Exploring the Implications of the Deformation Parameter and Minimal Length in the Generalized Uncertainty Principle

The breakdown of the Heisenberg Uncertainty Principle occurs when energies approach the Planck scale, and the corresponding Schwarzschild radius becomes similar to the Compton wavelength. Both of these quantities are approximately equal to the Planck length. In this context, we have introduced a model that utilizes a combination of Schwarzschild’s radius and Compton length to quantify the gravitational length of an object. This model has provided a novel perspective in generalizing the uncertainty principle. Furthermore, it has elucidated the significance of the deforming linear parameter β and its range of variation from unity to its maximum value.

Generalized uncertainty principle from long-range kernel effects:The case of the Hawking black hole temperature

We prove the existence of an analogy between spatial long-range interactions,which are of the convolution-type introduced in non-relativistic quantum mechanics,and the generalized uncertainty principle predicted from quantum gravity theories.As an illustration,black hole temperature effects are discussed.It is observed that for specific choices of the moment's kernels,cold black holes may emerge in the theory.

Generalized uncertainty principle and tunneling radiation of the SAdS_5 black hole

After considering the generalized uncertainty principle, we discuss the quantum tunneling radiation of a fivedimensional Sehwarzschild anti de Sitter black hole. The radiation spectrum and the correction value of the Bekenstein-- Hawking entropy are derived. In a five-dimensional black hole the one order correction term in the Bekenstein-Hawking entropy correction term is proportional to the third power of the area, and the logarithmic correction term is a twoorder small quantity. The correction term is related to the dimension constant introduced in the generalized uncertainty principle. Because the black hole entropy is not divergent, the lowest value of the five-dimensional Schwarzschild anti de Sitter black hole horizon radius is obtained. After considering the generalized uncertainty principle, the radiation spectrum is still consistent with normalization theory.

Thermodynamic properties of massless Dirac–Weyl fermions under the generalized uncertainty principle

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.

Black hole evaporation and its remnants with the generalized uncertainty principle including a linear term

In recent years,researchers have investigated the evaporation of Schwarzschild black holes using various forms of the generalized uncertainty principle(GUP),metric quantum correction,and noncommutative geometry,respectively.However,there are differences between the GUP correction and the other two methods in terms of describing the later stages of black hole evaporation.Furthermore,some studies argue that the GUP with a negative parameter cannot effectively correct black hole evaporation,while others contend that the positivity or negativity of the GUP parameters should not affect the correction results.Taking the above into consideration,we reconsider black hole evaporation with the generalized uncertainty principle including a linear term(LGUP),and examine the case of negative parameters.The results indicate that the evaporation behavior of both Schwarzschild black holes and Reissner–Nordstr?m black holes,under LGUP correction,is consistent with the results of metric quantum correction and non-commutative geometry.Additionally,the negative parameter LGUP can also effectively correct for black hole evaporation.

The effect of different generalized uncertainty principles on Jeans mass modification

Jeans mass is regarded as a crucial factor in the study of nebula collapse.Astronomical data shows that Jeans mass is larger in theory than it is in observation.Someone mentioned that Jeans mass can be modified by using the generalized uncertainty principle(GUP).However,different physical backgrounds lead to different forms of GUP expression.In order to make the theoretical values of Jeans mass and its observed values match better,we use three distinct types of GUPs to correct Jeans mass in this paper.We find that the corrected Jeans masses are smaller than the uncorrected ones,where the Pedram corrected Jeans mass is the minimum and is close to the observed value.In addition,we consider the impact of temperature T and the GUP parameters(η,βandγ)for the corrected Jeans mass.

Thermodynamics of the black holes under the extended generalized uncertainty principle with linear terms

In this paper,we employ the extended generalized uncertainty principle with linear terms(LEGUP)to investigate the thermodynamics properties of the Schwarzschild and Reissner–Nordstr?m(RN)black holes.Firstly,by constructing the theoretical framework of LEGUP,the minimal temperature of the Schwarzschild black hole and the modified mass–temperature function for the black hole are calculated.Furthermore,the heat capacity function for the Schwarzschild black hole is obtained.After that,we compare LEGUP black hole thermodynamics with EGUP black hole and with the usual forms.Besides,the modification of black hole entropy is discussed,which involves a heuristic analysis of particles absorbed by the black hole.Finally,we derive the LEGUP-corrected temperature,heat capacity and entropy functions of the RN black hole.

