Entropy corrections for Schwarzschild black holes

Recently it is shown that the Bekenstein–Hawking entropy for black holes receives logarithmic corrections due to thermodynamic fluctuations. Schwarzschild black hole which possesses a negative specific heat is thermodynamically unstable, so the entropy corrections cannot be obtained directly. In this Letter, Schwarzschild black hole will be put in the center of a spherical cavity of finite radius to achieve equilibrium with surroundings, so that a thermodynamically stable solution is obtained based on a uniformly spaced area spectrum approach. Our conclusion show that there are two correction terms for Schwarzschild black holes. The sign of the second correction term depends on the size of the cavity.     

Entropy of higher-dimensional charged Gauss–Bonnet black hole in de Sitter space

The fundamental equation of the thermodynamic system gives the relation between the internal energy, entropy and volume of two adjacent equilibrium states. Taking a higher-dimensional charged Gauss–Bonnet black hole in de Sitter space as a thermodynamic system, the state parameters have to meet the fundamental equation of thermodynamics. We introduce the effective thermodynamic quantities to describe the black hole in de Sitter space. Considering that in the lukewarm case the temperature of the black hole horizon is equal to that of the cosmological horizon, we conjecture that the effective temperature has the same value. In this way, we can obtain the entropy formula of spacetime by solving the differential equation. We find that the total entropy contains an extra term besides the sum of the entropies of the two horizons. The corrected term of the entropy is a function of the ratio of the black hole horizon radius to the cosmological horizon radius, and is independent of the charge of the spacetime.     

Area Entropy and Quantized Mass of Black Holes from Information Theory

In this paper, we present a derivation of the black hole area entropy with the relationship between entropy and information. The curved space of a black hole allows objects to be imaged in the same way as camera lenses. The maximal information that a black hole can gain is limited by both the Compton wavelength of the object and the diameter of the black hole. When an object falls into a black hole, its information disappears due to the no-hair theorem, and the entropy of the black hole increases correspondingly. The area entropy of a black hole can thus be obtained, which indicates that the Bekenstein–Hawking entropy is information entropy rather than thermodynamic entropy. The quantum corrections of black hole entropy are also obtained according to the limit of Compton wavelength of the captured particles, which makes the mass of a black hole naturally quantized. Our work provides an information-theoretic perspective for understanding the nature of black hole entropy.     

Quantum Corrections for Regular Black Holes with Charge and Coupling Constant

In this paper, we use semi-classical tunneling approach to calculate the quantum corrections to the Hawking temperature as well as entropy of the Kehagias-Sftesos asymptotically flat black hole solution and charged regular black hole with Fermi-Dirac distribution. For this purpose, we apply the first law of black hole thermodynamics to investigate the semi-classical entropy of both black holes having mass as well as charge or coupling constant. For both black holes, the entropy corrections contain the logarithmic term as a leading order correction term. For Kehagias-Sftesos asymptotically flat black hole, the semi-classical Hawking temperature and black hole entropy will behave asymptotically by considering the vanishing coupling constant b = 0. We have obtained the same analysis for the corrected thermodynamical quantities for this BH. For charged regular black hole with Fermi-Dirac distribution, if we neglect the charged effects in our analysis, i.e., q = 0, then these corrections approximately leads to the Schwarzschild black hole which is already given in the literature.     

Thermodynamic effects of Bardeen black hole surrounded by perfect fluid dark matter under general uncertainty principle

The thermodynamics of Bardeen black hole surrounded by perfect fluid dark matter is investigated. We calculate the analytical expresses of corresponding thermodynamic variables, e.g., the Hawking temperature, entropy of the black hole. In addition, we derive the heat capacity to analyze the thermal stability of the black hole. We also compute the rate of emission in terms of photons through tunneling. By numerical method, an obvious phase transition behavior is found. Furthermore, according to the general uncertainty principle, we study the quantum corrections to these thermodynamic quantities and obtain the quantum-corrected entropy containing the logarithmic term. Lastly, we investigate the effects of the magnetic charge g, the dark matter parameter k and the generalized uncertainty principle parameter α on the thermodynamics of Bardeen black hole surrounded by perfect fluid dark matter under general uncertainty principle.     

Black Hole Entropy with Modified Dispersion Relations

There is much interest in resolving the quantum corrections to Bekenstein-Hawking entropy with a large length scale limit. The leading correction term is given by the logarithm of black hole area with a model-dependent coefficient. Recently the research for quantum gravity implies the emergence of a modification of theenergy-momentum dispersion relation (MDR), which plays an importantrole in the modified black hole thermodynamics. In this paper, we investigate the quantum corrections to Bekenstein-Hawking entropy in four-dimensional Schwarzschild black hole and Reissner-Nordström black hole respectively based on MDR.     

