Generalized Uncertainty Principle Research Articles

Effects of a generalized uncertainty principle on the MIT bag model equation of state

AbstractThe Generalized Uncertainty Principle (GUP) is motivated by the premise that spacetime fluctuations near the Planck scale impose a lower bound on the achievable resolution of distances, leading to a minimum length. Inspired by a semiclassical method that integrates the GUP into the partition function by deforming its phase space, we induce a modification on the thermodynamic quantities of the MIT bag model that we propose serves as an effective semiclassical description of deconfined quark matter in a space with minimal length. We investigate the consequences of this deformation on the zero‐temperature limit, revealing a saturation limit for the energy density, pressure, and baryon number density and an overall decrease of the thermodynamic quantities which suggests an enhanced stability against gravitational collapse. These findings extend existing research on GUP‐deformed Fermi gases. Ultimately, our description introduces the effects of quantum gravity in the equations of state for compact stars in a mathematically simple manner, suggesting the potential for extension to more complex systems.

Gravitational observations and LQGUP

Motivated by recent works, we employ the bounds on the dimensionless quantum-gravity parameter obtained from six solar system-based gravitational tests in order to obtain bounds on the dimensionless parameter of the generalized uncertainty principle with linear and quadratic terms in momentum. The bounds obtained here are much tighter than those obtained, from the same six solar system-based gravitational tests, for the dimensionless parameter of the uncertainty principle with only quadratic terms in momentum.

Unveiling phase space modifications: A clash of modified gravity and the generalized uncertainty principle

Unveiling phase space modifications: A clash of modified gravity and the generalized uncertainty principle

Thermodynamics in a quantum corrected Reissner–Nordström–AdS black hole and its GUP-corrections

We calculate the thermodynamic quantities in the quantum corrected Reissner–Nordström–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.

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

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

Hawking radiation under generalized uncertainty principle

The generalized uncertainty relation is expected to be an essential element in a theory of quantum gravity. In this work, we examine its effect on the Hawking radiation of a Schwarzschild black hole formed from collapse by incorporating a minimal uncertainty length scale into the radial coordinate of the background. This is implemented in both the ingoing Vaidya coordinates and a family of freely falling coordinates. We find that, regardless of the choice of the coordinate system, Hawking radiation is turned off at around the scrambling time. Interestingly, this phenomenon occurs while the Hawking temperature remains largely unmodified.

Non-singular collapse scenario from generalized uncertainty principle

Non-singular collapse scenario from generalized uncertainty principle

Constraining Snyder and GUP models with low-mass stars

We investigate the application of an equation of state that incorporates corrections derived from the Snyder model (and the Generalized Uncertainty Principle) to describe the behaviour of matter in a low-mass star. Remarkably, the resulting equations exhibit striking similarities to those arising from modified Einstein gravity theories. By modeling matter with realistic considerations, we are able to more effectively constrain the theory parameters, surpassing the limitations of existing astrophysical bounds. The bound we obtain is β0≤4.5×1047\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\beta _0 \\le 4.5 \ imes 10^{47}$$\\end{document}. We underline the significance of realistic matter modeling in order to enhance our understanding of effects arising in quantum gravity phenomenology and implications of quantum gravitational corrections in astrophysical systems.

Constraints via the Event Horizon Telescope for Black Hole Solutions with Dark Matter under the Generalized Uncertainty Principle Minimal Length Scale Effect

AbstractFour spherically symmetric but non‐asymptotically flat black hole solutions surrounded with spherical dark matter distribution perceived under the minimal length scale effect is derived via the generalized uncertainty principle. Here, the effect of this quantum correction, described by the parameter , is considered on a toy model galaxy with dark matter and the three well‐known dark matter distributions: the cold dark matter, scalar field dark matter, and the universal rotation curve. The aim is to find constraints to by applying these solutions to the known supermassive black holes: Sagittarius A (Sgr. A*) and Messier 87* (M87*), in conjunction with the available Event Horizon telescope. The effect of is then examined on the event horizon, photonsphere, and shadow radii, where unique deviations from the Schwarzschild case are observed. As for the shadow radii, bounds are obtained for the values of on each black hole solution at confidence level. The results revealed that under minimal length scale effect, black holes can give positive (larger shadow) and negative values (smaller shadow) of , which are supported indirectly by laboratory experiments and astrophysical or cosmological observations, respectively.

