Abstract:We obtain the mass expression of the three-and five-dimensional Lifshitz black holes by employing the recently proposed quasilocal formulation of conserved charges, which is based on the off-shell extension of the ADT formalism. Our result is consistent with the first law of black hole thermodynamics and resolves the reported discrepancy between the ADT formalism and the other conventional methods. The same mass expression of Lifshitz black holes is obtained by using another quasilocal method by Padmanabhan. We also discuss the reported discrepancy in the context of the extended first law of black hole thermodynamics by allowing the pressure term.

We study the thermodynamic phase transition in the rainbow Schwarzschild black hole where the metric depends on the energy of the test particle. Identifying the black hole temperature with the energy from the modified dispersion relation, we obtain the modified entropy and thermodynamic energy along with the modified local temperature in the cavity to provide well defined black hole states. It is found that apart from the conventional critical temperature related to Hawking-Page phase transition there appears an additional critical temperature which is of relevance to the existence of a locally stable tiny black hole; however, the off-shell free energy tells us that this black hole should eventually tunnel into the stable large black hole. Finally, we discuss the reason why the temperature near the horizon is finite in the rainbow black hole by employing the running gravitational coupling constant, whereas it is divergent near the horizon in the ordinary Schwarzschild black hole.

To see how the gravity's rainbow works for black hole complementary, we evaluate the required energy for duplication of information in the context of black hole complementarity by calculating the critical value of the rainbow parameter in the certain class of the rainbow Schwarzschild black hole. The resultant energy can be written as the well-defined limit for the vanishing rainbow parameter which characterizes the deformation of the relativistic dispersion relation in the freely falling frame. It shows that the duplication of information in quantum mechanics could not be allowed below a certain critical value of the rainbow parameter; however, it might be possible above the critical value of the rainbow parameter, so that the consistent formulation in our model requires additional constraints or any other resolutions for the latter case. *

We investigate the validity of weak cosmic censorship conjecture for electrically charged black holes in the presence of gravity's rainbow under charged particle absorption. The rainbow effect is shown to play an important role when the black hole is modified by a particle carrying energy and electric charge. Remarkably, we prove that the rainbow-charged black hole can be overspun beyond the extremal condition under charged particle absorption. Further, it is demonstrated that the second law of thermodynamics and cosmic censorship conjecture are violated owing to the rainbow effect. 1 yongwan89@sogang.ac.kr

The conventional Tolman temperature based on the assumption of the traceless condition of energymomentum tensor for matter fields is infinite at the horizon if Hawking radiation is involved. However, we note that the temperature associated with Hawking radiation is of relevance to the trace anomaly, which means that the traceless condition should be released. So, a trace anomaly-induced Stefan-Boltzmann law is newly derived by employing the first law of thermodynamics and the property of the temperature independence of the trace anomaly. Then, the Tolman temperature is quantum-mechanically generalized according to the anomaly-induced Stefan-Boltzmann law. In an exactly soluble model, we show that the Tolman factor does not appear in the generalized Tolman temperature which is eventually finite everywhere, in particular, vanishing at the horizon. It turns out that the equivalence principle survives at the horizon with the help of the quantum principle, and some puzzles related to the Tolman temperature are also resolved.