arXiv subjects

Hideo Iguchi

Publications and source records attributed to Hideo Iguchi.

At least 19 recordsLinked to original sources

arXiv2025

Hawking-Rényi thermodynamics of rotating black holes from locally Kiselev-type behavior

The Hawking-Rényi model requires the Rényi entropy thermodynamic temperature of a black hole to be identical with the surface gravity defined-, Hawking temperature. We investigate this approach for stationary black hole space-times, and show that a locally Kiselev-type behavior around the horizon with a coupled anisotropic fluid is sufficient to provide a solution to the problem. In addition, due to the rotating motion, an extra shift has also to be present in the effective mass of the black hole, which is determined by the rotation parameter, $a$, and the Rényi parameter, $λ$. We consider space-times with and without electric charge, and show that the functional form of the solution is the same for both cases. A full thermodynamic analysis of the model falls beyond the scope of this Letter, the main achievements are the derivation and interpretation of the solution.

gr-qc↗

arXiv2025

Hawking-Rényi black hole thermodynamics, Kiselev solution, and cosmic censorship

Explicit example, where the Hawking temperature of a black hole horizon is compatible with the black hole's Rényi entropy thermodynamic description, is constructed. It is shown that for every static, spherically symmetric, vacuum black hole space-time, a corresponding black hole solution can be derived, where the Hawking temperature is identical with the Rényi temperature, i.e. the one obtained from the Rényi entropy of the black hole via the 1st law of thermodynamics. In order to have this Hawking-Rényi type thermodynamic property, the black holes must be surrounded by an anisotropic fluid in the form of a Kiselev metric, where the properties of the fluid are uniquely determined by the mass of the black hole, $M$, and the Rényi parameter, λ. In the simplest Schwarzschild scenario, the system is found to be thermodynamically unstable, and the 3rd law of thermodynamics seems to play the role of a cosmic censor via placing an upper bound on the black hole's mass, by which preventing the black hole from loosing its horizon(s).

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arXiv2025

Gravitational Entropy of Hayward Black Hole

We analyze the gravitational entropy defined by the Weyl curvature for the Hayward black hole, which is one of the regular black holes without singularity in the event horizon. Using the definition by the ratio of the Weyl curvature scalar and the Kretschmann scalar as the entropy measure, we evaluate the gravitational entropy on the outer and inner horizons. We derive an expression for the curvature tensor of the Hayward black hole that is as independent as possible of the parameter added to the black hole and give an equation for the entropy measure explicitly independent of that parameter. The gravitational entropy density used in previous studies presents questions from the standpoint of mathematical rigor while we discuss possible improvements in its definition. We compare the results for the Hayward black hole with the analysis for the Reisner-Nordstöm black hole and discuss the effect of singularity resolution on gravitational entropy.

gr-qc↗

arXiv2020

Volume dependent extension of Kerr-Newman black hole thermodynamics

We show that the Hawking--Bekenstein entropy formula is modified by a factor of $8/3$ if one also considers a work term in the 1st law of thermodynamics by a pressure stemming from the Hawking radiation. We give an intuitive definition for the corresponding thermodynamical volume by the implicit definition $ε=Mc^2/V$, which is the average energy density of the Hawking radiation. This volume scales as $V \sim M^5$, agreeing with other suggestions. As a result the corresponding Smarr relation describes an extensive entropy and a stable effective equation of state $S(E,V)\sim E^{3/4}V^{1/4}$. These results pertain for charged and rotating Kerr-Newman black holes.

gr-qc↗

arXiv2018

Black hole horizons can hide positive heat capacity

Regarding the volume as independent thermodynamic variable we point out that black hole horizons can hide positive heat capacity and specific heat. Such horizons are mechanically marginal, but thermally stable. In the absence of a canonical volume definition, we consider various suggestions scaling differently with the horizon radius. Assuming Euler-homogeneity of the entropy, besides the Hawking temperature, a pressure and a corresponding work term render the equation of state at the horizon thermally stable for any meaningful volume concept that scales larger than the horizon area. When considering also a Stefan--Boltzmann radiation like equation of state at the horizon, only one possible solution emerges: the Christodoulou--Rovelli volume, scaling as $V\sim R^5$, with an entropy $S = \frac{8}{3}S_{BH}$.

gr-qc↗

arXiv2017

Thermodynamics, stability and Hawking-Page transition of Kerr black holes from Rényi statistics