Corrections on the Paper “The Quantum Corrections on Kerr-Newman Black Hole Thermodynamics by the Generalized Uncertainty Principle”

Corrections on the Paper “The Quantum Corrections on Kerr-Newman Black Hole Thermodynamics by the Generalized Uncertainty Principle”

Extended Ginzburg-Landau theory of superconductivity from generalized momentum operator and position-dependent mass

The concept of generalized momentum operator which is motivated from the generalized uncertainty principle has been extensively investigated in quantum mechanics and various aspects of theoretical and applied physics. In this study, we have applied this formalism to Ginzburg-Landau theory of superconductvity and Abrikosov vortex lattice in type II-superconductors. After deriving the extended Ginzburg-Landau equations, we have discussed several independent structures of the auxiliary function of position operator in the generalized momentum operator and we have analyzed their features in both Ginzburg-Landau and London theories. Comparable properties to the basic formalism have been obtained even without the presence of the cubic nonlinear term in Ginzburg-Landau equations. However, not all structures of the auxiliary function of position operator result on the exclusion of the magnetic field from a superconductor when it's below its critical temperature. But, only specific forms may succeed to eliminate the magnetic field. This approach has been generalized by considered a position-dependent mass of the electric charge. Amazingly, for a position-dependent mass of hyperbolic soliton-like structure, the extended Ginzburg-Landau wave function is identical to the result obtained in the conventional formalism and besides, for specific correlations between the auxiliary function of the position operator and position-dependent mass, the exclusion of the magnetic field is conceivable. We have also discussed the Abrikosov vortex lattice solution based on the extended Ginzburg-Landau formalism with position-dependent mass of the electric charge. It was observed that, for a specific structure of the position-dependent mass and for a quantum number n=0, a transition between a type-II and type-I superconductor takes place if the Ginzburg-Landau parameter is κ=121+257≈2.0634. For large n, the problem depends on the asymptotic form of the Hermite polynomial and periodicity occurs if the electric charge is quantized. Further details are obtained and analyzed.

Class of charged traversable Casimir wormholes in f(R,T) gravity

This article investigates the existence and viability of some traversable wormholes involving electric charge effects in f(R,T) gravity. We use the negative energy density obtained from the Casimir source in this regard, and the consequences of the electromagnetic field produced by an electric charge are taken into account. In order to obtain wormhole shape function, we apply some noteworthy Casimir energy density systems like two parallel plates, two parallel cylinders, two spheres that are placed far apart, and the generalized uncertainty principle (GUP) correction. We analyze the fundamental wormhole conditions as well as the validity of null energy condition by taking variations of coupling parameter λ of f(R,T) gravity and the electric charge Q. Next, we explore the dynamics of gravitational active mass of the formulated wormhole solutions depending on Q. Furthermore, we study the volume integral quantifier of these charged Casimir wormhole solutions and also, determine the corresponding values of complexity factor. It is shown that the obtained wormhole solutions exhibit valid behavior and the respective values of complexity factor always fall within a certain range.

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.

