arXiv subjects

Wontae Kim

Publications and source records attributed to Wontae Kim.

At least 55 records · Page 3Linked to original sources

arXiv2019

The role of the cosmological constant as a pressure in the (2+1)-dimensional black string

It has been claimed that the cosmological constant in AdS black holes such as the BTZ black hole plays the role of the thermodynamic variable of a pressure in the thermodynamic first law and the Smarr relation from the scaling law of the Christodoulou-Ruffini formula. However, the dual solution of the BTZ black hole is the black string which is asymptotically flat despite the presence of the cosmological constant, and so the explicit form of the pressure with the role of the cosmological constant is unclear in the black string since the pressure is subject to the choice of the energy-momentum tensor. Thus, we show that if the pressure of the black string is still assumed to be proportional to the cosmological constant similar to the case of the BTZ black hole, then the thermodynamic first law is consistent with the Smarr relation from the Christodoulou-Ruffini formula, and the thermodynamic quantities for the pressure are well-behaved under the dual transformation.

gr-qc↗

arXiv2019

An existence result for nonhomogeneous quasilinear parabolic equations beyond the duality pairing

In this paper, we prove existence of \emph{very weak solutions} to nonhomogeneous quasilinear parabolic equations beyond the duality pairing. The main ingredients are a priori esitmates in suitable weighted spaces combined with the compactness argument developed in \cite{bulicek2018well}. In order to obtain the a priori estimates, we make use of the full Calderón-Zygmund machinery developed in the past few years and combine it with some sharp bounds for the subclass of Muckenhoupt weights considered in this paper.

math.AP↗

arXiv2018

Partial existence result for Homogeneous Quasilinear parabolic problems beyond the duality pairing

In this paper, we study the existence of distributional solutions solving \cref{main-3} on a bounded domain $Ω$ satisfying a uniform capacity density condition where the nonlinear structure $\mathcal{A}(x,t,\nabla u)$ is modelled after the standard parabolic $p$-Laplace operator. In this regard, we need to prove a priori estimates for the gradient of the solution below the natural exponent and a higher integrability result for very weak solutions at the initial boundary. The elliptic counterpart to these two estimates are fairly well developed over the past few decades, but no analogous theory exists in the quasilinear parabolic setting. Two important features of the estimates proved here are that they are non-perturbative in nature and we are able to take non-zero boundary data. \emph{As a consequence, our estimates are new even for the heat equation on bounded domains.} This partial existence result is a nontrivial extension of the existence theory of very weak solutions from the elliptic setting to the quasilinear parabolic setting. Even though we only prove partial existence result, nevertheless we establish the necessary framework that when proved would lead to obtaining the full result for the homogeneous problem.

math.AP↗

arXiv2018

Unruh effect of nonlocal field theories with a minimal length

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.

physics.gen-ph↗

arXiv2018

Unruh temperatures in circular and drifted Rindler motions

We study the temperatures for the circular and drifted Rindler motions by employing the Unruh-DeWitt detector method. In the circular motion, the temperature is increasing along the radius of the circular motion until it reaches the maximum, and then it is decreasing and eventually vanishing at the limit to the radius where the proper acceleration is infinite. In fact, the temperature is proportional to the proper acceleration quadratically near the origin of the circular motion as compared to the usual Unruh effect depending on the linear proper acceleration. On the other hand, in the drifted Rindler motion, the observer moves with a relative velocity in the direction transverse to the acceleration. If the detector is moving slowly in the transverse direction with a finite proper acceleration, then the temperature behaves like the usual Unruh temperature, while it vanishes for the speed of light in the transverse direction according to the infinite proper acceleration. Consequently, it turns out that the temperatures behave nonlinearly with respect to the proper acceleration and the infinite proper acceleration would not always permit the divergent temperature.

gr-qc↗

arXiv2018

Black hole complementarity with the generalized uncertainty principle in gravity's rainbow