Thermodynamics of rotating black holes described by the Rényi formula as equilibrium and zeroth law compatible entropy function is investigated. We show that similarly to the standard Boltzmann approach, isolated Kerr black holes are stable with respect to axisymmetric perturbations in the Rényi model. On the other hand, when the black holes are surrounded by a bath of thermal radiation, slowly rotating black holes can also be in stable equilibrium with the heat bath at a fixed temperature, in contrast to the Boltzmann description. For the question of possible phase transitions in the system, we show that a Hawking-Page transition and a first order small black hole/large black hole transition occur, analogous to the picture of rotating black holes in AdS space. These results confirm the similarity between the Rényi-asymptotically flat and Boltzmann-AdS approaches to black hole thermodynamics in the rotating case as well. We derive the relations between the thermodynamic parameters based on this correspondence.

gr-qc↗

arXiv2015

Rényi entropy and the thermodynamic stability of black holes

Thermodynamic stability of black holes, described by the Rényi formula as equilibrium compatible entropy function, is investigated. It is shown that within this approach, asymptotically flat, Schwarzschild black holes can be in stable equilibrium with thermal radiation at a fixed temperature. This implies that the canonical ensemble exists just like in anti-de Sitter space, and nonextensive effects can stabilize the black holes in a very similar way as it is done by the gravitational potential of an anti-de Sitter space. Furthermore, it is also shown that a Hawking-Page-like black hole phase transition occurs at a critical temperature which depends on the $q$-parameter of the Rényi formula.

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arXiv2011

Systematic solution-generation of five-dimensional black holes

Solitonic solution-generating methods are powerful tools to construct nontrivial black hole solutions of the higher-dimensional Einstein equations systematically. In five dimensions particularly, the solitonic methods can be successfully applied to the construction of asymptotically Minkowski spacetimes with multiple horizons. We review the solitonic methods applicable to higher-dimensional vacuum spacetimes and present some five-dimensional examples derived from the methods.

gr-qc↗

arXiv2011

Thermodynamic black di-rings

Previously the five dimensional $S^1$-rotating black rings have been superposed in a concentric way by some solitonic methods, and regular systems of two $S^1$-rotating black rings were constructed by the authors and then Evslin and Krishnan (we called these solutions "black di-rings"). In this place we show some characteristics of the solutions of five dimensional black di-rings, especially in thermodynamic equilibrium. After the summary of the di-ring expressions and their physical quantities, first we comment on the equivalence of the two different solution sets of the black di-rings. Then the existence of thermodynamic black di-rings is shown, in which both isothermality and isorotation between the inner black ring and the outer black ring are realized. We also give detailed analysis of peculiar properties of the thermodynamic black di-ring including discussion about a certain kind of thermodynamic stability (instability) of the system.

hep-th↗

arXiv2008

Black diring and infinite nonuniqueness

We show that the $S^1$-rotating black rings can be superposed by the solution generating technique. We analyze the black diring solution for the simplest case of multiple rings. There exists an equilibrium black diring where the conical singularities are cured by the suitable choice of physical parameters. Also there are infinite numbers of black dirings with the same mass and angular momentum. These dirings can have two different continuous limits of single black rings. Therefore we can transform the fat black ring to the thin ring with the same mass and angular momentum by way of the diring solutions.

hep-th↗

arXiv2007

Boosted Black Holes on Kaluza-Klein Bubbles

We construct an exact stationary solution of black hole -- bubble sequence in the five dimensional Kaluza-Klein theory by using solitonic solution generating techniques. The solution describes two boosted black holes with topology S^3 on a Kaluza-Klein bubble and has a linear momentum component in the compactified direction. The ADM mass and the linear momentum depend on the two boosted velocity parameters of black holes. In the effective four dimensional theory, the solution has an electric charge which is proportional to the linear momentum. The solution includes the static solution found by Elvang and Horowitz and a limit of single boosted black string.

hep-th↗

arXiv2007

Rotating Black Holes on Kaluza-Klein Bubbles

Using the solitonic solution generating techniques, we generate a new exact solution which describes a pair of rotating black holes on a Kaluza-Klein bubble as a vacuum solution in the five-dimensional Kaluza-Klein theory. We also investigate the properties of this solution. Two black holes with topology S^3 are rotating along the same direction and the bubble plays a role in holding two black holes. In static case, it coincides with the solution found by Elvang and Horowitz.

