arXiv subjects

Hyeong-Chan Kim

Publications and source records attributed to Hyeong-Chan Kim.

At least 37 records · Page 2Linked to original sources

arXiv2022

Heat conduction in general relativity

We study the problem of heat conduction in general relativity by using Carter's variational formulation. We write the creation rates of the entropy and the particle as combinations of the vorticities of temperature and chemical potential. We pay attention to the fact that there are two additional degrees of freedom in choosing the relativistic analog of Cattaneo equation for the parts binormal to the caloric and the number flows. Including the contributions from the binormal parts, we find a $\textit{new}$ heat-flow equations and discover their dynamical role in thermodynamic systems. The benefit of introducing the binormal parts is that it allows room for a physical ansatz for describing the whole evolution of the thermodynamic system. Taking advantage of this platform, we propose a proper ansatz that deals with the binormal contributions starting from the physical properties of thermal equilibrium systems. We also consider the stability of a thermodynamic system in a flat background. We find that $\textit{new}$ "Klein" modes exist in addition to the known ones. We also find that the stability requirement is less stringent than those in the literature.

gr-qc↗

arXiv2022

Local temperature in general relativity

We examine the Tolman temperature by using Carter's variational formalism of thermodynamics. We restrict our interests to fluids in thermal equilibrium that the heat does not propagate. We show that this condition presents a general formula for the local temperature gradient. We suggest a resolution of the recently addressed conflict in Tolman temperature when a chemical potential does not vanish.

gr-qc↗

arXiv2022

Nonadiabaticity of Quantum harmonic oscillators

We propose a quantity, ${\mathcal{A}\!\!\!/}$, as a measure describing the nonadiabaticity of a thermodynamic process. For this purpose, we use a schematic method to find the measure of the `degree of nonadiabaticity'. The method utilizes an `invariant' thermal state constructed from the Ermakov-Lewis-Riesenfeld invariant. Specifically, we study a frequency-modulated quantum harmonic oscillator as a thermodynamic system. Naturally, we write the first law of thermodynamics with ${\mathcal{A}\!\!\!/}$ as a measurable quantity. We discuss universality for the method and some possible applications.

quant-ph↗

arXiv2021

Motions of a billiard ball after a cue stroke

We study the collision between the cue and the ball in the game of billiards. After studying the collision process in detail, we write the (rotational) velocities of the ball and the cue after the collision. We also find the squirt angle of the ball for an oblique collision which represents the deviation of the ball from the intended direction.

nlin.CD↗

arXiv2020

Rotating black holes with an anisotropic matter field

We present a family of new rotating black hole solutions to Einstein's equations that generalizes the Kerr-Newman spacetime to include an anisotropic matter. The geometry is obtained by employing the Newman-Janis algorithm. In addition to the mass, the charge and the angular momentum, an additional hair exists thanks to the negative radial pressure of the anisotropic matter. The properties of the black hole are analyzed in detail including thermodynamics. This black hole can be used as a better engine than the Kerr-Newman one in extracting energy.

gr-qc↗

arXiv2019

Entropy of a Wormhole from the Constituent

We obtain the entropy of a static spherically symmetric wormhole from the entropy of matter consisting it. Some exact wormhole solutions are analyzed in detail and their entropies are obtained. We display the asymptotic forms of the entropy for solutions having regular asymptotic regions in which matter spreads to infinity. In the analysis, we find that the combination of ADM masses $\mathcal{M}\equiv α_+ M_+ + α_- M_-$ plays an important role in thermodynamics of a wormhole, where $\displaystyle α_\pm \equiv \lim_{r\to \infty} \sqrt{-g_{tt}}$ in the upper/lower half, respectively.

gr-qc↗

arXiv2019

Spherically Symmetric Wormholes with anisotropic matter

We study the geometry of a wormhole spacetime filled with anisotropic matter in the context of general relativity. In the course of the study, new static and spherically symmetric solutions, analytic and numerical ones, are found. We specify the existence condition for a wormhole throat. We analyze properties of the solutions after categorizing them based on the spacetime regularity and the signature of energy density. The necessary conditions which allow a wormhole spacetime to be nonsingular are described.

