Effects Of Generalized Uncertainty Principle Research Articles

Minimal length scale correction in the noise of gravitons

In this paper we have considered a quantized and linearly polarized gravitational wave interacting with a gravitational wave detector (interferometer detector) in the generalized uncertainty principle (GUP) framework. Following the analysis in Phys. Rev. Lett. 127:081602 (2021), we consider a quantized gravitational wave interacting with a gravitational wave detector (LIGO/VIRGO etc.) using a path integral approach. Although the incoming gravitational wave was quantized, no Planck-scale quantization effects were considered for the detector in earlier literatures. In our work, we consider a modified Heisenberg uncertainty relation with a quadratic order correction in the momentum variable between the two phase space coordinates of the detector. Using a path integral approach, we have obtained a stochastic equation involving the separation between two point-like objects. It is observed that random fluctuations (noises) and the correction terms due to the generalized uncertainty relation plays a crucial role in dictating such trajectories. Finally, we observe that the solution to the stochastic equation leads to time dependent standard deviation due to the GUP insertion, and for a primordial gravitational wave (where the initial state is a squeezed state) both the noise effect and the GUP effects exponentially enhance which may be possible to detect in future generation of gravitational wave detectors. We have also given a plot of the dimensionless standard deviation with time depicting that the GUP effect will carry a distinct signature which may be detectable in the future space based gravitational wave observatories.

Quantum Gravity effect on accretion disk of Schwarzschild black hole

This paper is concerned with the effect of quantum gravity, that is represented by generalized uncertainty principle (GUP), which admits a presence of a minimum measurable length, on the accretion disk about Schwarzschild black hole. The modification in the metric due to GUP was determined. The problem of spherically symmetric, steady state, adiabatic accretion onto a modified Schwarzschild black hole was considered. By assuming a polytropic accreting gas, analytical formulation of the problem is achieved in general relativity framework. Despite the decrease in the effective mass of the black hole due GUP affect, the rate of mass accretion is accelerated and there is an increase in the critical radius and in critical speed of sound with a decrease in critical gas velocity. Also, the gas pressure and temperature profile of the gas below the critical point and at event horizon were considered and is found they increased due to GUP effect.

Effect of generalized uncertainty principle on anharmonic oscillator

The minimal length Generalized Uncertainty Principle (GUP) is a proposed theory based on the basic phenomenology of Quantum Gravity (QG) to study the effect of gravity in the quantum realm in a nonrelativistic way. In this paper, we study the GUP effect on anharmonic oscillator by the ladder operator and perturbation theory. Taking different orders of perturbation from the potential of anharmonic oscillator, the first and second order energy corrections and the first order correction of wavefunction have been derived. We have also studied the variation of energy spectrum in general harmonic and anharmonic oscillator in an undergraduate nonrelativistic approach.

Quantum-corrected scattering of a Schwarzschild black hole with GUP effect

In this research, we find the quantum correction of the Schwarzschild black hole metric based on the generalized uncertainty principle (GUP). We assume a massless field scalar field, with an effective potential according to the GUP effect. After obtaining the effective potential numerically, we apply approximation on the effective potential to find the phase shift of the scattered wave function. Moreover, the GUP corrected reflection and transmission coefficient of scattered radial wave function are calculated with the Pösch-Teller method.

Modified Brans–Dicke cosmology with minimum length uncertainty

We consider a modification of the Brans-Dicke gravitational Action Integral inspired by the existence of a minimum length uncertainty for the scalar field. In particular, the kinetic part of the Brans-Dicke scalar field is modified such that the equation of motion for the scalar field be modified according to the quadratic Generalized Uncertainty Principle (GUP). For the background geometry, we assume the homogeneous and isotropic Friedmann--Lema\^{\i}tre--Robertson--Walker metric. We investigate the dynamics and the cosmological evolution for the dynamical variables of the theory and we compare the results with the unmodified Brans-Dicke theory. It follows that in consideration because of the additional degrees of freedom in the energy-momentum tensor the dynamical variables describe various aspects of the cosmological history. This is one of the first studies on the effects of GUP in a Machian gravitational theory.

