Generalized Uncertainty Principle Research Articles

Thermodynamic properties of massless Dirac–Weyl fermions under the generalized uncertainty principle* *Project supported by the National Natural Science Foundation of China (Grant No. 11565009).

The Dirac–Weyl equation characterized quasi-particles in the T3 lattice are studied under external magnetic field using the generalized uncertainty principle (GUP). The energy spectrum of the quasi-particles is found by the Nikiforov–Uvarov method. Based on the energy spectrum obtained, the thermodynamic properties are given, and the influence of the GUP on the statistical properties of systems is discussed. The results show that the energy and thermodynamic functions of massless Dirac–Weyl fermions in the T3 lattice depend on the variation of the GUP parameter.

Wigner functions in quantum mechanics with a minimum length scale arising from generalized uncertainty principle

In this paper, we generalize the concept of Wigner function in the case of quantum mechanics with a minimum length scale arising due to the application of a generalized uncertainty principle. We present the phase space formulation of such theories following GUP and show that the Weyl transform and the Wigner function satisfy most of their known properties in standard quantum mechanics. We utilize the generalized Wigner function to calculate the phase space average of the Hamiltonian of a quantum harmonic oscillator satisfying deformed Heisenberg algebra. It is also shown that averages of certain quantum mechanical operators in such theories may restrict the value of the deformation parameter specifying the degree of deformation of Heisenberg algebra. All the results presented are for pure states. The results can be generalized for mixed states.

Exotic criticality of the BTZ black hole

We investigate semi-classical Hawking radiation of the BTZ black hole under the generalized uncertainty principle modified with the Zitterbewegung’ particles and argue quantum gravity effects to the modified thermodynamics. We find that the BTZ black hole can have critical behavior, but exotic critical behavior, similar to the van der Waals fluid, and also find the critical compression factor is higher than its universal value. Locally stable/unstable regions can exist maintaining the global stability.

Noncommutative correction to the entropy of Schwarzschild black hole with GUP

In this paper we study through tunneling formalism, the effect of noncommutativity to Hawking radiation and the entropy of the noncommutative Schwarzschild black hole. In our model we have considered the noncommutativity implemented via the Lorentzian distribution. We obtain noncommutative corrections to the Hawking temperature using the Hamilton–Jacobi method and the Wentzel–Kramers–Brillouin (WKB) approximation. In addition, we found corrections of the logarithmic and other types due to noncommutativity and quantum corrections from the generalized uncertainty principle (GUP) for the entropy of the Schwarzschild black hole.

Nonextensive black hole entropy and quantum gravity effects at the last stages of evaporation

We analyze the generalized uncertainty principle (GUP) impact onto the nonextensive black hole thermodynamics by using R\'enyi entropy. We show that when introducing GUP effects, both R\'enyi entropy and temperature associated with black holes have finite values at the end of the evaporation process. We also study the sparsity of the radiation, associated with R\'enyi temperature, and compare it with the sparsity of Hawking radiation. Finally, we investigate GUP modifications to the sparsity of the radiation when GUP effects are introduced into R\'enyi temperature.

Schwarzschild Black Hole Thermodynamics and Generalized Uncertainty Principle

In this paper, a linear generalized uncertainty principle (GUP), which suggests a minimum measurable length and a maximal measurable momentum, is used in analyzing COW experiment and Einstein-Bohr’s a photon box experiment. Based in these experiments a modified Schwarzschild metric was obtained in order to calculate a quantum corrections in Schwarzschild black hole thermodynamics and tunneling probability. It was found that GUP placed restrictions on the minimum mass, size and temperature of the black hole, indicating that there was a black hole remnant after the completion of the evaporation process. The resulting values of minimum mass and size of the black hole are identical to that values predicted by quadratic GUP, which points out that the two models are equivalence in Planck scale measurements.

Observational tests of the generalized uncertainty principle: Shapiro time delay, gravitational redshift, and geodetic precession

This paper is based on the study of the paper of Scardigli and Casadio (2015) [56] where the authors computed the light deflection and perihelion precession for the Generalized Uncertainty Principle (GUP) modified Schwarzschild metric. In the present work, we computed the gravitational tests such as Shapiro time delay, gravitational redshift, and geodetic precession for the GUP modified Schwarzschild metric. Using the results of Solar system experiments and observations, we obtain upper bounds for the GUP parameter β. Finally, we compare our bounds with other bounds in the literature.

