Rainbow gravity corrections to the entropic force

The entropic force attracts a lot of interest for its multifunctional properties. For instance, Einstein's field equation, Newton's law of gravitation and the Friedmann equation can be derived from the entropic force. In this paper, utilizing a new kind of rainbow gravity model that was proposed by Magueijo and Smolin, we explore the quantum gravity corrections to the entropic force. First, we derive the modified thermodynamics of a rainbow black hole via its surface gravity. Then, according to Verlinde's theory, the quantum corrections to the entropic force are obtained. The result shows that the modified entropic force is related not only to the properties of the black hole but also the Planck length $\ell_p$, and the rainbow parameter $\gamma$. Furthermore, based on the rainbow gravity corrected entropic force, the modified Einstein's field equation and the modified Friedmann equation are also derived.Comment: 10 page

Thermodynamic phase transition of a black hole in rainbow gravity

In this letter, using the rainbow functions that were proposed by Magueijo and Smolin, we investigate the thermodynamics and the phase transition of rainbow Schwarzschild black hole. First, we calculate the rainbow gravity corrected Hawking temperature. From this modification, we then derive the local temperature, free energy, and other thermodynamic quantities in an isothermal cavity. Finally, we analyze the critical behavior, thermodynamic stability, and phase transition of the rainbow Schwarzschild black hole. The results show that the rainbow gravity can stop the Hawking radiation in the final stages of black holes' evolution and lead to the remnants of black holes. Furthermore, one can observe that the rainbow Schwarzschild black hole has one first-order phase transition, two second-order phase transitions, and three Hawking-Page-type phase transitions in the framework of rainbow gravity theory.Comment: 7 pages, 3 figures, accepted for publication in Physical Letter B. arXiv admin note: substantial text overlap with arXiv:1608.0682

Fermions Tunneling from Higher-Dimensional Reissner-Nordstr\"om Black Hole: Semiclassical and Beyond Semiclassical Approximation

Based on semiclassical tunneling method, we focus on charged fermions tunneling from higher-dimensional Reissner-Nordstr\"{o}m black hole. We first simplify the Dirac equation by semiclassical approximation, and then a semiclassical Hamilton-Jacobi equation is obtained. Using the Hamilton-Jacobi equation, we study the Hawking temperature and fermions tunneling rate at the event horizon of the higher-dimensional Reissner-Nordstr\"{o}m black hole spacetime. Finally, the correct entropy is calculation by the method beyond semiclassical approximation.Comment: 7 page

Novel Non-equilibrium Phase Transition Caused by Non-linear Hadronic-quark Phase Structure

We consider how the occurrence of first-order phase transitions in non-constant pressure differs from those at constant pressure. The former has shown the non-linear phase structure of mixed matter, which implies a particle number dependence of the binding energies of the two species. If the mixed matter is mixed hadron-quark phase, nucleon outgoing from hadronic phase and ingoing to quark phase probably reduces the system to a non-equilibrium state, in other words, there exists the imbalance of the two phases when deconfinement takes place. This novel non-equilibrium process is very analogous to the nuclear reactions that nuclei emit neutrons and absorb them under appropriate conditions. We present self-consistent thermodynamics in description for the processes and identify the microphysics responsible for the processes. The microphysics is an inevitable consequence of non-linear phase structure instead of the effect of an additional dissipation force. When applying our findings to the neutron star containing mixed hadron-quark matter, it is found that the newly discovered energy release might strongly change the thermal evolution behavior of the star.Comment: 18pages,3figures;to be accepted for publication in Physics Letters