Effect of GUP on the large scale structure formation in the universe

We study the clustering of galaxies in generalized uncertainty principle (GUP) modified Newtonian potential. We compute the corrected N-particle partition function which leads to the modified equations of state. The GUP corrected clustering parameter is compared with the original clustering parameter. An investigation of the distribution function for the system of galaxies is also made. Moreover, we analyze the effect of GUP on the two-point correlation function of the system. In order to find the optimal value of the clustering parameter we perform data analysis and compare our model with the data.

Microstructure of charged AdS black hole with minimal length effects* *Supported by NSFC (11947408, 12047573)

In this work, the microstructure of charged AdS black holes under minimal length effects is investigated. We study the thermodynamics of black holes in the extended phase space, where the cosmological constant is regarded as the thermodynamic pressure. The modified Hawking temperature and phase transition are obtained based on the generalized uncertainty principle (GUP). Then, using thermodynamic geometry, the microstructure of black holes can be determined by the ratio of the GUP parameter to charge. For a small ratio, the black hole exhibits the typical RN-AdS microstructure with van der Waals phase transition and repulsive/attractive interactions. As the ratio increases, the reentrant phase transition is observed, and both the repulsion-attraction coexisted and the attraction dominated black holes are noted. For a large ratio, the black hole behaves like a Schwarzchild-AdS black hole in which neither phase transition nor repulsive interaction are observed. These results suggest that the GUP effect will reduce the repulsive interaction presented by the charged AdS black hole.

Relativistic tunneling time under the generalized uncertainty principle

The one-dimensional Dirac equation is studied for square-well potential in the presence of generalized uncertainty principle (GUP). Based on the exact solution, the general and explicit relation between the phase time and the dwell time is given and quantified. The phase time, dwell time and self-interference delay are calculated as well and it is shown that the GUP has effects on the tunneling time. Moreover, the effect of GUP on the tunneling time showed a slight change with the change of mass, and goes to zero with the increase of kinetic energy.

Higher-order generalized uncertainty principle applied to gravitational baryogenesis

The gravitational baryogenesis plays an important role in the study of baryon asymmetry. However, the original mechanism of gravitational baryogenesis in the radiation-dominated era leads to the asymmetry factor η equal to zero, which indicates this mechanism may not generate a sufficient baryon asymmetry in the early Universe. In this paper, we investigate the gravitational baryogenesis for the generation of baryon asymmetry in the early Universe by using a new higher-order generalized uncertainty principle (GUP). It is demonstrated that the entropy and the Friedman equation of the Universe deviate from the original cases due to the effect of the higher-order GUP. Those modifications break the thermal equilibrium of the Universe, and in turn produce a non-zero asymmetry factor η. In particular, our results satisfy all of Sakharov's conditions, which indicates that the scheme of explaining baryon asymmetry in the framework of higher-order GUP is feasible. In addition,combining our theoretical results with the observational data, we constraint the GUP parameter β 0, whose bound is between 8.4 × 1010 ∼ 1.1 × 1013.

The generalized uncertainty principle effect in acoustic black holes

We obtain an effective acoustic metric with quantum corrections that are provided by a minimum length implemented by the generalized Heisenberg uncertainty principle (GUP) in the Abelian Higgs model. The effective acoustic metric now depends on the contribution of scalar and vector potentials. We also explore the Hawking radiation and entropy by considering the effective canonical acoustic black hole and find that the modified Hawking temperature leads to logarithm corrections to the entropy. Finally, we investigate the dispersion relations of the model to establish the relationships among the deviations of the group velocity, frequency and temperature due to the GUP.

