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

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

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 dd-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

Charged AdS black hole heat engines

We study the heat engine by a $d$-dimensional charged anti-de Sitter black hole by making a comparison between the small-large black hole phase transition and the liquid-vapour phase transition of water. With the help of the first law and equal-area law, we obtain an exact formula for the efficiency of a black hole engine modeled with a Rankine cycle with or without a back pressure mechanism. When the low temperature is fixed, both the heat and work decreases with the high temperature $T_{1}$. And the efficiency increases with $T_{1}$, while decreases with the charge $q$. For a Rankine cycle with a back pressure mechanism, we find that both the maximum work and efficiency can be approached at the high temperature $T_{1}$. In the reduced parameter space, it also confirms the similar result. Moreover, we observe that the work and efficiency of the black hole heat engine rapidly increase with the number of spacetime dimensions. Thus higher-dimensional charged anti-de Sitter black hole can act as a more efficient power plant producing the mechanical work, and might be a possible source of the power gamma rays and ultrahigh-energy cosmic rays.Comment: 14 pages, 17 figures, 1 tabl