Searcharxiv⌕ Search

arXiv subjects

Wontae Kim

Publications and source records attributed to Wontae Kim.

At least 37 records · Page 2Linked to original sources
arXiv2024

The quasilocal energy and thermodynamic first law in accelerating AdS black holes

We scrutinize the conserved energy of an accelerating AdS black hole by employing the off-shell quasilocal formalism, which amalgamates the ADT formalism with the covariant phase space approach. In the presence of conical singularities in the accelerating black hole, the energy expression is articulated through the surface term derived from our formalism. The essence of our analysis of the quasilocal energy resides in the surface contributions coming from the conical singularities as well as the conventional radial boundary. Consequently, the resultant conserved quasilocal energy naturally conforms the thermodynamic first law for the black hole without necessitating any augmentation of thermodynamic variables.

hep-th↗
arXiv2024

Calderón-Zygmund type estimate for the parabolic double-phase system

This paper provides a local and global Calderón-Zygmund type estimate of a weak solution to the parabolic double-phase system. The proof of local estimate is based on comparison estimates and the scaling invariant property of the parabolic double-phase system in the intrinsic cylinders of the stopping time argument setting. For the proof of the global estimate, we have applied the reflection and approximation techniques.

math.AP↗
arXiv2024

Investigation of black hole complementarity in AdS$_2$ black holes

Black hole complementarity plays a pivotal role in resolving the information loss paradox by treating Hawking radiation as carriers of information, apart from the complicated mechanisms involved in decoding information from this radiation. The thought experiment proposed by Susskind and Thorlacius, as well as the criteria set forth by Hayden and Preskill, provide deep insights into the intricate relationship of black hole complementarity between fiducial and infalling observers. We execute the Alice-Bob thought experiment in the context of two-dimensional anti-de Sitter black holes. It turns out that information cloning can be avoided in the case of a large black hole. According to the Hayden-Preskill criteria, the scale parameter associated with the explicit breaking of the one-dimensional group of reparametrizations must significantly exceed the squared mass of the black hole to effectively prevent information cloning.

hep-th↗
arXiv2024

Gradient higher integrability for singular parabolic double-phase systems

We prove a local higher integrability result for the gradient of a weak solution to parabolic double-phase systems of $p$-Laplace type when $\tfrac{2n}{n+2}< p\le2$. The result is based on a reverse Hölder inequality in intrinsic cylinders combining $p$-intrinsic and $(p,q)$-intrinsic geometries. A singular scaling deficits affects the range of $q$.

math.AP↗
arXiv2023

Borderline gradient regularity estimates for quasilinear parabolic systems with data independent of time

In this paper, we study some regularity issues concerning the gradient of weak solutions of $u_t - {\rm div} \mathcal{A}(x,t,\nabla u) = g$, where $\mathcal{A}(x,t,\nabla u)$ is modeled after the $p$-Laplace operator. The main results we are interested in is to obtain optimal conditions on the datum $g$ (independent of time) such that borderline higher integrability of the gradient and Lipschitz estimates for the weak solution holds. Moreover, we develop a theory where we can obtain elliptic type estimates using parabolic theory, which gives improved potential estimates for the elliptic systems.

math.AP↗
arXiv2023

On the regularity theory for mixed anisotropic and nonlocal $p$-Laplace equations and its applications to singular problems

We establish existence results for a class of mixed anisotropic and nonlocal $p$-Laplace equation with singular nonlinearities. We consider both constant and variable singular exponents. Our argument is based on an approximation method. To this end, we also discuss the necessary regularity properties of weak solutions of the associated non-singular problems. More precisely, we obtain local boundedness of subsolutions, Harnack inequality for solutions and weak Harnack inequality for supersolutions.

math.AP↗
arXiv2023

Batalin-Tyutin quantization of dynamical boundary of AdS$_2$

In a two-dimensional AdS space, a dynamical boundary of AdS space was described by a one-dimensional quantum-mechanical Hamiltonian with a coupling between the bulk and boundary system. In this paper, we present a Lagrangian corresponding to the Hamiltonian through the Legendre transformation with a constraint. In Dirac's constraint analysis, we find two primary constraints without secondary constraints; however, they are fully second-class. In order to make the second-class constraint system into a first-class constraint system, we employ the Batalin-Tyutin Hamiltonian method, where the extended system reduces to the original one for the unitary gauge condition. In the spirit of the AdS/CFT correspondence, it raises a question whether a well-defined extended bulk theory corresponding to the extended boundary theory can exist or not.