Quantum gravity and the square of Bell operators

The Bell’s inequality is a strong criterion to distinguish classical and quantum mechanical aspects of reality. Its violation is the net effect of the existence of non-locality in systems, an advantage for quantum mechanics over classical physics. The quantum mechanical world is under the control of the Heisenberg uncertainty principle that is generalized by quantum gravity scenarios, called generalized uncertainty principle (GUP). Here, the effects of GUP on the square of Bell operators of qubits and qutrits are studied. The achievements claim that the violation quality of the square of Bell inequalities may be a tool to get a better understanding of the quantum features of gravity. In this regard, it is obtained that the current accuracy of the Stern–Gerlach experiments implies upper bounds on the values of the GUP parameters.

Zitterbewegung particles tunneling from Reissner-Nordström AdS black hole surrounded by quintessence

We study quantum gravity corrections to the thermodynamic quantities of Reissner-Nordström anti-de Sitter black hole surrounded by quintessence by evaluating the Hawking radiation of zitterbewegung particles under the Generalized Uncertainty Principle (GUP) effect. By using the modified Hawking temperature of the black hole, we derive the thermodynamic equation of state and the Helmholtz free energy. We discuss global stability conditions and phase transitions by plotting the and planes. We also assume that the black hole is a heat engine where the Carnot cycle is performed. We observe that the efficiency under the GUP effect is higher than the standard one when attractive Coulomb interaction is considered with the influence of zitterbewegung particles.

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.

GUP effect on thermodynamical properties of the noncommutative rotating BTZ black hole

In this paper, we investigated the quantum gravity effects on the thermal properties of the [Formula: see text]-dimensional noncommutative rotating Banados–Teitelboim–Zanelli (NCR-BTZ) black hole in the context of quantum tunneling of relativistic particles. These include Hawking temperature, the thermally local and global stability conditions, and the phase transitions. For this purpose, in the framework of the generalized uncertainty principle (GUP), we used the Hamilton–Jacobi approach to calculate the tunneling probability for a massive scalar, Dirac, and vector boson particles from the [Formula: see text]-dimensional NCR-BTZ black hole. We found that the modified Hawking temperature of the black hole depends on the black hole properties, on the tunneling particle properties, on the noncommutative parameter, and on the GUP parameter. Using the modified Hawking temperature, we calculated the modified heat capacity, and then we discussed the local thermodynamic stability conditions for the black hole. The black hole may undergo a first-type phase transition to become stable under the scalar particle tunneling whereas, it might undergoes both the first and the second-type phase transitions under the both Dirac and vector boson particles tunneling process. Furthermore, we calculated the Gibbs free energy of the black hole, and we investigated the global stability conditions. We observed that Hawking–Page phase transition may occur in the presence of the quantum gravity effect under the tunneling process of scalar, Dirac, and vector boson particles. In the context of quantum gravity effect, we also derived the modified equation of state to investigate the critical behavior of the commutative rotating BTZ black hole. Finally, we shown that Van der Waals-like phase transition may occur in the context of tunneling process of both Dirac and vector boson particle, whereas it may not occur for the tunneling of scalar particle.

Quantum Gravity Correction to Hawking Radiation of the 2+1-Dimensional Wormhole

We carry out the Hawking temperature of a 2+1-dimensional circularly symmetric traversable wormhole in the framework of the generalized uncertainty principle (GUP). Firstly, we introduce the modified Klein-Gordon equation of the spin-0 particle, the modified Dirac equation of the spin-1/2 particle, and the modified vector boson equation of the spin-1 particle in the wormhole background, respectively. Given these equations under the Hamilton-Jacobi approach, we analyze the GUP effect on the tunneling probability of these particles near the trapping horizon and, subsequently, on the Hawking temperature of the wormhole. Furthermore, we have found that the modified Hawking temperature of the wormhole is determined by both wormhole’s and tunneling particle’s properties and indicated that the wormhole has a positive temperature similar to that of a physical system. This case indicates that the wormhole may be supported by ordinary (nonexotic) matter. In addition, we calculate the Unruh-Verlinde temperature of the wormhole by using Kodama vectors instead of time-like Killing vectors and observe that it equals to the standard Hawking temperature of the wormhole.

