97 research outputs found
Thermodynamics, stability and Hawking-Page transition of Kerr black holes from R\'enyi statistics
Thermodynamics of rotating black holes described by the R\'enyi 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 R\'enyi 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 R\'enyi-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.Comment: 29 pages, 20 figure
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.Comment: Invited review for Prog. Theor. Phys. Suppl., 33 pages, 13 figures.
v2: References added v3: published versio
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
-rotating black ring. The obtained solution has more parameters than the
Emparan and Reall's -rotating black ring. We found the conditions of
parameters to reduce the solution to the -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.Comment: 5 pages, 4 figures ; accepted version, several details are remove
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 , with an entropy .Comment: 5 pages, no figures, to be published in Phys. Lett.
Thermodynamic black di-rings
Previously the five dimensional -rotating black rings have been
superposed in a concentric way by some solitonic methods, and regular systems
of two -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.Comment: 26 pages,10 figures; references added, typos corredte
Naked singularities and quantum gravity
There are known models of spherical gravitational collapse in which the
collapse ends in a naked shell-focusing singularity for some initial data. If a
massless scalar field is quantized on the classical background provided by such
a star, it is found that the outgoing quantum flux of the scalar field diverges
in the approach to the Cauchy horizon. We argue that the semiclassical
approximation (i.e. quantum field theory on a classical curved background) used
in these analyses ceases to be valid about one Planck time before the epoch of
naked singularity formation, because by then the curvature in the central
region of the star reaches Planck scale. It is shown that during the epoch in
which the semiclassical approximation is valid, the total emitted energy is
about one Planck unit, and is not divergent. We also argue that back reaction
in this model does not become important so long as gravity can be treated
classically. It follows that the further evolution of the star will be
determined by quantum gravitational effects, and without invoking quantum
gravity it is not possible to say whether the star radiates away on a short
time scale or settles down into a black hole state.Comment: 16 pages, paper rewritten into sections, conclusions unchanged, 4
references added, to appear in Phys. Rev. D (Rapid Communication
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.Comment: 6 pages, 3 figures;typos corrected, presentations improved,
references added;accepted versio
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