Modified Hawking radiation of Schwarzschild-like black hole in bumblebee gravity model

In this article, we study the Hawking radiation of the Schwarzschild black hole within the bumblebee gravity model (SBHBGM). Considering classical approaches involving Killing vectors and the standard Hamilton-Jacobi method, the Hawking radiation of SBHBGM is computed. The Painlevé-Gullstrand, ingoing Eddington-Finkelstein, and Kruskal-Szekeres coordinate systems are introduced as alternatives to the naive coordinates, providing insights into gravitational behavior around massive objects like black holes. We thus examine whether Hawking radiation’s temperature depends on the chosen coordinate system or not. Incorporating the Generalized Uncertainty Principle (GUP) into the Hamilton-Jacobi equation, a modified equation characterizing particle behavior near the event horizon is obtained. By calculating the tunneling probability using the modified action, the GUP-induced modifications to the emitted particle’s behavior are considered, resulting in the derivation of the modified temperature of the SBHBGM. In conclusion, we explore the quantum-adjusted entropy of SBHBGM and its associated temperature and assess the findings we have acquired.

Casimir Wormholes driven by non-commutative geometries in higher dimensional Einstein Gauss–Bonnet gravity

This manuscript investigates the construction of a new class of wormhole solutions motivated by non-commutative geometry in fusion with Casimir wormholes in Einstein Gauss–Bonnet (EGB) gravity . It is not likely to ensure that the violation at small scales is significant enough to produce a macroscopic wormhole by depending merely on the Casimir effect. In our strategy, we solely utilised modifications to the energy–momentum tensor (EMT) in the non-commutative background, coupled with the impact of Casimir phenomena. On the other hand, the Einstein tensor remains unchanged in the Einstein field equations. In this regard, we have assumed four cases of non-commutative effects combined with the Casimir wormholes. We have investigated the non-commutative effects using Gaussian and Lorentzian distributions. Also, we incorporated the Casimir and Generalised Uncertainty Principle (GUP) corrected Casimir wormholes to study the basic features of wormhole solutions. The dynamics of a theory that relates the Gauss–Bonnet (GB) parameters (μ) and non-commutative parameter (β) have been addressed graphically, with a particular focus on analysing null energy conditions (NEC) through contour plots to identify the presence of exotic matter. Furthermore, embedding diagrams have been used to investigate the geometry of newly produced asymptotically flat wormholes. Additionally, the active gravitational mass has been calculated and plotted up to the radius r in the area around the wormhole throat. We have discussed equilibrium conditions to analyse the stability of obtained wormhole solutions. Finally, to understand the complexity of wormhole solutions, we have examined the complexity factor graphically.

Space-time is doomed! Introducing Planck scale physics in the classroom

This article provides an overview of some tentative ideas relating to Planck scale physics at a level suitable for advanced high school students, beginning undergraduate students, and teachers. After discussing the ratio of the electric and gravitational forces, Heisenberg’s uncertainty principle is combined with Einstein’s theory of special relativity to estimate the scale at which the strength of gravity becomes comparable to the electrostatic force. It is shown that the energy required to probe a region of space smaller than the Planck length may lead to the formation of a black hole, placing a fundamental lower limit on the distances that can be meaningfully probed in Nature. The Planck length, mass and time are then obtained using a combination of dimensional analysis and the fundamental constants appearing in theories of quantum mechanics, relativity and gravity. Finally, a heuristic derivation of the generalised uncertainty principle is provided.

Dymnikova GUP-corrected black holes

We consider the impact of Generalized Uncertainty Principle (GUP) effects on the Dymnikova regular black hole. The minimum length scale introduced by the GUP modifies the energy density associated with the gravitational source, referred to as the Dymnikova vacuum, based on its analogy with the gravitational counterpart of the Schwinger effect. We present an approximated analytical solution (together with exact numerical results for comparison) that encompasses a wide range of black hole sizes,whose properties crucially depend on the ratio between the de Sitter core radius and the GUP scale. The emergence of a wormhole inside the de Sitter core in the innermost region of the object is one of the most relevant features of this family of solutions. Our findings demonstrate that these solutions remain singularity free, confirming the robustness of the Dymnikova regular black hole under GUP corrections. Regarding energy conditions, we find that the violation of the strong, weak, and null energy conditions which is characteristic of the pure Dymnikova case does not occur at Planckian scales in the GUP corrected solution. This contrast suggests a departure from conventional expectations and highlights the influence of quantum corrections and the GUP in modifying the energy conditions near the Planck scale.