Generalized uncertainty principle and stochastic gravitational wave background spectrum

This paper concerned with the effect of generalized uncertainty principle (GUP) on the stochastic gravitational wave (SGW) background signal that produced during first order cosmological QCD phase transition in early universe. A modified formula of entropy is used to calculate the temporal evolution of temperature of the universe as a function of the Hubble parameter. The pressure that results from the recent lattice calculations, which provides parameterizations of the pressure due to u,d,s quarks and gluons, with trace anomaly is used to describe the equation of state around QCD epoch. A redshift in the peak frequency of SGW at current epoch is calculated. The results indicate an increase in the frequency peak due to GUP effect, which improves the ability to detect it. Taking into account bubble wall collisions (BWC) and turbulent magnetohydrodynamics (MHD) as a source of SGW, a fractional energy density is investigated. It is found that the GUP effect weakens the SGW signal generated during QCD phase transition in comparison to its counterpart in the absence of GUP. These results support understanding the cosmological QCD phase transition and test the effectiveness of the GUP theory.

Noncommutative Correction to the Entropy of BTZ Black Hole with GUP

We investigate the effect of noncommutativity and quantum corrections to the temperature and entropy of a BTZ black hole based on a Lorentzian distribution with the generalized uncertainty principle (GUP). To determine the Hawking radiation in the tunneling formalism, we apply the Hamilton-Jacobi method by using the Wentzel-Kramers-Brillouin (WKB) approach. In the present study, we have obtained logarithmic corrections to entropy due to the effect of noncommutativity and GUP. We also address the issue concerning stability of the noncommutative BTZ black hole by investigating its modified specific heat capacity.

Solution of the Dirac equation with exponential-type potential under the GUP

In quantum gravity theories, when the scattering energy is comparable to the Planck energy, the usual Heisenberg uncertainty principle breaks down and is replaced by generalized uncertainty principle (GUP). In this paper, the Dirac equation is studied for a single particle with spin and pseudospin symmetry in the presence of GUP, in [Formula: see text] dimensions. For arbitrary wave [Formula: see text], the Dirac equation with multiparameter exponential-type potential is solved by applying the approximation of the centrifugal term and the Nikiforov–Uvarov method. The corresponding energy spectra and eigenvalue function are obtained in the closed form and depend on the GUP parameter. In addition, several interesting cases have been discussed.

Consequences of minimal length discretization on line element, metric tensor, and geodesic equation

When minimal length uncertainty emerging from a generalized uncertainty principle (GUP) is thoughtfully implemented, it is of great interest to consider its impacts on gravitational Einstein field equations (gEFEs) and to try to assess consequential modifications in metric manifesting properties of quantum geometry due to quantum gravity. GUP takes into account the gravitational impacts on the noncommutation relations of length (distance) and momentum operators or time and energy operators and so on. On the other hand, gEFE relates classical geometry or general relativity gravity to the energy–momentum tensors, that is, proposing quantum equations of state. Despite the technical difficulties, we intend to insert GUP into the metric tensor so that the line element and the geodesic equation in flat and curved space are accordingly modified. The latter apparently encompasses acceleration, jerk, and snap (jounce) of a particle in the quasi‐quantized gravitational field. Finite higher orders of acceleration apparently manifest phenomena such as accelerating expansion and transitions between different radii of curvature and so on.

A minimal length uncertainty approach to cosmological constant problem

AbstractBased on quantum mechanical framework for the minimal length uncertainty, we demonstrate that the generalized uncertainty principle (GUP) parameter could be best constrained by recent gravitational waves observations on one hand. On the other hand, this suggests modified dispersion relations (MDRs) enabling an estimation for the difference between the group velocity of gravitons and that of photons. Utilizing features of the UV/IR correspondence and the obvious similarities between GUP (including non‐gravitating and gravitating impacts on Heisenberg uncertainty principle) and the discrepancy between the theoretical and the observed cosmological constant (apparently manifesting gravitational influences on the vacuum energy density), we suggest a possible solution for the cosmological constant problem.

Quantum Gravity Corrections to a System of Self-gravitating Fermions

The generalized uncertainty principle (GUP) is a generalization of the Heisenberg principle motivated by several theories of quantum gravity such as string theory. It predicts the existence of a minimal distance and/or maximum momentum. Here, we study some consequences of the GUP in the context of the statistical mechanics of self-gravitating fermions. Using the GUP discretization of phase space, we formulate a gravitational Thomas-Fermi model in consistency with the minimal length prescription and analyse its physical consequences.

Looking at the Physics of What a Quark Star-Black Hole Binary Would Create in Terms of GW Signals and New Physics

A quark star, black hole pairing as a would-be Gravitational wave generator is brought up. Quark stars are, anyway, likely to be black holes, above a certain mass limit, whereas a quark star in itself obey thermodynamic “laws” which in certain ways differ from the traditional black hole models. We list some of the probable consequences of such a binary, and make predictions as to certain GW phenomenon which will have observational consequences. i.e., a GW “change in energy” from a black hole—Quark star pair would likely be within 90% of that of comparatively massed black hole—black hole binary pair. The electromagnetic “profile” of the two cases would differ dramatically, and we conclude our inquiry with an open question if a generalized uncertainty principle could play a role in comparing the 7th and 8th equations of our presentation.

