Area and Entropy Spectrum of Gauss-Bonnet Gravity in de Sitter Space-Times for Black Hole Event Horizon

In this paper, we use the modified Hod's treatment and the Kunstatter's method to study the horizon area spectrum and entropy spectrum in Gauss-Bonnet de-Sitter space-time, which is regarded as the natural generalization of Einstein gravity by including higher derivative correction terms to the original Einstein-Hilbert action. The horizon areas have some properties that are very different from the vacuum solutions obtained from the frame of Einstein gravity. With the new physical interpretation of quasinormal modes, the area/entropy spectrum for the event horizon for nearextremal Gauss-Bonnet de Sitter black holes are obtained. Meanwhile, we also extend the discussion of area/entropy quantization to the non-extremal black holes solutions.     

Entropy Quantization of Schwarzschild Black Hole

The surface gravity of Schwarzschild black hole can be quantized from the test particle moving around different energy states analog to the Bohr's atomic model. We have quantized the Hawking temperature and entropy of Schwarzschild black hole from quantization of surface gravity. We also have shown that the change of entropy reduces to zero when the boundary shrinks to very small size.     

Bekenstein-Hawking Cosmological Entropy and Correction Term Corresponding Cosmological Horizon of Rotating and Charged Black String

Utilizing the quantum statistical method and applying the new state density equation motivated by generalized uncertainty principle in quantum gravitaty, we avoid the difficulty in solving wave equation and directly calculate the partition function of bosonic and fermionic field on the background of rotating and charged black string. Then near the cosmological horizon, entropies of bosonic and fermionic field are calculated on the background of black string. When constant A introduced in generalized uncertainty principle takes a proper value, we derive Bekenstein- Hawking entropy and the correction value corresponding cosmologicaJ horizon on the background of rotating and charged black string. Because we use the new state density equation, in our calculation there are not divergent term and small mass approximation in the original brick-wall method. From the view of quantum statistic mechanics, the correction value to Bekenstein-Hawking entropy of the black string is derived. It makes people deeply understand the correction value to the entropy of the black string cosmological horizon in non-spherical coordinate spacetime.     

Bekenstein-Hawking Cosmological Entropy and Correction Term Corresponding Cosmological Horizon of Rotating and Charged Black String

Utilizing the quantum statistical method and applying the new state density equation motivated by generalized uncertainty principle in quantum gravitaty, we avoid the difficulty in solving wave equation and directly calculate the partition function ofbosonic and fermionic field on the background of rotating and charged black string. Then near the cosmological horizon, entropies of bosonic and fermionic field are calculated on the background of black string. When constant λ introduced ingeneralized uncertainty principle takes a proper value, we derive Bekenstein-Hawking entropy and the correction value corresponding cosmological horizon on the background of rotating and charged black string. Because we use the new state density equation, in our calculation there are not divergent term and small massapproximation in the original brick-wall method. From the view of quantum statistic mechanics, the correction value to Bekenstein-Hawking entropy of the black string is derived. It makes people deeply understand the correction value to the entropyof the black string cosmological horizon in non-spherical coordinate spacetime.     

Area Spectrum of D-Dimensional Large Schwarzschild-AdS Black Hole from Asymptotic Quasinormal Modes

We investigate the area and entropy spectra of D-dimensional large Schwarzschild black holes. By utilizing the new physical interpretation of quasinormal mode frequency we find that a large Schwarzschild-AdS black hole has an equally spaced area spectrum and an equidistant entropy spectrum; both are dependent on the spacetime dimension.     

On Quantization Errors in Approximate and Sample Entropy

Approximate and sample entropies are acclaimed tools for quantifying the regularity and unpredictability of time series. This paper analyses the causes of their inconsistencies. It is shown that the major problem is a coarse quantization of matching probabilities, causing a large error between their estimated and true values. Error distribution is symmetric, so in sample entropy, where matching probabilities are directly summed, errors cancel each other. In approximate entropy, errors are accumulating, as sums involve logarithms of matching probabilities. Increasing the time series length increases the number of quantization levels, and errors in entropy disappear both in approximate and in sample entropies. The distribution of time series also affects the errors. If it is asymmetric, the matching probabilities are asymmetric as well, so the matching probability errors cease to be mutually canceled and cause a persistent entropy error. Despite the accepted opinion, the influence of self-matching is marginal as it just shifts the error distribution along the error axis by the matching probability quant. Artificial lengthening the time series by interpolation, on the other hand, induces large error as interpolated samples are statistically dependent and destroy the level of unpredictability that is inherent to the original signal.     

Remarks on Black Hole Instabilities and Closed String Tachyons

Physical arguments stemming from the theory of black-hole thermodynamics are used to put constraints on the dynamics of closed-string tachyon condensation in Scherk–Schwarz compactifications. A geometrical interpretation of the tachyon condensation involves an effective capping of a noncontractible cycle, thus removing the very topology that supports the tachyons. A semiclassical regime is identified in which the matching between the tachyon condensation and the black-hole instability flow is possible. We formulate a generalized correspondence principle and illustrate it in several different circumstances: an Euclidean interpretation of the transition from strings to black holes across the Hagedorn temperature and instabilities in the brane-antibrane system.     

Entropy of a Uniformly Accelerating Black Hole

Kinnersley has discussed the space–time of an arbitrarily accelerating point mass. We select a simple case in which the black hole is uniformly accelerated and the mass does not vary with time. We adopt thin film brick-wall model to calculate the entropy of black hole. We find that both the temperature and the entropy density of black hole can be calculated at every point on the horizon. This result indicates that the conclusion that black hole entropy is proportional to its area can be applied to horizon not only globally, but also locally.     