Effect of GUP on Hawking radiation of BTZ black hole

The Hawking radiation of BTZ black hole is investigated based on generalized uncertainty principle effect by using Hamilton–Jacobi method and Dirac equation. The tunneling probability and the Hawking temperature of the spin-1/2 particles of the BTZ black hole are investigated using the modified Dirac equation based on the GUP. The modified Hawking temperature for fermion crossing the black hole horizon includes the mass parameter of the black hole, angular momentum, energy and also outgoing mass of the emitted particle. Besides, considering the effect of GUP into account, the modified Hawking radiation of massless particle from a BTZ black hole is investigated using Damour and Ruffini method, tortoise coordinate transformation and modified Klein–Gordon equation. The relation between the modified Hawking temperature obtained by using Damour–Ruffini method and the energy of the emitted particle is derived. The original Hawking temperature is also recovered in the absence of quantum gravity effect. There is a possibility of negative Hawking temperature for emission of Dirac particles under quantum gravity effects.

Traversable wormholes supported by GUP corrected Casimir energy

In this paper, we investigate the effect of the Generalized Uncertainty Principle (GUP) in the Casimir wormhole spacetime recently proposed by Garattini (Eur Phys J C 79: 951, 2019). In particular, we consider three types of GUP relations, firstly the Kempf, Mangano and Mann (KMM) model, secondly the Detournay, Gabriel and Spindel (DGS) model, and finally the so-called type II model for the GUP principle. To this end, we consider three specific models of the redshift function along with two different equations of state (EoS), given by {mathcal {P}}_r(r)=omega _r(r) rho (r) and {mathcal {P}}_t(r)=omega _t (r){mathcal {P}}_r(r) and obtain a class of asymptotically flat wormhole solutions supported by Casimir energy under the effect of GUP. Furthermore we check the null, weak, and strong condition at the wormhole throat with a radius r_0, and we show that in general the classical energy conditions are violated by some arbitrary quantity at the wormhole throat. Importantly, we examine the wormhole geometry with semiclassical corrections via embedding diagrams. We also consider the ADM mass of the wormhole, the volume-integral quantifier to calculate the amount of the exotic matter near the wormhole throat, and the deflection angle of light.

GUP deformed phase-space and axiomatic thermodynamic self-consistency

Based on the generalized uncertainty principle (GUP) with a deformation of the phase-space, the partition function has recently been modified. In the present work, we analyze the self-consistency of the axiomatic thermodynamics derived from the deformed partition function. First, we set up the thermodynamic quantities such as pressure, energy density, entropy and number density, then we extend the study for testing the approval of consistency. We found that the deformed phase-space satisfies the axiomatic self-consistency of thermodynamics. We would expect the effects of GUP to be more pronounced at high frequencies, but the used deformed phase-space factor would still diverge as [Formula: see text] approaches [Formula: see text].

The GUP Effect on Tunneling of Massive Vector Bosons from The 2+1 Dimensional Black Hole

In this study, the Generalized Uncertainty Principle (GUP) effect on the Hawking radiation formed by tunneling of a massive vector boson particle from the 2+1 dimensional new-type black hole was investigated. We used modified massive vector boson equation based on the GUP. Then, the Hamilton-Jacobi quantum tunneling approach was used to work out the tunneling probability of the massive vector boson particle and Hawking temperature of the black hole. Due to the GUP effect, the modified Hawking temperature was found to depend on the black hole properties, on the AdS3 radius, and on the energy, mass, and total angular momentum of the tunneling massive vector boson. In the light of these results, we also observed that modified Hawking temperature increases by the total angular momentum of the particle while it decreases by the energy and mass of the particle and the graviton mass. Also, in the context of the GUP, we see that the Hawking temperature due to the tunneling massive vector boson is completely different from both that of the spin-0 scalar and that of the spin-1/2 Dirac particles obtained in the previous study. We also calculate the heat capacity of the black hole using the modified Hawking temperature and then discuss influence of the GUP on the stability of the black hole.