Minimal lengths in 3D via the generalized uncertainty principle

We investigate an extension of the Generalized Uncertainty Principle (GUP) in three dimensions by modifying the three dimensional position and momentum operators in a manner that remains coordinate-independent and retains as much of the standard position-momentum commutators as possible. Moreover, we bound the physical momentum which leads to an effective minimal length in every coordinate direction. The physical consequences of these modified operators are explored in two scenarios: (i) when a spherically-symmetric wave function is ‘compressed’ into the smallest possible volume; (ii) when the momentum is directed in a single direction. In case (ii), we find that the three dimensional GUP exhibits interesting phenomena that do not occur in one dimension: the minimal distance in the direction parallel to a particle's momentum is different from the minimal distance in the orthogonal directions.

Thermodynamics of FLRW apparent horizon in the presence of UV/IR mixing

Generalized uncertainty principle (GUP) and Extended uncertainty principle (EUP) are well-known phenomenological gates to the issue of the so-called Gravitational Quantum Mechanics. Two fundamental impacts of the GUP and EUP are the concepts of minimal measurable length and minimal measurable momentum. The minimal measurable length as the possible smallest uncertainty in position measurement can remove the spacetime singularities arising from the general theory of relativity in UV regime. On the other hand, the minimal measurable momentum as the possible smallest uncertainty in momentum measurement puts an IR cutoff on the late-time (low energy) dynamics of the universe. This minimal momentum essentially arises due to the curvature of the background spacetime manifold. A combination of GUP and EUP gives a UV–IR complete uncertainty principle which is called usually as EGUP in literature. Motivated by these facts, we aim to study the impact of the EGUP with minimal measurable length and minimal measurable momentum on Friedmann equations. We first find the EGUP-modified entropy expression in Friedmann–Lemaître–Robertson–Walker (FLRW) universe. Then, we obtain the EGUP-corrected Friedmann equations by employing the unified first law of thermodynamics. We explore the deceleration parameter in the EGUP setup. We then check whether the generalized second law of thermodynamics is fulfilled and then study some related issues. As a result, we find some constraints on the EGUP parameters.

A Wheeler–DeWitt Non-Commutative Quantum Approach to the Branch-Cut Gravity

In this contribution, motivated by the quest to understand cosmic acceleration, based on the theory of Hořava–Lifshitz and on the branch-cut gravitation, we investigate the effects of non-commutativity of a mini-superspace of variables obeying the Poisson algebra on the structure of the branch-cut scale factor and on the acceleration of the Universe. We follow the guiding lines of a previous approach, which we complement to allow a symmetrical treatment of the Poisson algebraic variables and eliminate ambiguities in the ordering of quantum operators. On this line of investigation, we propose a phase-space transformation that generates a super-Hamiltonian, expressed in terms of new variables, which describes the behavior of a Wheeler–DeWitt wave function of the Universe within a non-commutative algebraic quantum gravity formulation. The formal structure of the super-Hamiltonian allows us to identify one of the new variables with a modified branch-cut quantum scale factor, which incorporates, as a result of the imposed variable transformations, in an underlying way, elements of the non-commutative algebra. Due to its structural character, this algebraic structure allows the identification of the other variable as the dual quantum counterpart of the modified branch-cut scale factor, with both quantities scanning reciprocal spaces. Using the iterative Range–Kutta–Fehlberg numerical analysis for solving differential equations, without resorting to computational approximations, we obtained numerical solutions, with the boundary conditions of the wave function of the Universe based on the Bekenstein criterion, which provides an upper limit for entropy. Our results indicate the acceleration of the early Universe in the context of the non-commutative branch-cut gravity formulation. These results have implications when confronted with information theory; so to accommodate gravitational effects close to the Planck scale, a formulation à la Heisenberg’s Generalized Uncertainty Principle in Quantum Mechanics involving the energy and entropy of the primordial Universe is proposed.