Generalized uncertainty principle and black hole thermodynamics

Banerjee-Ghosh's work shows that the singularity problem can be naturally avoided by the fact that black hole evaporation stops when the remnant mass is greater than the critical mass when including the generalized uncertainty principle(GUP)effects with first-and second-order corrections.In this paper,we first follow their steps to reexamine Banerjee-Ghosh's work,but we find an interesting result:the remnant mass is always equal to the critical mass at the final stage of black hole evaporation with the inclusion of the GUP effects.Then,we use Hossenfelder's GUP,i.e.,another GUP model with higher-order corrections,to restudy the final evolution behavior of the black hole evaporation,and we confirm the intrinsic self-consistency between the black hole remnant and critical masses once more.In both cases,we also find that the thermodynamic quantities are not singular at the final stage of black hole evaporation.

Thermodynamics in a quantum corrected Reissner-Nordstr?m-AdS black hole and its GUP-corrections

We calculate the thermodynamic quantities in the quantum corrected Reissner-Nordstr?m-AdS(RN-AdS)black hole,and examine their quantum corrections.By analyzing the mass and heat capacity,we give the critical state and the remnant state,respectively,and discuss their consistency.Then,we investigate the quantum tunneling from the event horizon of massless scalar particle by using the null geodesic method,and charged massive boson W^(±)and fermions by using the Hamilton-Jacob method.It is shown that the same Hawking temperature can be obtained from these tunneling processes of different particles and methods.Next,by using the generalized uncertainty principle(GUP),we study the quantum corrections to the tunneling and the temperature.Then the logarithmic correction to the black hole entropy is obtained.

Information entropy for static spherically symmetric black holes

By using the new equation of state density derived from the generalized uncertainty relation, the number of the quantum states near event horizon is obtained, with which then the information entropy of static spherically symmetric black holes has been discussed. It is found that the divergent integral of quantum states near the event horizon can be naturally avoided if using the new equation of state density without introducing the ultraviolet cut-off. The information entropy of black holes can be obtained precisely by the residue theorem, which is shown to be proportional to the horizon area. The information entropy of black holes obtained agrees with the Bechenstein-Hawking entropy when the suitable cutoff factor is adopted.

Entropy of a rotating and charged black string to all orders in the Planck length

By using the entanglement entropy method, this paper calculates the statistical entropy of the Bose and Fermi fields in thin films, and derives the Bekenstein-Hawking entropy and its correction term on the background of a rotating and charged black string. Here, the quantum field is entangled with quantum states in the black string and thin film to the event horizon from outside the rotating and charged black string. Taking into account the effect of the generalized uncertainty principle on quantum state density, it removes the difficulty of the divergence of state density near the event horizon in the brick-wall model. These calculations and discussions imply that high density quantum states near the event horizon of a black string are strongly correlated with the quantum states in a black string and that black string entropy is a quantum effect. The ultraviolet cut-off in the brick-wall model is not reasonable. The generalized uncertainty principle should be considered in the high energy quantum field near the event horizon. From the viewpoint of quantum statistical mechanics, the correction value of Bekenstein-Hawking entropy is obtained. This allows the fundamental recognition of the correction value of black string entropy at nonspherical coordinates.

The ringing of quantum corrected Schwarzschild black hole with GUP

Schwarzschild black holes with quantum corrections are studied under scalar field perturbations and electromagnetic field perturbations to analyze the effect of the correction term on the potential function and quasinormal mode(QNM).In classical general relativity,spacetime is continuous and there is no existence of the so-called minimal length.The introduction of the correction items of the generalized uncertainty principle,the parameterβ,can change the singularity structure of the black hole gauge and may lead to discretization in time and space.We apply the sixth-order WKB method to approximate the QNM of Schwarzschild black holes with quantum corrections and perform numerical analysis to derive the results of the method.Also,we find that the effective potential and QNM in scalar fields are larger than those in electromagnetic fields.

Quantized space-time and its influence on two physical problems

Based on Snyder＇s idea of quantized space-time, we derive a new generalized uncertainty principle and new modified density of states. Accordingly, we discuss the influence of the modified generalized uncertainty principle on the black hole entropy and the influence of the modified density of states on the Stefan-Boltzman law.

Microstructure of charged AdS black hole with minimal length effects

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.