Yongwan Gim

Thermodynamic phase transition in the rainbow Schwarzschild black hole

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.

The first law of thermodynamics in Lifshitz black holes revisited

A bstractWe 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.

Black hole complementarity in gravity's rainbow

To see how the gravitys 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.

Something special at the event horizon

We revisit the free-fall energy density of scalar fields semiclassically by employing the trace anomaly on a two-dimensional Schwarzschild black hole with respect to various black hole states in order to clarify whether something special at the horizon happens or not. For the Boulware state, the energy density at the horizon is always negative divergent, which is independent of initial free-fall positions. However, in the Unruh state the initial free-fall position is responsible for the energy density at the horizon and there is a critical point to determine the sign of the energy density at the horizon. In particular, a huge negative energy density appears when the freely falling observer is dropped just near the horizon. For the Hartle–Hawking state, it may also be positive or negative depending on the initial free-fall position, but it is always finite. Finally, we discuss physical consequences of these calculations.

A quantal Tolman temperature

The conventional Tolman temperature based on the assumption of the traceless condition of energy-momentum 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.

Hawking, fiducial, and free-fall temperature of black hole on gravity’s rainbow

On gravity’s rainbow, the energy of test particles deforms the geometry of a black hole in such a way that the corresponding Hawking temperature is expected to be modified. It means that the fiducial and free-fall temperatures on the black hole background should also be modified according to deformation of the geometry. In this work, the probing energy of test particles is assumed as the average energy of the Hawking particle in order to study the particle back reaction of the geometry by using the advantage of gravity’s rainbow. We shall obtain the modified fiducial and free-fall temperatures, respectively. The behaviors of these two temperatures on the horizon tell us that black hole complementarity is still well defined on gravity’s rainbow.

On the thermodynamic origin of the initial radiation energy density in warm inflation

In warm inflation scenarios, radiation always exists, so that the radiation energy density is also assumed to be finite when inflation starts. To find out the origin of the non-vanishing initial radiation energy density, we revisit thermodynamic analysis for a warm inflation model and then derive an effective Stefan-Boltzmann law which is commensurate with the temperature-dependent effective potential by taking into account the non-vanishing trace of the total energy-momentum tensors. The effective Stefan-Boltzmann law shows that the zero energy density for radiation at the Grand Unification epoch increases until the inflation starts and it becomes eventually finite at the initial stage of warm inflation. By using the above effective Stefan-Boltzmann law, we also study the cosmological scalar perturbation, and obtain the sufficient radiation energy density in order for GUT baryogenesis at the end of inflation.

Thermodynamic phase transition based on the nonsingular temperature

The Hawking temperature for the Schwarzschild black hole is divergent when the mass of the black hole vanishes; however the corresponding geometry becomes the Minkowski spacetime whose intrinsic temperature is zero. In connection with this issue, we construct a non-singular temperature which follows the Hawking temperature for the large black hole while it vanishes when the black hole completely evaporated. In order for thermodynamic significances of this modified temperature, we calculate thermodynamic quantities and study phase transitions. It turns out that even the small black hole can be stable below a certain temperature, and the hot flat space is always metastable so that it decays into the stable small black hole or the stable large black hole.

Effective Tolman temperature induced by trace anomaly

Despite the finiteness of stress tensor for a scalar field on the four-dimensional Schwarzschild black hole in the Israel–Hartle–Hawking vacuum, the Tolman temperature in thermal equilibrium is certainly divergent on the horizon due to the infinite blue-shift of the Hawking temperature. The origin of this conflict is due to the fact that the conventional Tolman temperature was based on the assumption of a traceless stress tensor, which is, however, incompatible with the presence of the trace anomaly responsible for the Hawking radiation. Here, we present an effective Tolman temperature which is compatible with the presence of the trace anomaly by using the modified Stefan–Boltzmann law. Eventually, the effective Tolman temperature turns out to be finite everywhere outside the horizon, and so an infinite blue-shift of the Hawking temperature at the event horizon does not appear any more. In particular, it is vanishing on the horizon, so that the equivalence principle is exactly recovered at the horizon.

Unruh effect of nonlocal field theories with a minimal length

Abstract The nonlocal field theory commonly requires a minimal length, and so it appears to formulate the nonlocal theory in terms of the doubly special relativity which makes the speed of light and the minimal length invariant simultaneously. We set up a generic nonlocal model having the same set of solutions as the local theory but allowing Lorentz violations due to the minimal length. It is exactly corresponding to the model with the modified dispersion relation in the doubly special relativity. For this model, we calculate the modified Wightman function and the rate of response function by using the Unruh–DeWitt detector method. It turns out that the Unruh effect should be corrected by the minimal length related to the nonlocality in the regime of the doubly special relativity. However, for the Lorentz-invariant limit, it is shown that the Wightman function and the Unruh effect remain the same as those of the local theory.