gr-qc↗

arXiv2019

Entropy of Self-Gravitating Anisotropic Matter

We examine the entropy of self-gravitating anisotropic matter confined to a box in the context of generalrelativity. The configuration of self-gravitating matter is spherically symmetric, but has anisotropic pressure of which angular part is different from the radial part. We deduce the entropy from the relation between the thermodynamical laws and the continuity equation. The variational equation for this entropy is shown to reproduce the gravitational field equation for the anisotropic matter. This result re-assures us the correspondence between gravity and thermodynamics. We apply this method to calculate the entropies of a few objects such as compact star and wormholes.

hep-th↗

arXiv2019

Thermodynamic Equilibrium of a Wormhole Station

We study the thermodynamic equilibrium of matter in a wormhole `station' which connects various distinct asymptotic regions of a spacetime. An example of the `station' is a traversable wormhole connecting two distant regions. The temperatures of matter in the `station' measured at various asymptotic regions are not necessarily the same. We propose a generalized `temperature' which characterizes the thermal equilibrium in the spacetime with the `station'. We additionally discuss how thermal `equilibrium' works for a multiply connected spacetime.

gr-qc↗

arXiv2019

Radial Acceleration Relation from Ultra-light Scalar Dark matter

We show that ultra-light scalar dark matter (fuzzy dark matter) in galaxies has a quantum mechanical typical acceleration scale about $10^{-10}\,\mbox{ms}^{-2}$, which leads to the baryonic Tully-Fisher relation. Baryonic matter at central parts of galaxies acts as a boundary condition for dark matter wave equation and influences stellar rotation velocities in halos. Without any modification of gravity or mechanics this model also explains the radial acceleration relation and MOND-like behavior of gravitational acceleration found in galaxies having flat rotation curves. This analysis can be extended to the Faber-Jackson relation.

astro-ph.GA↗

arXiv2018

Simple Black Holes with Anisotropic Fluid

We study a spherically symmetric spacetime made of anisotropic fluid of which radial equation of state is given by $p_1 = -ρ$. This provides analytic solutions and a good opportunity to study the static configuration of black hole plus matter. For a given equation-of-state parameter $w_2 = p_2/ρ$ for angular directions, we find exact solutions of the Einstein's equation described by two parameters. We classify the solution into six types based on the behavior of the metric function. Depending on the parameters, the solution can have event and cosmological horizons. Out of these, one type corresponds to a generalization of the Reissiner-Nordström black hole, for which the thermodynamic properties are obtained in simple forms. The solutions are stable under radial perturbations.

gr-qc↗

arXiv2018

Holographic Dark Energy and Quantum Entanglement

In this paper, we briefly review the holographic dark energy model and introduce the idea that dark energy is a kind of thermal energy related to the quantum entanglement of the vacuum across a cosmic future event horizon. The holographic dark energy model comes from a theoretical attempt to apply the holographic principle to the dark energy problem and follows the idea that the short distance cut-off or ultraviolet (UV) cut-off is related to the long distance cut-off or infrared (IR) cut-off. The IR cut-off relevant to dark energy is the size of the future event horizon. This model gives a holographic dark energy comparable to the observational data. Though this model is in good agreement with observational data, some problems (non-locality, circular logic, causality problem, $\it etc.$) exist due to the use of the future event horizon as a present IR cut-off. These problems of the holographic dark energy model are considerably resolved using action principle and equations of motion. Finally, we discuss the relation between quantum entanglement and dark energy which is connected to the more fundamental relation between entanglement and gravity.

gr-qc↗

arXiv2018

Growth of a Black Hole on a Self-Gravitating Radiation

We feed a black hole on a self-gravitating radiation and observe what happens during the process. Considering a spherical shell of radiation, we show that the contribution of self-gravity makes the thermodynamic interaction through the bottom of the shell be distinguished from thermodynamic interaction through its top. The growth of a black hole horizon appears to be a sudden jump rather than a sequential increase. We additionally show that much of the entropy will be absorbed into the black hole only at the last moment of the collapse.

