A Generalized Uncertainty Principle in Quantum Gravity

Abstract

We discuss a Gedanken experiment for the measurement of the area of the apparent horizon of a black hole in quantum gravity. Using rather general and model-independent considerations we find a generalized uncertainty principle which agrees with a similar result obtained in the framework of string theories. The result indicates that a minimum length of the order of the Planck length emerges naturally from any quantum theory of gravity, and that the concept of black hole is not operationally defined if the mass is smaller than the Planck mass.

10 pages, 1 figure (not included), IFUP-TH 3/93

References in corpus (2)

• Quantum Hair on Black Holes
• Splitting of an Extremal Reissner-Nordström Throat via Quantum Tunneling

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• Comments on the cosmological constant in generalized uncertainty models
• Generalized Uncertainty Principle theories and their classical interpretation
• Thermodynamics of black holes and the symmetric generalized uncertainty principle
• Quantum Theory at Planck Scale, Limiting Values, Deformed Gravity and Dark Energy Problem
• Minimum-length deformed quantization of a free field on de Sitter background and corrections to the inflaton perturbations
• Charged shells and elementary particles
• Squeezed atom laser for Bose-Einstein condensate with minimal length
• Minimum length, extra dimensions, modified gravity and black hole remnants
• Time Measurement in Quantum Gravity
• Generalized relativistic kinematics in Poincaré-invariant models
• Dark Matter Production at LHC from Black Hole Remnants
• Effective models of quantum gravity induced by Planck scale modifications in the covariant quantum algebra
• Deformed spaces and loop cosmology
• Generalised Uncertainty Relations from Finite-Accuracy Measurements
• The Mass Gap of the Space-time and its Shape
• Probable ratio of the vacuum energy in a Schwarzchild-de Sitter space
• Cosmology from quantum potential in a system of oscillating branes
• Microscopic black hole and uncertainty principle with minimal length and momentum
• Quantum Entanglement with Generalized Uncertainty Principle
• Quantum gravitational decoherence of a mechanical oscillator from spacetime fluctuations
• A covariant tapestry of linear GUP, metric-affine gravity, their Poincaré algebra and entropy bound
• Relation of deformed nonlinear algebras with linear ones
• Time-Dependent Strain in Graphene
• Information Theoretical Approach to Detecting Quantum Gravitational Corrections
• Exactly solvable dynamical models with a minimal length uncertainty
• Laser propagation in Rindler accelerated reference frame based on matrix optics
• Minimal-length quantum field theory: a first-principle approach
• Non-Relativistic Anti-Snyder Model and Some Applications
• Measurable Maximal Energy and Minimal Time Interval
• Generalized Uncertainty principle and momentum-dependent effective mass Schrodinger equation
• Space-time uncertainty relation and operational definition of dimension
• Virtual Black Holes from Generalized Uncertainty Principle and Proton Decay
• HBAR entropy of Infalling Atoms into a GUP-corrected Schwarzschild Black Hole and equivalence principle
• Discreteness Of Curved Space-Time From GUP
• Dual DSR
• Dynamics of the Mixmaster Universe in a non-commutative Generalized Uncertainty Principle framework
• Note on uncertainty relations in doubly special relativity and rainbow gravity
• Theoretical and Observational Implications of Planck's Constant as a Running Fine Structure Constant
• Field theory on evolving fuzzy two-sphere
• Some consequences of GUP induced ultraviolet wavevector cutoff in one-dimensional Quantum Mechanics
• Photon velocity, power spectrum in Unruh effect with modified dispersion relation
• Rényi and von Neumann entropies of thermal state in Generalized Uncertainty Principle-corrected harmonic oscillator
• A New Approach to Generalised Uncertainty Relations
• Quantum Cosmology with Dynamical Vacuum in a Minimal-Length Scenario
• Generalized uncertainty principle in quantum cosmology for the maximally symmetric space
• Generalized Uncertainty Principle and Quantum Gravity Phenomenology
• Discreteness of Space from Anisotropic Spin-Orbit Interaction
• Another look on the connections of Hubble tension with the Heisenberg Uncertainty Principle
• Generalized Uncertainty Relation in Thermodynamics
• Semiclassical resolution of the black hole singularity inspired in the minimal uncertainty approach
• Comment on 'Large-scale non-locality in "doubly special relativity" with an energy-dependent speed of light'
• Position and momentum uncertainties of a particle in a V-shaped potential under the minimal length uncertainty relation
• Generalized uncertainty principle and neutrino phenomenology