THERMODYNAMICS OF GLOBAL MONOPOLE ANTI-DE-SITTER BLACK HOLE IN GRAND CANONICAL ENSEMBLE

In this paper, we investigate the thermodynamics of the global monopole anti-de-Sitter black hole in the grand canonical ensemble following the York's formalism. The black hole is enclosed in a cavity with a finite radius where the temperature and potential are fixed. We have studied some thermodynamical properties, i.e. the reduced action, thermal energy and entropy. By investigating the stability of the solutions, we find stable solutions and instantons.     

Generalized Uncertainty Principle and Correction Value to the Kerr Black Hole Entropy

Recently, there has been much attention devoted to resolving the quantum corrections to the Bekenstein-Hawking black hole entropy. In particular, many researchers have expressed a vested interest in the coefficient of the logarithmic term of the black hole entropy correction term. In this paper, we calculate the correction value of the black hole entropy by utilizing the generalized uncertainty principle and obtain the correction term caused by the generalized uncertainty principle. Because in our calculation we think that the Bekenstein-Hawking area theorem is still valid after considering the generalized uncertainty principle, we derive that the coefficient of the logarithmic term of the black hole entropy correction term is positive. This result is different from the known result at present. Our method is valid not only for single horizon spacetime but also for spin axial symmetric spacetimes with double horizons. In the whole process, the physics idea is clear and calculation is simple. It offers a new way for studying the entropy correction of the complicated spacetime.     

Quantum Thermal Effect of Nonstationary Kerr-Newman Black Hole

The Hawking radiation and the entropy of non-stationary Kerr-Newman black hole whose metric changes slowly are calculated via the method of Damour etc. and the thin film brick-wall model. First, we obtain the Hawking radiation temperature and the thermal spectrum formula. Second, we get the entropy density at every point of the horizon surface as well as the total entropy of the black hole, which is just the Bekenstein-Hawking entropy and relies on the notion of the local equilibrium crucially that can be met if the evaporation and the accretion of the black hole is negligible. The results show that the temperature of the event horizon depends on the time and the angle, and the entropy of the non-stationary black hole is also proportional to the horizon area with appropriate cutoff relationship as in the case of stationary black holes.     

Generalized Uncertainty Principle and Black Hole Entropy of Higher-Dimensional de Sitter Spacetime

Recently, there has been much attention devoted to resolving the quantum corrections to the Bekenstein-- Hawking black hole entropy. In particular, many researchers have expressed a vested interest in the coetticient of the logarithmic term of the black hole entropy correction term. In this paper, we calculate the correction value of the black hole entropy by utilizing the generalized uncertainty prlnciple and obtain the correction term caused by the generalized uncertainty principle. Because in our calculation we think that the Bekenstein-Hawking area theorem is still valid after considering the generalized uncertainty principle, we derive that the coefficient of the logarithmic term of the black hole entropy correction term is positive. This result is different from the known result at present. Our method is valid not only for four-dimensional spacetimes but also for higher-dimensional spacetimes. In the whole process, the physics idea is clear and calculation is simple. It offers a new way for studying the entropy correction of the complicated spacetime.     

Generalized uncertainty principle and tunnelin gradiation of the SAdS5 black hole

After considering the generalized uncertainty principle, we discuss the quantum tunneling radiation of a five-dimensional Schwarzschild anti de Sitter black hole. The radiation spectrum and the correction value of the Bekenstein-Hawking entropy are derived. In a five-dimensional black hole the one order correction term in the Bekenstein-Hawking entropy correction term is proportional to the third power of the area, and the logarithmic correction term is a two-order small quantity. The correction term is related to the dimension constant introduced in the generalized uncertainty principle. Because the black hole entropy is not divergent, the lowest value of the five-dimensional Schwarzschild anti de Sitter black hole horizon radius is obtained. After considering the generalized uncertainty principle, the radiation spectrum is still consistent with normalization theory.     

Thermodynamics of the black holes under the extended generalized uncertainty principle with linear terms

In this paper, we employ the extended generalized uncertainty principle with linear terms (LEGUP) to investigate the thermodynamics properties of the Schwarzschild and Reissner–Nordström (RN) black holes. Firstly, by constructing the theoretical framework of LEGUP, the minimal temperature of the Schwarzschild black hole and the modified mass–temperature function for the black hole are calculated. Furthermore, the heat capacity function for the Schwarzschild black hole is obtained. After that, we compare LEGUP black hole thermodynamics with EGUP black hole and with the usual forms. Besides, the modification of black hole entropy is discussed, which involves a heuristic analysis of particles absorbed by the black hole. Finally, we derive the LEGUP-corrected temperature, heat capacity and entropy functions of the RN black hole.     

Generalized Uncertainty Principle and Black Hole Entropy of Higher-Dimensional de Sitter Spacetime

Recently, there has been much attention devoted to resolving the quantum corrections to the BekensteinHawking black hole entropy. In particular, many researchers have expressed a vested interest in the coefficient of the logarithmic term of the black hole entropy correction term. In this paper, we calculate the correction value of the black hole entropy by utilizing the generalized uncertainty principle and obtain the correction term caused by the generalized uncertainty principle. Because in our calculation we think that the Bekenstein-Hawking area theorem is still valid after considering the generalized uncertainty principle, we derive that the coefficient of the logarithmic term of the black hole entropy correction term is positive. This result is different from the known result at present. Our method is valid not only for four-dimensional spacetimes but also for higher-dimensional spacetimes. In the whole process, the physics idea is clear and calculation is simple. It offers a new way for studying the entropy correction of the complicated spacetime.     

