzmann description. For the question of possible phase transitions in the system, we show that a Hawking-Page transition and a first order small black hole/large black hole transition occur, analogous to the picture of rotating black holes in AdS space. These results confirm the similarity between the R��nyi-asymptotically flat and Boltzmann-AdS approaches to black hole thermodynamics in the rotating case as well. We derive the relations between the thermodynamic parameters based on this correspondence., 29 pages, 20 figures

Thermodynamic stability of black holes, described by the R��nyi formula as equilibrium compatible entropy function, is investigated. It is shown that within this approach, asymptotically flat, Schwarzschild black holes can be in stable equilibrium with thermal radiation at a fixed temperature. This implies that the canonical ensemble exists just like in anti-de Sitter space, and nonextensive effects can stabilize the black holes in a very similar way as it is done by the gravitational potential of an anti-de Sitter space. Furthermore, it is also shown that a Hawking-Page-like black hole phase transition occurs at a critical temperature which depends on the $q$-parameter of the R��nyi formula., 6 pages, 6 figures, accepted for publication in Phys. Lett. B

Publicado em "Progress in mathematical relativity, gravitation and cosmology : proceedings of the Spanish Relativity Meeting ERE2012", part II, ISBN 978-3-642-40156-5. Series : Springer proceedings in mathematics & statistics, vol. 60, Thickness corrections to static, axisymmetric Dirac-Nambu-Goto branes embedded into spherically symmetric black hole spacetimes with arbitrary number of dimensions are studied. First, by applying a perturbative approximation, it is found that the thick solutions deviate significantly in their analytic properties from the thin ones near the axis of the system, and perturbative approaches around the thin configurations can not provide regular thick solutions above a certain dimension. For the general case, a non-perturbative, numerical approach is applied and regular solutions are obtained for arbitrary brane and bulk dimensions. As a special case, it has been found that 2-dimensional branes are exceptional, as they share their analytic properties with the thin branes rather than the thick solutions of all other dimensions., Fundação para a Ciência e a Tecnologia (FCT); Japan Society for the Promotion of Science, Contract No. P06816; Hungarian National Research Fund, OTKA No. K67790

By regarding the Hawking-Bekenstein entropy of Schwarzschild black hole horizons as a non-extensive Tsallis entropy, its formal logarithm, the R��nyi entropy, is considered. The resulting temperature - horizon-radius relation has the same form as the one obtained from a 3+1-dimensional black hole in anti-de Sitter space using the original entropy formula. In both cases the temperature has a minimum. A semi-classical estimate of the horizon radius at this minimum leads to a Bekenstein bound for the q-parameter in the R��nyi entropy of micro black holes, (q >= 1 + 2/pi^2), which is surprisingly close to fitted q-parameters of cosmic ray spectra and power-law distribution of quarks coalescing to hadrons in high energy accelerator experiments., 5 pages, 1 figure, to be published in Phys. Lett. B. arXiv admin note: text overlap with arXiv:1011.3442