• Notes on several phenomenological laws of quantum gravity
• On Some Quantum Correction to the Coulomb Potential in Generalized Uncertainty Principle Approach
• The end of spacetime
• Generalized Uncertainty Principle effects in the Hořava-Lifshitz quantum theory of gravity
• The generalized uncertainty principle in the presence of extra dimensions
• World-line Path integral for the Propagator expressed as an ordinary integral: Concept and Applications
• Minimal length estimation on the basis of studies of the Sun-Earth-Moon system in deformed space
• The Stark Effect with Minimum Length
• Exact solutions for two-body problems in 1D deformed space with minimal length
• Non-Local Deformation of a Supersymmetric Field Theory
• Effects of a Maximal Energy Scale in Thermodynamics for Photon Gas and Construction of Path Integral
• Non-unitary evolutions of noncommutative worlds with symmetry
• Fundamental Length,Deformed Density Matrix and New View on the Black Hole Information Paradox
• Casimir effect in polymer scalar field theory
• The Hierarchy Problem: From the Fundamentals to the Frontiers
• On the algebraic approach to GUP in anisotropic space
• The noncommutative space of light-like worldlines
• A proposal for Heisenberg uncertainty principle and STUR for curved backgrounds: an application to white dwarf, neutron stars and black holes
• A minimal Length Uncertainty Approach to Cosmological Constant Problem
• Random versus holographic fluctuations of the background metric. I. (Cosmological) running of space-time dimension
• Generalized Uncertainty Principle, Modified Dispersion Relation and Barrier penetration by a Dirac particle
• Propagation of spinors on a noncommutative spacetime: equivalence of the formal and the effective approach
• Modified Brans-Dicke cosmology with Minimum Length Uncertainty
• Fate of Mixmaster Chaos in a Deformed Algebra framework
• Generalized Uncertainty Relations,Fundamental Length and Density Matrix
• Signature Change by GUP
• Free Motion of a Dirac Particle with a Minimum Uncertainty in Position
• Reconciling microscopic and macroscopic tests of the Compton-Schwarzschild correspondence
• Minimum Length - Maximum Velocity
• Rainbow Spacetime from a Nonlocal Gravitational Uncertainty Principle
• Kinetic energy properties and weak equivalence principle in a space with GUP
• Zero-point gravitational field equations
• A Stringy Effect on Hawking Radiation
• Spinning Toroidal Brane Cosmology; A Classical and Quantum Survey
• Towards new relativistic doubly $\kappa$-deformed D=4 quantum phase spaces
• Testing quantum gravity with dilute dipolar Bose gases
• Non-commutative coordinates from quantum gravity
• Generalized Uncertainty Principle from the Regularized Self-Energy
• Derivation of the deformed Heisenberg algebra from discrete spacetime
• Observational Viability of the Intermediate DBI Inflation in the Presence of a Minimal Length
• Relativistic Generalized Uncertainty Principle and Its Implications
• Quantum-gravitational corrections to the hydrogen atom and harmonic oscillator
• Entropic uncertainty relation based on generalized uncertainty principle
• Quantum Gravity Constraints on Fine Structure Constant from GUP in Braneworlds
• Quantized space-time and its influences on some physical problems
• Hawking Temperature in Taub-NUT (A)dS spaces via the Generalized Uncertainty Principle
• Szekeres Universes with GUP corrections
• f(R) in Holographic and Agegraphic Dark Energy Models and the Generalized Uncertainty Principle
• Tunneling and entropy analysis of parameterized black hole with rotating case
• Tidal effects based on GUP-induced effective metric
• Possible polarisation and spin dependent aspects of quantum gravity
• A consistent approach to the path integral formalism of quantum mechanics based on the maximum length uncertainty
• Scalar field inflation driven by a modification of the Heisenberg algebra
• Bounded compactness from G(E)UP
• Gravitational renormalization of quantum field theory: a "conservative" approach
• Thermal and Optical Signatures of Einstein-Dyonic ModMax Black Holes with GUP and Plasma Modifications
• Effects of the generalized uncertainty principle on the thermal properties of Kemmer oscillator
• Deformed Quantum Field Theory, Thermodynamics at Low and High Energies, and Gravity. I
• Quantum Klein Space and Superspace
• Extra-dimensional generalization of minimum-length deformed QM/QFT and some of its phenomenological consequences
• Lorentz invariance without trans-Planckian physics?
• Friedmann equations from GUP-modified equipartition law
• Removing the divergence of Chandrasekhar limit caused by generalized uncertainty principle
• Effects of modified dispersion relations on free Fermi gas: equations of state and applications in astrophysics
• A Poincaré Covariant Noncommutative Spacetime?
