4,261 research outputs found

### Novel equal area law and analytical charge-electric potential criticality for charged Anti-de Sitter black holes

We study the equal area law and charge-electric potential criticality for the
charged Anti-de Sitter black holes. Considering that the black hole charge is a
double-valued function of the electric potential, we investigate the equal area
law in detail. We find that the equal area law has two different expressions
when the thermodynamic quantities are near the critical point and far from the
critical point. For these two different cases, we obtain the analytical
coexistence curve for the low and high electric potential black hole phases by
using these two expressions of the equal area law. Based on the result, we
analytically study the phase diagram and the critical phenomena in the
charge-electric potential plane.Comment: 10 pages, 3 figures, structures are re-organize

### Extended thermodynamics and microstructures of four-dimensional charged Gauss-Bonnet black hole in AdS space

The discovery of new four-dimensional black hole solutions presents a new
approach to understand the Gauss-Bonnet gravity in low dimensions. In this
paper, we test the Gauss-Bonnet gravity by studying the phase transition and
microstructures for the four-dimensional charged AdS black hole. In the
extended phase space, where the cosmological constant and the Gauss-Bonnet
coupling parameter are treated as thermodynamic variables, we find that the
thermodynamic first law and the corresponding Smarr formula are satisfied. Both
in the canonical ensemble and grand canonical ensemble, we observe the
small-large black hole phase transition, which is similar to the case of the
van der Walls fluid. This phase transition can also appear in the neutral black
hole system. Furthermore, we construct the Ruppeiner geometry, and find that
besides the attractive interaction, the repulsive interaction can also dominate
among the microstructures for the small black hole with high temperature in a
charged or neutral black hole system. This is quite different from the
five-dimensional neutral black hole, for which only dominant attractive
interaction can be found. The critical behaviors of the normalized scalar
curvature are also examined. These results will shed new light into the
characteristic property of four-dimensional Gauss-Bonnet gravity.Comment: 17 pages, 9 figures, and 2 tables, references added. Accepted for
publication in PR

### Equatorial and quasi-equatorial gravitational lensing by Kerr black hole pierced by a cosmic string

In the present paper, we study numerically the equatorial lensing and
quasiequatorial lensing by Kerr black hole pierced by a cosmic string in the
strong deflection limit. We calculate the strong deflection limit coefficients
and the deflection angle, which are found to depend closely on the cosmic
string parameter $\beta$ and dimensionless spin $a_{*}$. The magnification and
positions of relativistic images are also computed in the strong deflection
limit and a two-dimensional lens equation is derived. The most important and
outstanding effect is that the caustics drift away from the optical axis and
shift in the clockwise direction with respect to the Kerr black hole. For fixed
$a_{*}$ of the black hole, the caustics drift farther away from the optical
axis for a large value of $\beta$. And for fixed $\beta$, they drift farther
for high $a_{*}$. We also obtain the intersections of the critical curves with
the equatorial plane, which decrease with $a_{*}$ and $\beta$. In particular,
we obtain a quantity $\bar{\mu}_{k+1}/\bar{\mu}_{k}$, which is independent of
the black hole spin and mass. Thus, through measuring it, one is allowed to
determine the value of $\beta$ from astronomical observations.Comment: 29 pages, 9 figure

### Clapeyron equations and fitting formula of the coexistence curve in the extended phase space of charged AdS black holes

In this paper, we first review the equal area laws and Clapeyron equations in
the extended phase space of the charged anti-de Sitter black holes. With
different fixed parameters, the Maxwell's equal area law holds not only in the
pressure-thermodynamic volume oscillatory line, but also in the charge-electric
potential and temperature-entropy oscillatory lines. The conventional Clapeyron
equation is generalized and two extra equations are found. Moreover, we show
that the coexistence curve of the small and large charged black holes is charge
independent in the reduced parameter space for any dimension of spacetime. The
highly accurate fitting formula for the coexistence curve is also presented.
Using this fitting formula of the coexistence curve, we find that the Clapeyron
equations are highly consistent with the calculated values. The fitting formula
is also very useful for further study on the thermodynamic property of the
system varying along the coexistence curve.Comment: 13 pages, 7 figures, 2 tables. The coexistence curves are refitted,
and the figures and tables are changed accordingly. Accepted for publication
in PR

