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.     

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.     

Noncommutativity, Generalized Uncertainty Principle and FRW Cosmology

We consider the effects of noncommutativity and the generalized uncertainty principle on the FRW cosmology with a scalar field. We show that, the cosmological constant problem and removability of initial curvature singularity find natural solutions in this scenarios.     

Generalized Uncertainty Principle and Deformed Dispersion Relation Induced by Nonconformal Metric Fluctuations

Considering the existence of nonconformal stochastic fluctuations in the metric tensor a generalized uncertainty principle and a deformed dispersion relation (associated to the propagation of photons) are deduced. Matching our model with the so called quantum -Poincaré group will allow us to deduce that the fluctuation-dissipation theorem could be fulfilled without needing a restoring mechanism associated with the intrinsic fluctuations of spacetime. In other words, the loss of quantum information is related to the fact that the spacetime symmetries are described by the quantum -Poincaré group, and not by the usual Poincaré symmetries. An upper bound for the free parameters of this model will also be obtained.     

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.     

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.     

(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.     

（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 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.     

Generalized Uncertainty Principle in a Simple Varying Speed of Light Model

In this paperwewill derive a generalized uncertainty principle (GUP) in a simple varying speed of light (VSL) model. First we will show that VSL is an immediate consequence of GUP. Then, within the framework of a simple VSL model, we will show that GUP can be expressed as a function of cosmological scale factor. This expression gives two main results: uncertainties in position and momentum are actually cosmological models dependent and these uncertainties depend on mass and momentum of the particle under consideration. The relationship between matter content of the Universe and the values of uncertainties in early stages of the evolution of the Universe will be discussed in a mini-superspace approach.     

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.     

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.     

Dirac Oscillator Under the New Generalized Uncertainty Principle From the Concept Doubly Special Relativity

We discuss one-dimensional Dirac oscillator, by using the concept doubly special relativity. We calculate the energy spectrum by using the concept doubly special relativity. Then, we derive another representation that the coordinate operator remains unchanged at the high energy while the momentum operator is deformed at the high energy so that it may be bounded from the above. Actually, we study the Dirac oscillator by using of the generalized uncertainty principle version and the concept doubly special relativity.     

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.     

Entanglement,Identical Particles and the Uncertainty Principle

A new uncertainty relation (UR) is obtained for a system of N identical pure entangled particles if we use symmetrized observables when deriving the inequality. This new expression can be written in a form where we identify a term which explicitly shows the quantum correlations among the particles that constitute the system. For the particular cases of two and three particles, making use of the Schwarz inequality, we obtain new lower bounds for the UR that are different from the standard one.     

The Optimal Uncertainty Relation

Employing the lattice theory on majorization, the universal quantum uncertainty relation for any number of observables and general measurement is investigated. It is found that 1) the least bounds of the universal uncertainty relations can only be properly defined in the lattice theory; 2) contrary to variance and entropy, the metric induced by the majorization lattice implies an intrinsic structure of the quantum uncertainty; and 3) the lattice theory correlates the optimization of uncertainty relation with the entanglement transformation under local quantum operation and classical communication. Interestingly, the optimality of the universal uncertainty relation found can be mimicked by the Lorenz curve, initially introduced in economics to measure the wealth concentration degree of a society.