Wave function of perturbed Hamiltonian in graphene

In this paper, we use the generalized Dirac structure beyond the linear regime of graphene. This is probed using the a deformation of the Dirac structure in graphene by the generalized uncertainty principle. Here, the Planck length is replaced by the graphene lattice spacing. As the graphene sheet is bounded by two boundaries, we analyze this system with suitable boundary conditions. We solve the perturbed Hamiltonian and derive the wave function for this system. We observe that the energy of this system gets corrected due to this deformation. We explicitly calculate these corrections to the energy of this system.

Modified structure equations and mass–radius relations of white dwarfs arising from the linear generalized uncertainty principle

The generalized uncertainty principle (GUP) is a common feature among several approaches related to quantum gravity. An approach to GUP was recently developed that contains both linear and quadratic terms of momenta, from which an infinitesimal phase space volume was derived up to the linear term of momenta. We studied the effects of this linear GUP approach on the structure equations and mass–radius relation of zero-temperature white dwarfs. We formulated a linear GUP-modified Chandrasekhar equation of state (EoS) by deriving exact forms of the thermodynamic properties of ideal Fermi gases. This was then used to obtain the analytical form of the modified Newtonian structure equations for the white dwarfs. By imposing a constraint on the momenta of the particles in the white dwarf due to linear GUP, the structure equations were solved and the modified mass–radius relation of the white dwarfs were obtained. This was then extended in the context of general relativity (GR), which, like linear GUP, affects white dwarfs significantly in the high-mass regime. We found that linear GUP displays a similar overall effect as in GR — linear GUP supports gravitational collapse of the white dwarf, by decreasing its limiting (maximum) mass and increasing its corresponding limiting (minimum radius). We also found that GUP effects become evident only at large values of the GUP parameter, but these values are still within the estimated bounds. This effect gets more prominent as we increase the as-of-yet unestablished value of the parameter.

Modified Hawking effect from generalized uncertainty principle

We use the generalized uncertainty principle to compute the first correction to the Hawking temperature associated to Hawking effect. From this value we obtain a new evaporation time and entropy of any Schwarzschild black hole analyzing their expressions and consequences.

A proposal for Heisenberg uncertainty principle and STUR for curved backgrounds: an application to white dwarf, neutron stars and black holes

After a critical overview of the generalized uncertainty principle (GUP) applied to compact objects, we propose a texture of Heisenberg uncertainty principle in curved spacetimes (CHUP). CHUP allows to write down physically motivated STUR (spacetime uncertainty relations) in a generic background for a non commutative spacetime in terms of tetrad variables. In order to study possible quantum effects for compact astrophysical objects as white dwarf, neutron stars and black holes, an expression for quantum fluctuations is outlined. As a result, contrary to GUP-based claims, we found no evidence for quantum effects concerning equilibrium equation and critical mass M c for white dwarf and neutron stars. Conversely, our expression for CHUP confirms that general relativistic effects strongly reduce the Oppenheimer–Volkoff Newtonian limit for very compact astrophysical objects as neutron stars. In particular, we found that for a degenerate relativistic Fermi gas, the maximum mass decreases for increasing compactness of the star with a minimum critical mass M c ≃ 0.59M ⊙ at the Buchdahl limit. Finally, we study possible non commutative effects near the event horizon of a black hole.

Influence of dark matter on phase transitions of XCDM black hole in braneworld based on the framework of GUP

In this paper, under the framework of generalized uncertainty principle (GUP), based on the quantum tunneling radiation, we discuss the influence of dark matter on thermodynamics and phase transition from the X-cold dark matter (XCDM) black hole in Braneworld. It turns out that the existence of the dark matter can give rise to some new relations such as local temperature–mass, heat capacity–mass and local free energy–local temperature, and dark matter can play an important role in phase transitions. It is worth emphasizing that the first-order phase transition, second-order and Hawking–Page-like phase transitions can be observed from the new phase diagrams, and the novel and interesting thermodynamics behavior has been presented under the influence of GUP and dark matter.

Modelling Casimir wormholes in extended gravity

A model of traversable wormhole in an extended gravity theory has been proposed. The Casimir effect and Generalised Uncertainty Principle (GUP) arising out of the concept of minimal length have been considered to obtain the shape function, radial and tangential pressure of the wormhole. The effects of the GUP parameter and the parameter of the extended gravity theory on the wormhole properties have been discussed. The energy condition violation by the exotic matter of Casimir wormhole have been shown. Also we have calculated the exotic matter content of the Casimir wormhole that violate the null energy condition.