When gravitation is combined with quantum theory, the Heisenberg uncertainty principle could be extended to the generalized uncertainty principle accompanying a minimal length. To see how the generalized uncertainty principle works in the context of black hole complementarity, we calculate the required energy to duplicate information for the Schwarzschild black hole. It shows that the duplication of information is not allowed and black hole complementarity is still valid even assuming the generalized uncertainty principle. On the other hand, the generalized uncertainty principle with the minimal length could lead to a modification of the conventional dispersion relation in light of Gravity's Rainbow, where the minimal length is also invariant as well as the speed of light. Revisiting the gedanken experiment, we show that the no-cloning theorem for black hole complementarity can be made valid in the regime of Gravity's Rainbow on a certain combination of parameters.

gr-qc↗

arXiv2017

Validity of black hole complementarity in the BTZ black hole

Based on the gedanken experiment for black hole complementarity in the Schwarzschild black hole, we calculate the energy required to duplicate information in the BTZ black hole under the assumption of absorbing boundary condition and its dual solution of the black string, respectively, in order to justify the validity of the no-cloning theorem in quantum mechanics. For the BTZ black hole, the required energy for the duplication of information can be made fairly small, whereas for the black string it exceeds the total mass of the black string, although they are related to each other under the dual transformation. So, the duplication of information might be possible in the BTZ black hole in contrast to the case of the black string, so that the no-cloning theorem could be violated for the former case. To save the duplication of information for the BTZ black hole, we perform an improved gedanken experiment by using the local thermodynamic quantities near the horizon rather than those defined at infinity, and show that the no-cloning theorem could be made valid even in the BTZ black hole. We also discuss how this local treatment for the no-cloning theorem can be applied to the black string as well as the Schwarzschild black hole innocuously.

gr-qc↗

arXiv2017

The effective Tolman temperature in curved spacetimes

We review a recently proposed effective Tolman temperature and present its applications to various gravitational systems. In the Unruh state for the evaporating black holes, the free-fall energy density is found to be negative divergent at the horizon, which is in contrast to the conventional calculations performed in the Kruskal coordinates. We resolve this conflict by invoking that the Kruskcal coordinates could be no longer proper coordinates at the horizon. In the Hartle-Hawking-Israel state, despite the negative finite proper energy density at the horizon, the Tolman temperature is divergent there due to the infinite blueshift of the Hawking temperature. However, a consistent Stefan-Boltzmann law with the Hawking radiation shows that the effective Tolman temperature is eventually finite everywhere and the equivalence principle is surprisingly restored at the horizon. Then, we also show that the firewall necessarily emerges out of the Unruh vacuum, so that the Tolman temperature in the evaporating black hole is naturally divergent due to the infinitely blueshifted negative ingoing flux crossing the horizon, whereas the outgoing Hawking radiation characterized by the effective Tolman temperature indeed originates from the quantum atmosphere, not just at the horizon. So, the firewall and the atmosphere for the Hawking radiation turn out to be compatible, once we discard the fact that the Hawking radiation in the Unruh state originates from the infinitely blueshifted outgoing excitations at the horizon. Finally, as a cosmological application, the initial radiation energy density in warm inflation scenarios has been assumed to be finite when inflation starts. We successfully find the origin of the non-vanishing initial radiation energy density in the warm inflation by using the effective Tolman temperature.

gr-qc↗

arXiv2017

Proper temperature of Schwarzschild AdS black hole revisited

The Unruh temperature calculated from the global embedding of the Schwarzschild AdS spacetime into Minkowski spacetime was identified with the local temperature measured by a free-fall observer; however, it would be imaginary in a certain region outside the event horizon. So, the temperature was assumed to be zero of no thermal radiation for that region. In this paper, we revisit this issue in the exactly soluble two-dimensional Schwarzschild AdS black hole and present an alternative resolution to this problem by using the Tolman's procedure. However, the process is not straightforward in the sense that one should extend the original procedure to rest upon the traceless energy-momentum tensor in such a way that it could encompass the case of the non-vanishing trace of energy-momentum tensor in the presence of the trace anomaly. Consequently, we show that the free-fall temperature turns out to be real everywhere outside the event horizon without any imaginary value, in particular, it vanishes both at the horizon and at the asymptotic infinity.

gr-qc↗

arXiv2017

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 blueshift 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 there does not appear infinite blueshift of the Hawking temperature at the event horizon any more. In particular, it is vanishing on the horizon, so that the equivalence principle is exactly recovered at the horizon.

gr-qc↗

arXiv2017

Origin of Hawking Radiation: Firewall or Atmosphere?