A correction of (2+1) Dimensional BTZ Black Hole Entropy as a New Series with Dependence on Plank Constant

We investigate the corrected entropy and Hawking temperature of the BTZ black hole which obtained from (2 + 1) dimensional black hole. Besides, we generalize our analysis of black holes to the case of Friedmann-Robertson-Walker (FRW) universe. The corrections to the Hawking temperature and entropy of apparent horizon for FRW universe are also obtained. Comparing the results with the high energy black hole demonstrates how the semi-classic approximation affects the thermodynamics of the BTZ black hole, corrected terms, classical action and the entropy.     

缓变动态Kerr-Newman黑洞的量子热力学性质

引入局域热平衡概念，用Damour-Ruffini方法和薄膜模型研究了缓变动态Kerr-Newman黑洞的Hawking辐射和熵.得到了黑洞的Hawking温度和辐射谱公式，Hawking温度随时间和视界面上的位置而变化，辐射谱为准黑体谱；计算了黑洞熵，当取与静态球对称黑洞情况相同的截断关系时便得到了黑洞的Bekenstein-Hawking熵.结果表明，缓变动态黑洞的温度是局域量，缓变动态黑洞的熵与稳态黑洞情况一样正比于黑洞视界面面积. 关键词： 缓变动态黑洞 Hawking辐射 黑洞熵     

Generalized Uncertainty Principle and Thermodynamic Quantities of SAdS5 Black Hole

Recently, there has been much attention devoted to resolving the quantum corrections to the Bekenstein-Hawking black hole entropy. The different correction leading terms are obtained by the different methods. In this paper, we calculate the correction to SAdS₅ black hole thermodynamic quantity due to the generalized uncertainty principle. Furthermore we derive that the black hole entropy obeys Bekenstein-Hawking area theorem. The entropy has infinite correction terms. And every term is finite and calculable. The corrected Cardy-Verlinde formula is derived. In our calculation, Bekenstein-Hawking area theorem still holds after considering the generalized uncertainty principle. We have not introduced any hypothesis. The calculation is simple. Physics meaning is clear. We note that our results are quite general. It is not only valid for four-dimensional spacetime but also for higher-dimensional SAdS spacetime.     

(2+1)-Dimensional AdS Black Hole in Grand Canonical Ensemble

We investigate thermodynamics of the (2+1)-dimensional AdS black hole in grand canonical ensemble. In the York's formalism, the black hole is enclosed in a “box” with a finite radius and the boundary temperature, radius and potential are fixed in the grand canonical ensemble. We investigate the thermodynamical properties such as action, entropy, temperature, etc. We only find the stable solution for (2+1)-dimensional AdS black hole and do not find the instanton with the negative heat capacity.     

Entropy of Higher-Dimensional Charged de Sitter Black Holes and Phase Transition

From a new perspective, we discuss the thermodynamic entropy of (n+2)-dimensional Reissner-Nordströmde Sitter (RNdS) black hole and analyze the phase transition of the effective thermodynamic system. Considering the correlations between the black hole event horizon and the cosmological horizon, we conjecture that the total entropy of the RNdS black hole should contain an extra term besides the sum of the entropies of the two horizons. In the lukewarm case, the effective temperature of the RNdS black hole is the same as that of the black hole horizon and the cosmological horizon. Under this condition, we obtain the extra contribution to the total entropy. With the corrected entropy, we derive other effective thermodynamic quantities and analyze the phase transition of the RNdS black hole in analogy to the usual thermodynamic system.     

Reissner-Nordstrom几何中标量场的统计熵与能斯特定理

从Reissner-Nordstrom时空背景下的Klein-Gordon方程出发,利用改进的brick-wall方法膜模型,计算黑洞背景下标量场的自由能和熵.得到标量场的熵是由两部分组成的,根据熵是广延量的性质,得到黑洞熵是由两个子热力学系统贡献的.在此基础上给出了新的Bekenstein-Smarr公式.结果表明,用两个子热力学系统表达的熵,当黑洞的辐射温度趋于绝对零度时,黑洞的熵也趋于零,它满足能斯特定理,可视为黑洞的普朗克绝对熵. 关键词： brick-wall方法 膜模型 黑洞熵 能斯特定理     

起源于引力场的Vaidya-Bonner-de Sitter黑洞的量子熵

利用brick-wall模型研究了引力场对Vaidya-Bonner-de Sitter黑洞熵的量子修正.当黑洞事 件视界不随超前时间变化时，结果与Reissner-Nordstrm-de Sitter黑洞的量子熵完全相 同.