Entropy Corrections for a Charged Black Hole of String Theory

We study the entropy of the Gibbons-Maeda-Garfinkle-Horowitz-Strominger (GMGHS) charged black hole, originated from the effective action thatemerges in the low-energy of string theory, beyond semiclassical approximations. Applying the properties of exact differentials for three variables to the first law thermodynamics we derive the quantum correctionsto the entropy of the black hole. The leading (logarithmic) and non leading corrections to the area law are obtained.     

Entropy Correction for Kerr Black Hole

In this paper, we discuss leading-order corrections to the entropy of Kerr black hole due to thermal fluctuations in the finite cavity. Then temperature is constant, the solution of the black hole is obtained within a cavity, that is, the solution of the spacetime after considering the radiation of the black hole. Therefore, we derive that the location of the black hole horizon and specific heat are the functions of temperature and the radius of the cavity.Corrections to entropy also are related to the radius of the cavity. Through calculation, we obtain conditions of taking the value of the cavity‘s radius. We provide a new way for studying the corrections of complicated spacetimes.     

Entropy Correction for Kerr Black Hole

In this paper, we discuss leading-order corrections to the entropy of Kerr black hole due to thermal fluctuations in the finite cavity. Then temperature is constant, the solution of the black hole is obtained within a cavity, that is, the solution of the spacetime after considering the radiation of the black hole. Therefore, we derive that the location of the black hole horizon and specific heat are the functions of temperature and the radius of the cavity. Corrections to entropy also are related to the radius of the cavity. Through calculation, we obtain conditions of taking the value of the cavity＇s radius. We provide a new way for studying the corrections of complicated spacetimes.     

Quasilocal Energy for Static Charged Black Holes in String Theory

The Brown-York quasilocal energies of some static charged dilaton black holes are calculated, and then the validity of Martinez‘s conjecture is explored in string theory. It is shown that the energy is positive and monotonically decreases to the ADM mass at spatial infinity, and the conjecture that the Brown-York quasilocal energy at the outer horizon of black hole reduces to twice of its irreducible mass is still applicable for the static charged black holes in string theory. The result is different from Bose-Naing‘s one.``     

Comments on the Statistical Origin of Black Hole Entropy

This paper shows that the black hole entropy can be interpreted as emerging as a result of missing information about the exact state of the matter from which the black hole was formed.     

Spin Entropy for Kerr Black Holes

It is known that the entropy for a singular spacetime metric can be calculated in the framework of classical field theories by applying Noether's theorem to stationary solutions of Einstein's field equations, integrating a suitable form on a trapping surface for the singularity. When the Kerr solution is considered, two different horizons appear. The physical entropy for the system is well known to be related to the outer horizon. We investigate here which is the meaning of the entropy calculated (via first principle of black hole thermodynamics) on the inner horizon. We show that this entropy, which was earlier interpreted as a sort of "spin entropy" of the black hole, admits in fact an interpretation as a quantity associated to a conserved charge which is related to the rotational degrees of freedom of the system.     

Canonical Entropy of Reissner-Nordstrom Black Hole

Recently, Hawking radiation of the black hole has been studied using the tunnel effect method. It is found the radiation spectrum of the black hole is not a strictly pure thermal spectrum. How the departure from pure thermal spectrum affects the entropy? This is a very interesting problem. In this paper, we calculate the partition function by energy spectrum obtained by tunnel effect. Using the relation between the partition function and entropy, we derive the expression of entropy the general charged black hole. In our calculation, we not only consider the correction to the black hole entropy due to fluctuation of energy but also consider the effect of the change of the black hole charges on entropy. We discuss Reissner-Nordstrom black hole and obtain that Reissner-Nordstrom black hole cannot approach the extreme black hole by changing its charges.     

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 ＆ 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 the energy-momentum dispersion relation （MDR）, which plays an important role in the modified black hole thermodynamics. In this paper, we investigate the quantum corrections to Bekenstein-Hawking entropy in four-dimensional Sehwarzschild black hole and Reissner-Nordstrom black hole respectively based on MDR.     

Entropy of Dilatonic Black Hole

By using the method of quantum statistics, we directly derive the partition function of bosonic and fermionic field in dilatonic black hole and obtain the integral expression of the black hole's entropy, which avoids the difficulty in solving the wave equationof various particles. Then via the improved brick-wall method, membrane model, we obtain that we can choose proper parameter in order to let the thickness of film tend to zero and have it approach the surface of its horizon. Consequently the entropy of the black hole is proportional to the area of its horizon. In our result, the stripped term and the divergent logarithmic term in the original brick-wall method no longer exist. In the whole process, physics idea is clear; calculation is simple. We offer a new simple and direct way of calculating the entropy of different complicated black holes.     

Statistical Entropy of Black Cylinder

By using the method of quantum statistics, we directly derive the partition function of bosonic and fermionic fields in black cylinder. Then via the improved brick-wall method, membrane model, we obtain that if we choose the proper parameter, the entropy of black cylinder is proportional to the area of the horizon. In our result, the stripped term and the divergent logarithmic term in the original brick-wall method no longer exist. In the whole process, we do not take any approximation. We offer a new simple and direct way of calculating the entropy of different complicated black holes.     

Black Hole Radiation and Volume Statistical Entropy

The simplest possible equation for Hawking radiation and other black hole radiated power is derived in terms of black hole density, ρ . Black hole density also leads to the simplest possible model of a gas of elementary constituents confined inside a gravitational bottle of Schwarzchild radius at tremendous pressure, which yields identically the same functional dependence as the traditional black hole entropy S _bh∝ (kAc ³)/ℏ G. Variations of S _bh can be obtained which depend on the occupancy of phase space cells. A relation is derived between the constituent momenta and the black hole radius R _H, p = which is similar tothe Compton wavelength relation.     

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.