### Implementing black hole as efficient power plant

Treating the black hole molecules as working substance and considering its
phase structure, we study the black hole heat engine by a charged anti-de
Sitter black hole. In the reduced temperature-entropy chart, it is found that
the work, heat, and efficiency of the engine are free of the black hole charge.
Applying the Rankine cycle with or without a back pressure mechanism to the
black hole heat engine, the compact formula for the efficiency is obtained. And
the heat, work and efficiency are worked out. The result shows that the black
hole engine working along the Rankine cycle with a back pressure mechanism has
a higher efficiency. This provides a novel and efficient mechanism to produce
the useful mechanical work, and such black hole heat engine may act as a
possible energy source for the high energy astrophysical phenomena near the
black hole.Comment: 17 pages, 6 figures, and 2 table

### Observing the shadow of Einstein-Maxwell-Dilaton-Axion black hole

In this paper, the shadows cast by Einstein-Maxwell-Dilaton-Axion black hole
and naked singularity are studied. The shadow of a rotating black hole is found
to be a dark zone covered by a deformed circle. For a fixed value of the spin
$a$, the size of the shadow decreases with the dilaton parameter $b$. The
distortion of the shadow monotonically increases with $b$ and takes its maximal
when the black hole approaches to the extremal case. Due to the optical
properties, the area of the black hole shadow is supposed to equal to the
high-energy absorption cross section. Based on this assumption, the energy
emission rate is investigated. For a naked singularity, the shadow has a dark
arc and a dark spot or straight, and the corresponding observables are
obtained. These results show that there is a significant effect of the spin $a$
and dilaton parameter $b$ on these shadows. Moreover, we examine the
observables of the shadow cast by the supermassive black hole at the center of
the Milky Way, which is very useful for us to probe the nature of the black
hole through the astronomical observations in the near future.Comment: 16 pages, 7 figures, and 2 tables. arXiv admin note: text overlap
with arXiv:1112.6349 by other author

### Photon orbits and thermodynamic phase transition of $d$-dimensional charged AdS black holes

We study the relationship between the null geodesics and thermodynamic phase
transition for the charged AdS black hole. In the reduced parameter space, we
find that there exist non-monotonic behaviors of the photon sphere radius and
the minimum impact parameter for the pressure below its critical value. The
study also shows that the changes of the photon sphere radius and the minimum
impact parameter can serve as order parameters for the small-large black hole
phase transition. In particular, these changes have an universal exponent of
$\frac{1}{2}$ near the critical point for any dimension $d$ of spacetime. These
results imply that there may exist universal critical behavior of gravity near
the thermodynamic critical point of the black hole system.Comment: 11 pages, 6 figure

### Area Spectrum of the Large AdS Black Hole from Quasinormal Modes

Using the new physical interpretation of quasinormal modes proposed by
Maggiore, we calculate the area and entropy spectra for the 3-dimensioal and
5-dimensional large AdS black holes. The spectra are obtained by imposing the
Bohr-Sommerfeld quantization condition to the adiabatic invariant quantity.
With this semiclassical method, we find that the spacings of the area and
entropy spectra are equidistant and independent of the AdS radius of the black
hole for both the cases. However, the spacings of the spectra are not the same
for different dimension of space-time. The equidistant area spectra will be
broken when the black hole has other parameters (i.e., charge and angular
momentum) or in a non-Einstein's gravity theory.Comment: 10 pages, no figure

### Establishing a universal relation between gravitational waves and black hole lensing

Black hole lensing and gravitational waves are, respectively, closely
dependent of the property of the lens and radiation source. In this letter, a
universal relation between them is established for a rotating black hole acting
simultaneously as a lens and a gravitational wave source, in an asymptotically
flat spacetime. The relation only relies on the lens geometry and observable,
while is independent of the specific nature of the black hole. Therefore, the
possible gravitational wave sources could be located with modern astronomical
instrument from the side of the lensing without knowing the specific nature of
the black hole lens. Moreover, the low bound of the frequency of the
gravitational waves can also be well determined.Comment: 6 pages, 3 figure

### Insight into the Microscopic Structure of an AdS Black Hole from Thermodynamical Phase Transition

Comparing with an ordinary thermodynamic system, we investigate the possible
microscopic structure of a charged anti-de Sitter black hole completely from
the thermodynamic viewpoint. The number density of the black hole molecules is
introduced to measure the microscopic degrees of freedom of the black hole. We
found that the number density suffers a sudden change accompanied by a latent
heat when the black hole system crosses the small-large black hole coexistence
curve, while when the system passes the critical point, it encounters a
second-order phase transition with a vanishing latent heat due to the
continuous change of the number density. Moreover, the thermodynamic scalar
curvature suggests that there is a weak attractive interaction between two
black hole molecules. These phenomena might cast new insight into the
underlying microscopic structure of a charged anti-de Sitter black hole.Comment: 5 pages, 4 figures, accepted for publication in Phys. Rev. Let

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