hep-th↗
arXiv2022

Investigations of strong cosmic censorship in 3-dimensional black strings

Investigating the quasinormal modes of a massive scalar field on the 3-dimensional black string (3dBS), we study the strong cosmic censorship (SCC) conjecture for the 3dBS in the T-dual relationship with the 3-dimensional rotating anti-de-Sitter (BTZ) black hole. It is shown that even though geometries of the two spacetimes are quite different, such as asymptotically AdS for the BTZ black hole and asymptotically flat for the 3dBS, the BTZ black hole and the 3dBS share similar properties for the SCC. Concretely speaking, the SCC conjecture can be violated even for asymptotically flat spacetime, i.e. the 3dBS. These observations lead us to an assumption that the T-dual transformation preserves spacetime symmetries, at least, which are relevant to the SCC. In addition, we find a new feature of the quasinormal mode at the Cauchy horizon: in the case of the 3dBS, the spectral gap, $α_{\mathrm{BS}}$ at the Cauchy horizon is not determined by the `$ω$-frequency mode', but the `m-frequency mode'.

gr-qc↗
arXiv2022

Analytic approach to the formation of a three-dimensional black string from a dust cloud

In three-dimensional low-energy string theory, we study the formation of a black string from a dust cloud. We analytically obtain two distinct classes of exact solutions with arbitrary functions responsible for mass distributions of the dust cloud. The first and second kinds of solutions may describe collapsing dusts but the first kind is only for inhomogeneous dust distribution while the second kind has a homogeneous limit. The finite collapse time and the Israel junction conditions tell us that the first kind solution describes a desired collapsing phenomenon, whereas the scale factor in the inner spacetime for the second kind turns out to be trivial. In the first kind solution, specific collapsing models can be realized by choosing an appropriate inhomogeneous dust distribution consistent with the Israel junction conditions. Consequently, the inhomogeneous dust cloud eventually collapses to the black string although the homogeneous dust cloud does not guarantee the formation of the black string in our setting. The space-like curvature singularities occur at the finite collapse time and they can be cloaked by the horizon of the black string.

gr-qc↗
arXiv2022

Hawking-Page phase transition of the Schwarzschild AdS black hole with the effective Tolman temperature

A sufficiently large Schwarzschild AdS black hole with the Hawking temperature has a positive heat capacity and undergoes the Hawking-Page phase transition. Even though an arbitrary isothermal surface of a cavity is introduced, the essential features about the stability and phase transition of the Schwarzschild AdS black hole remain the same. In this paper, we study the stability and the Hawking-Page phase transition of the Schwarzschild AdS black hole by employing an alternative local temperature satisfying the Hartle-Hawking vacuum condition which states that the ingoing and outgoing fluxes vanish at the horizon so that the local temperature is naturally zero there. The different definition of the local temperature based on the stress tensor approach provides different types of stability and phase transition. For a AdS curvature radius below a critical one, the medium-sized black hole is found to be stable and the other small and large black holes turn out to be unstable regardless of the AdS curvature radius. Furthermore, we encounter various critical temperatures. The first one is for the Hawking-Page phase transition between the medium-sized black hole and thermal AdS, and the second one is for a phase transition between the large black hole and thermal AdS; however, the latter one is not essential because the large black hole and thermal AdS eventually collapse to the medium-sized black hole. Interestingly, we find an additional critical temperature related to the zeroth-order phase transition between the medium-sized black hole and thermal AdS. Consequently, the medium-sized black hole undergoes both the Hawking-Page phase transition and the zeroth-order phase transition.

gr-qc↗
arXiv2022

On thermal radiation of de Sitter space in the semiclassical Jackiw-Teitelboim model

In general, the Gibbons-Hawking temperature based on the Euclidean functional approach shows that de Sitter space in the Bunch-Davies vacuum is globally thermal. In the exactly soluble semiclassical Jackiw-Teitelboim model, we investigate thermal property of de Sitter space by taking into account the quantum back reaction of the geometry. The proper temperature of de Sitter space in the Bunch-Davies vacuum is found to vanish. In case of a certain quantum state breaking the de Sitter symmetry, de Sitter space can be made thermally exited; however, in this case the dilaton singularity cannot be avoided. Consequently, in the Jackiw-Teitelboim model the proper temperature of de Sitter space in the Bunch-Davies vacuum turns out to be zero and the Bunch-Davies vacuum is found to be the only physical vacuum without any naked singularities.

