（Anti-）de Sitter Black Hole Entropy and Generalized Uncertainty Principle

We generalize the method that is used to study corrections to Cardy-Verlinde formula due to generalized uncertainty principle and discuss corrections to Cardy-Verlinde formula due to generalized uncertainty principle in （anti）- de Sitter space. Because in de Sitter black hole spacetime the radiation temperature of the black hole horizon is different from the one of the cosmological horizon, this spacetime is a thermodynamical non-equilibrium spacetime.     

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.     

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 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-Vedinde 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.     

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.     

Entropy of Vaidya Black Hole on Event Horizon with Generalized Uncertainty Principle Revisited

In this note, we recalculate the entropy of the Vaidya black hole on the event horizon by considering the generalized uncertainty principle based on the brick-wall model. The result shows that we need not impose a cut-off by hand anymore and the result satisfies the Bekenstein-Hawking law as well.     

Generalized Uncertainty Principle Influences the Entropy of a Nonstationary Black Hole

The entropy of a scalar field at the horizon is investigated in the Vaidya space-time. We take into account the effect of the generalized uncertainty principle on the state density and the entropy. The divergence in the brick-wall model is removed and the entropy proportional to the horizon area is obtained.     

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.     

Statistical Entropy of Reissner-Nordstrom Black Hole Computed by Generalized Uncertainty Principle

The equation of state density is corrected by the generalized uncertainty principle. Statistical entropy of scalar field outside Reissner-Nordstrom black hole is computed by WKB approximation method. The result shows that this black hole entropy is proportional to its horizon area, which is the same as that given by brick-wall method. The difference from the brick-wall method is that the present result is convergent without any cutoff.     

Canonical Entropy of Black Hole in the Generalized Uncertainty Principle

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, based on the correction to black hole thermodynamic quantity due to the generalized uncertainty principle, we calculate the partition function by energy spectrum obtained using tunneling effect. Furthermore we derive the black hole entropy. In the expression, we not only consider the generalized uncertainty principle but also consider the departure of black hole radiation spectrum from pure thermal spectrum. According to criterion law of thermodynamic systems phase transition, we discuss the phase transition of AdS black hole and derive that the phase transition of AdS black hole is a secondary one.     

The Generalized Uncertainty Principle and Black Hole Remnants

In the current standard viewpoint small black holes are believed to emit black body radiation at the Hawking temperature, at least until they approach Planck size, after which their fate is open to conjecture. A cogent argument against the existence of remnants is that, since no evident quantum number prevents it, black holes should radiate completely away to photons and other ordinary stable particles and vacuum, like any unstable quantum system. Here we argue the contrary, that the generalized uncertainty principle may prevent their total evaporation in exactly the same way that the uncertainty principle prevents the hydrogen atom from total collapse: the collapse is prevented, not by symmetry, but by dynamics, as a minimum size and mass are approached.     

Entropy of Schwarzschild-de Sitter Black Hole with Generalized Uncertainty Principle Revisited

We study the entropy of Schwarzschild-de Sitter black holes based on generalized uncertainty principle with brick-wall method by counting degrees of freedom near the horizons and obtain the entropy proportional to the surface area at the horizons without cut-off. And reveal the possible value of the minimum length.     

Quantum Statistical Entropy of Five-Dimensional Black Hole

The generalized uncertainty relation is introduced to calculate quantum statistic entropy of a black hole. By using the new equation of state density motivated by the generalized uncertainty relation, we discuss entropies of Bose field and Fermi field on the background of the five-dimensional spacetime. In our calculation, we need not introduce cutoff. There is not the divergent logarithmic term as in the original brick-wall method. And it is obtained that the quantum statistic entropy corresponding to black hole horizon is proportional to the area of the horizon. Further it is shown that the entropy of black hole is the entropy of quantum state on the surface of horizon. The black hole's entropy is the intrinsic property of the black hole. The entropy is a quantum effect. It makes people further understand the quantum statistic entropy.     

Entropy of Reissner—Nordstrom—De Sitter Black Hole in Nonthermal Equilibrium

By making use of the method of quantum statistics,we directly derive the partition function of bosonic and fermionic fields in Reissner-Nordstrom-De Sitter black Hole and obtain the integral expression of black hole‘s entropy and the entropy to which the cosmic horizon surface corresponds.It avoids the difficulty in solving the wave equation of various particles.Then via the improved brick-wall method,i.e.the membrane model,we calculate black hole‘s entropy and cosmic entropy and find out that if we let the integral upper limit and lower limit both tend to the horizon,the entropy of black hole is proportional to the area of horizon and the entropy to which cosmic horizon surface corresponds is proportional to the area of cosmic 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,the physical idea is clear and the calculation is simple.We offer a new simple and direct way for calculating the entropy of different complicated black holes.     

Generalized Uncertainty Principle and Quantum Electrodynamics

In the present work the role that a generalized uncertainty principle could play in the quantization of the electromagnetic field is analyzed. It will be shown that we may speak of a Fock space, a result that implies that the concept of photon is properly defined. Nevertheless, in this new context the creation and annihilation operators become a function of the new term that modifies the Heisenberg algebra, and hence the Hamiltonian is not anymore diagonal in the occupation number representation. Additionally, we show the changes that the energy expectation value suffers as result of the presence of an extra term in the uncertainty principle. The existence of a deformed dispersion relation is also proved.     

The Free Energy and Entropy of Schwarzschild Black Hole Due to Scalar Field

Using the thin film brick-wall model,taking into account the effect of the generalized uncertainty principle on the equation of the density of the states, we calculate the free energy and entropy of schwarzschild black hole due to scalar field, we obtain the entropy proportional to the event horizon area without cutoff. This implies that quantum theory of gravity can remove the divergence of the state density on the event horizon and avoid the cutoff in the original brick-wall model, these results also mean that the thin film brick-wall model is universal. PACS: 0420;9760L.     

Entropy of Four-Dimensional Spherically Symmetric Black Holes with Planck Length

Considering corrections to all orders in Planck length on the quantum state density from a generalized uncertainty principle （GUP）, we calculate the statistical entropy of the Bose field and Fermi field on the background of the four-dimensional spherically symmetric black holes without any cutoff. It is obtained that the statistical entropy is directly proportional to the area of horizon.     

Generalized Uncertainty Principle and the Quantum Entropy of Rotating Black Hole

The entropy of rotating Kerr-Newman-Kasuya black hole due to massive charged fields （bosons and fermions） is calculated by using the new equation of state density motivated by the generalized uncertainty relation. The result shows the entropy does not depend on the mass and the charge but the parameter A, the area A and the spin of the fields. Moreover, an improved approximation is provided to calculate the scalar entropy.     

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.