gr-qc↗

arXiv2017

Heat capacity of a self-gravitating spherical shell of radiations

We study the heat capacity of a static system of self-gravitating radiations analytically in the context of general relativity. To avoid the complexity due to a conical singularity at the center, we excise the central part and replace it with a regular spherically symmetric distribution of matters of which specifications we are not interested in. We assume that the mass inside the inner boundary and the locations of the inner and the outer boundaries are given. Then, we derive a formula relating the variations of physical parameters at the outer boundary with those at the inner boundary. Because there is only one free variation at the inner boundary, the variations at the outer boundary are related, which determines the heat capacity. To get an analytic form for the heat capacity, we use the thermodynamic identity $δS_{\rm rad} = βδM_{\rm rad}$ additionally, which is derived from the variational relation of the entropy formula with the restriction that the mass inside the inner boundary does not change. Even if the radius of the inner boundary of the shell goes to zero, in the presence of a central conical singularity, the heat capacity does not go to the form of the regular sphere. An interesting discovery is that another legitimate temperature can be defined at the inner boundary which is different from the asymptotic one $β^{-1}$.

gr-qc↗

arXiv2017

Black hole in closed spacetime with an anisotropic fluid

We study spherically symmetric geometries made of anisotropic perfect fluid based on general relativity. The purpose of the work is to find and classify black hole solutions in closed spacetime. In a general setting, we find that a static and closed space exists only when the radial pressure is negative but its size is smaller than the density. The Einstein equation is eventually casted into a first order autonomous equation on two-dimensional plane of scale-invariant variables, which are equivalent to the Tolman-Oppenheimer-Volkoff (TOV) equation in general relativity. Then, we display various solution curves numerically. An exact solution describing a black hole solution in a closed spacetime was known in Ref. [1], which solution bears a naked singularity and negative energy era. We find that the two deficits can be remedied when $ρ+3p_1>0$ and $ρ+p_1+2p_2< 0$, where the second violates the strong energy condition.

gr-qc↗

arXiv2017

Equation of State in the Presence of Gravity

We investigate how an equation of state for matter is affected when a gravity is present. For this purpose, we consider a box of ideal gas in the presence of Newtonian gravity. In addition to the ordinary thermodynamic quantities, a characteristic variable that represents a weight per unit area relative to the average pressure is required in order to describe a macroscopic state of the gas. Although the density and the pressure are not uniform due to the presence of gravity, the ideal gas law itself is satisfied for the thermodynamic quantities when averaged over the system. Assuming that the system follows an adiabatic process further, we obtain a {\it new} relation between the averaged pressure and density, which differs from the conventional equation of state for the ideal gas in the absence of gravity. Applying our results to a small volume in a Newtonian star, however, we find that the conventional one is reliable for most astrophysical situations when the characteristic scale is small. On the other hand, gravity effects become significant near the surface of a Newtonian star.

gr-qc↗

arXiv2017

Matter Equation of State in General Relativity

We study how a strong gravity affects the equation of state of matters. For this purpose, we employ a canonical ensemble of classical monoatomic ideal gas inside a box in a Rindler spacetime. The total energy decreases monotonically with the increase of the external gravity representing its attractiveness. It is however bounded below, which is different from that of the Newtonian gravity case. As for the entropy, it decreases with the external gravity in the Newtonian regime. However, in the presence of strong gravity or ultra-relativistic high temperature, the entropy increases with the gravity. This result can be a resolution of the negative entropy problem of the ideal gas in the Newtonian gravity. In the presence of strong gravity, the bottom of the box is very close to the event horizon of the Rindler spacetime mimicking a blackhole and the gas behaves as if it is on an effective two dimensional surface located at the bottom of the box. Investigating the equation of state in the strong gravity regime, the temperature of the system is found to be not a free parameter but to approach a fixed value proportional to the external gravity, which is reminiscent of the Unruh temperature.

gr-qc↗

arXiv2017

Classifying self-gravitating radiations

We study a static system of self-gravitating radiations confined in a sphere by using numerical and analytical calculations. Due to the scaling symmetry of radiations, most of main properties of a solution can be represented as a segment of a solution curve on a plane of two-dimensional scale invariant variables. We define an `approximate horizon' (AH) from the analogy with an apparent horizon. Any solution curve contains a unique point which corresponds to the AH. A given solution is uniquely labelled by three parameters representing the solution curve, the size of the AH, and the sphere size, which are an alternative of the data at the outer boundary. Various geometrical properties including the existence of an AH and the behaviors around the center can be identified from the parameters. We additionally present an analytic solution of the radiations on the verge of forming a blackhole. Analytic formulae for the central mass of the naked singularity are given.

gr-qc↗