The Unruh vacuum not admitting any outgoing flux at the horizon implies that the origin of the outgoing Hawking radiation is the atmosphere of a near-horizon quantum region without resort to the firewall; however, the existence of the firewall of superplanckian excitations at the horizon can be supported by the infinite Tolman temperature at the horizon. In an exactly soluble model, we explicitly show that the firewall necessarily emerges out of the Unruh vacuum so that the Tolman temperature in the Unruh vacuum is divergent in essence due to the infinitely blueshifted negative ingoing flux crossing the horizon rather than the outgoing flux. We also show that the outgoing Hawking radiation in the Unruh vacuum indeed originates from the atmosphere, not just at the horizon, which is of no relevance to the infinite blueshift. Consequently, the firewall from the infinite Tolman temperature and the Hawking radiation from the atmosphere turn out to be compatible, once we waive the claim that the Hawking radiation in the Unruh vacuum originates from the infinitely blueshifted outgoing excitations at the horizon.

hep-th↗

arXiv2016

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.

gr-qc↗

arXiv2016

Note on the speed of GW150914 in gravity's rainbow

Without breaking Lorentz invariance, we investigate the speed of graviton in event GW150914 by using the modified dispersion relation from gravity's rainbow. The proper range of the parameter in the modified dispersion relation is determined by taking into account the gap between the speed of the graviton and that obtained from event GW150914.

gr-qc↗

arXiv2016

Hawking, Fiducial, and Free-fall Temperatures of Black Hole on Gravity's Rainbow

On gravity's rainbow, the energy of particles affects the geometry of black hole in such a way that the Hawking temperature of black hole is appropriately modified. It means that the fiducial and free-fall temperatures on the background of black hole should also be modified according to deformation of the geometry. We find that the fiducial temperature takes the blue-shifted modified Hawking temperature so that it is divergent at the horizon, while the free-fall temperature defined by employing the thermodynamic Stefan-Boltzmann relation on gravity's rainbow is finite everywhere without the blue-shift effect; in particular, it is vanishing at the horizon. In this respect, the behaviors of the two-different temperatures at the horizon show that black hole complementarity is still required on gravity's rainbow.

gr-qc↗

arXiv2016

Semiclassical approach for the evaporating black hole revisited

A recent calculation shows that the observed energy density in the Unruh state at the future event horizon as seen by a freely falling observer is finite if the observer is released from rest at any positive distance outside the horizon; however, it is getting larger and larger so that it is negatively divergent at the horizon in the limit that the observer starts falling from rest at the horizon, which corresponds to the infinite boost with respect to the freely falling observer at a finite distance from the horizon. In order to resolve some conflicts between the recent calculation and the conventional ones in the well-known literatures, the calculation of the free-fall energy density is revisited and some differences are pointed out.

gr-qc↗

arXiv2015

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.

gr-qc↗

arXiv2015

Black Hole Complementarity in Gravity's Rainbow

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.

gr-qc↗

arXiv2015

Free-fall energy density and flux in the Schwarzschild black hole

In the four-dimensional background of Schwarzschild black hole, we investigate the energy densities and fluxes in the freely falling frames for the Boulware, Unruh, and Israel-Hartle-Hawking states. In particular, we study their behaviors near the horizon and asymptotic spatial infinity by using the trace anomaly of a conformally invariant scalar field. In the Boulware state, both the energy density and flux are negative divergent when the observer is dropped at the horizon, and asymptotically vanish. In the Unruh state, the energy density is also negative divergent at the horizon while it is positive finite asymptotically. The flux in the Unruh state is always positive and divergent at the horizon. In the Israel-Hartle-Hawking state, the energy density depends on the angular motion of free fall, and fluxes vanish at the horizon and the spatial infinity. Finally, we discuss the role of the negative energy density near the horizon in the evaporating black hole.

gr-qc↗