hep-th↗

arXiv2006

Solitonic generation of vacuum solutions in five-dimensional General Relativity

We describe a solitonic solution-generating technique for the five-dimensional General Relativity. Reducing the five-dimensional problem to the four-dimensional one, we can systematically obtain single-rotational axially symmetric vacuum solutions. Applying the technique for a simple seed solution, we have previously obtained the series of stationary solutions which includes $S^2$-rotating black ring. We analyze the qualitative features of these solutions, e.g., conical singularities, closed timelike curves, and spacetime curvatures. We investigate the rod structures of seed and solitonic solutions. We examine the relation between the expressions of the metric in the prolate-spheroidal coordinates and in the C-metric coordinates.

hep-th↗

arXiv2006

Relationship Between Solitonic Solutions of Five-Dimensional Einstein Equations

We give the relation between the solutions generated by the inverse scattering method and the Bäcklund transformation applied to the vacuum five-dimensional Einstein equations. In particular, we show that the two-solitonic solutions generated from an arbitrary diagonal seed by the Bäcklund transformation are contained within those generated from the same seed by the inverse scattering method.

hep-th↗

arXiv2006

Solitonic generation of five-dimensional black ring solution

Using the solitonic solution-generating technique we rederived the one-rotational five-dimensional black ring solution found by Emparan and Reall. The seed solution is not the Minkowski metric, which is the seed of $S^2$-rotating black ring. The obtained solution has more parameters than the Emparan and Reall's $S^1$-rotating black ring. We found the conditions of parameters to reduce the solution to the $S^1$-rotating black ring. In addition we examined the relation between the expressions of the metric in the prolate-spheroidal coordinates and in the canonical coordinates.

hep-th↗

arXiv2006

New Axisymmetric Stationary Solutions of Five-dimensional Vacuum Einstein Equations with Asymptotic Flatness

New axisymmetric stationary solutions of the vacuum Einstein equations in five-dimensional asymptotically flat spacetimes are obtained by using solitonic solution-generating techniques. The new solutions are shown to be equivalent to the four-dimensional multi-solitonic solutions derived from particular class of four-dimensional Weyl solutions and to include different black rings from those obtained by Emparan and Reall.

hep-th↗

arXiv2005

Spherically symmetric perfect fluid in area-radial coordinates

We study the spherically symmetric collapse of a perfect fluid using area-radial coordinates. We show that analytic mass functions describe a static regular centre in these coordinates. In this case, a central singularity can not be realized without an infinite discontinuity in the central density. We construct mass functions involving fluid dynamics at the centre and investigate the relationship between those and the nature of the singularities.

gr-qc↗

arXiv2003

A Classification of Spherically Symmetric Kinematic Self-Similar Perfect-Fluid Solutions. II

We give a classification of spherically symmetric kinematic self-similar solutions. This classification is complementary to that given in a previous work by the present authors [Prog. Theor. Phys. 108, 819 (2002)]. Dust solutions of the second, zeroth and infinite kinds, perfect-fluid solutions and vacuum solutions of the first kind are treated. The kinematic self-similarity vector is either parallel or orthogonal to the fluid flow in the perfect-fluid and vacuum cases, while the `tilted' case, i.e., neither parallel nor orthogonal case, is also treated in the dust case. In the parallel case, there are no dust solutions of the second (except when the self-similarity index $α$ is 3/2), zeroth and infinite kinds, and in the orthogonal case, there are no dust solutions of the second and infinite kinds. Except in these cases, the governing equations can be integrated to give exact solutions. It is found that the dust solutions in the tilted case belong to a subclass of the Lema{\^ i}tre-Tolman-Bondi family of solutions for the marginally bound case. The flat Friedmann-Robertson-Walker (FRW) solution is the only dust solution of the second kind with $α=3/2$ in the tilted and parallel cases and of the zeroth kind in the orthogonal case. The flat, open and closed FRW solutions with $p=-μ/3$, where $p$ and $μ$ are the pressure and energy density, respectively, are the only perfect-fluid first-kind self-similar solutions in the parallel case, while a new exact solution with $p=μ$, which we call the ``singular stiff-fluid solution'', is the only such solution in the orthogonal case. The Minkowski solution is the only vacuum first-kind self-similar solution both in the parallel and orthogonal cases. Some important corrections and complements to the authors' previous work are also presented.

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