gr-qc↗
arXiv2021

Entanglement entropy of asymptotically flat non-extremal and extremal black holes with an island

The island rule for the entanglement entropy is applied to an eternal Reissner-Nordström black hole. The key ingredient is that the black hole is assumed to be in thermal equilibrium with a heat bath of an arbitrary temperature and so the generalized entropy is treated as being off-shell. Taking the on-shell condition to the off-shell generalized entropy, we find the generalized entropy and then obtain the entanglement entropy following the island rule. For the non-extremal black hole, the entanglement entropy grows linearly in time and can be saturated after the Page time as expected. The entanglement entropy also has a well-defined Schwarzschild limit. In the extremal black hole, the island prescription provides a logarithmically growing entanglement entropy in time and a constant entanglement entropy after the Page time. In the extremal black hole, the boundary of the island hits the curvature singularity where the semi-classical approximations appear invalid. To avoid encountering the curvature singularity, we apply this procedure to the Hayward black hole regular at the origin. Consequently, the presence of the island in extremal black holes can provide a finite entanglement entropy, which might imply non-trivial vacuum configurations of extremal black holes.

hep-th↗
arXiv2021

Quantum radiation of a collapsing shell in three-dimensional AdS spacetime revisited

In three-dimensional AdS space, we consider the gravitational collapse of dust shell and then investigate the quantum radiation from the collapsing shell by employing the functional Schrödinger formalism. In the formation of the BTZ black hole, the interior geometry of the shell can be chosen as either the massless black hole or the global AdS space. In the incipient black hole limit, we obtain the wave function exactly from the time-dependent Schrödinger equation for a massless scalar field. Then, we show that the occupation number of excited states can be written by analytic expressions, and the radiation temperature is in agreement with the Hawking temperature, irrespective of the specific choice of the interior geometries.

gr-qc↗
arXiv2020

Formation of the Hayward black hole from a collapsing shell

We consider a collapsing shell of matter to form the Hayward black hole and investigate semiclassically quantum radiation from the shell. Using the Israel's formulation, we obtain the mass relation between the collapsing shell and the Hayward black hole. By using the functional Schrödinger formulation for the massless quantum radiation, the evolution of a vacuum state for a scalar field is shown to be unitary. We find that the number of quanta at a low frequency decreases for a large length parameter characterizing the Hayward black hole. Moreover, in the limit of low frequency, the Hawking temperature can be read off from the occupation number of excited states when the shell approaches its own horizon.

gr-qc↗
arXiv2019

Test of quantum atmosphere in the dimensionally reduced Schwarzschild black hole

It has been suggested by Giddings that the origin of Hawking radiation in black holes is a quantum atmosphere of near-horizon quantum region by investigating both the total emission rate and the stress tensor of Hawking radiation. Revisiting this issue in the exactly soluble model of a dimensionally reduced Schwarzschild black hole, we shall confirm that the dominant Hawking radiation in the Unruh vacuum indeed occurs at the quantum atmosphere, not just at the horizon by exactly calculating the out-temperature responsible for outgoing Hawking particle excitations. Consequently we show that the out-temperature vanishes at the horizon and has a peak at a scale whose radial extent is set by the horizon radius, and then decreases to the Hawking temperature at infinity. We also discuss bounds of location of the peak for the out-temperature in our model.

gr-qc↗
arXiv2019

Hawking effect of AdS$_2$ black hole in the Jackiw-Teitelboim model

It might be tempting to consider that the two-dimensional anti-de Sitter black hole in the Jackiw-Teitelboim model is thermally hot by invoking the non-vanishing surface gravity. So, one might expect that the local temperature would also be blue-shifted near the horizon, while it would vanish at infinity because of the Tolman factor of the local temperature. In this paper, we will show that the local temperature vanishes everywhere, which respects the equivalence principle perfectly in contrast to the case of the asymptotically flat black holes recovering the equivalence principle just at the horizon. In other words, the origin of radiation for a fixed observer comes from the Unruh effect rather than the Hawking effect. If the inward and outward fluxes are defined non-trivially at the horizon, then the local temperature of the black hole takes the usual Tolman form; however, the divergent Tolman temperature at the horizon is incompatible with the finite local energy density there.

gr-qc↗