• Bose-Einstein Condensate and Liquid Helium He${}^4$: Implications of GUP and Modified Gravity Correspondence
• Thermodynamic modifications to Bardeen black holes surrounded by quintessence based on the new higher order GUP
• Holographic Cosmology from BIonic Solutions
• Some Implications of the Density Matrix Deformation in Statistical Mechanics of the Early Universe
• Noncommutative kappa-Minkowski phi4 theory: Construction, properties and propagation
• Noncommutative dispersion relation and mass-radius relation of white dwarfs
• Effects of a Generalized Uncertainty Principle on the MIT Bag Model Equation of State
• Corrections to the thermodynamic quantities of Bose system by the generalized uncertainty principle
• Problems with Modified Commutators
• Uncertainty principle and gravity
• Finite Temperature Considerations in the Structure of Quadratic GUP-modified White Dwarfs
• Quantum hoop conjecture and a natural cutoff for vacuum energy of a scalar field
• Minimal Quantities and Measurability. Gravity in Measurable Format and Natural Transition to High Energies
• A Note on Coherent States with Quantum Gravity Effects
• Quantum-gravitational running/reduction of space-time dimension
• Lorentz-covariant sampling theory for fields
• Gravitational effective action at mesoscopic scales from the quantum microstructure of spacetime
• Prospect of Chandrasekhar's limit against modified dispersion relation
• Towards quantum Mechanics on the curved cotangent bundle
• Generalized uncertainty principles and black hole temperatures in rainbow gravity
• Many-body probes for quantum features of spacetime
• Generalized Uncertainty Principle: from the harmonic oscillator to a QFT toy model
• Thermal effects of a photon gas with a deformed Heisenberg algebra
• $\lambda {\varphi }^4$ Kink and sine-Gordon Soliton in the GUP Framework
• The tunneling radiation of Kehagias-Sfetsos black hole under generalized uncertainty principle
• Dynamical Features of Maggiore's Generalised Commutation Relations
• Short Distance Modification of a Gravitational System and its Optical Analog
• Wave Propagation and IR/UV Mixing in Noncommutative Spacetimes
• Kinematics and uncertainty relations of a quantum test particle in a curved space-time
• Quantum Black Hole as a Harmonic Oscillator from the Perspective of the Minimum Uncertainty Approach
• On the origin of generalized uncertainty principle from compactified M5-brane
• Quantum speed limit as a sensitive probe of Planck-scale effects
• A novel mechanism for probing the Planck scale with wavepackets following general distributions
• Hartmann potential with a minimal length and generalized recurrence relations for matrix elements
• Statistical Entropy Based on the Generalized-Uncertainty-Principle-Induced Effective Metric
• Remarks on the quasi-position representation in models of generalized uncertainty principle
• Emergent GUP from Modified Hawking Radiation in Einstein-NED Theory
• GUP, Lorentz Invariance (Non)-Violation, and Non-Commutative Geometry
• Non-commutative correction of ideal gas thermodynamics
• Energy-time uncertainty relation from entropy measures
• Minimal Proper-time in Quantum Field Theory
• Regularization of ${\delta }^{\prime }$ potential in general case of deformed space with minimal length
• Particle in a cavity in one-dimensional bandlimited quantum mechanics
• Towards a Quantum Erlangen Program
• Non-Heisenbergian quantum mechanics
• Density Matrix Deformations in Quantum and Statistical Mechanics at Planck-Scale
• The Black Hole Quantum Entropy and Its Minimal Value
• From minimal-length quantum theory to modified gravity
• Unitary equivalence in Generalized Uncertainty Principle theories
• Bouncing Bianchi Models with Deformed Commutation Relations
• Deformation of Nanowires and Nanotubes
• Uncertainty Principles and Non-local Black Holes
• Quantum gravity, the cosmological constant, and parity transformation
• Revealing some cosmological aspects of Kaniadakis entropy
• Self-adjoint extensions for a $p^4$-corrected Hamiltonian of a particle on a finite interval
• Quantum Spacetime and the Universe at the Big Bang, vanishing interactions and fading degrees of freedom
• Random versus holographic fluctuations of the background metric. II. Note on the dark energies arising due to microstructure of space-time
• Charged Massive Particle's Tunneling From Charged Non-Rotating Micro Black Hole
• Higher order GUP black hole based on COW experiment and Einstein-Bohr's photon box
• Quantum Hairy Black Hole Formation and Horizon Quantum Mechanics
• Time Evolution in Quantum Mechanics with a Minimal Time Scale
• Quantum Gravity Corrections to the Mean Field Theory of Nucleons
• Solution for a non linear Schrödinger equation via Hopf-Cole transformation
• Revisiting the algebraic structure of the generalized uncertainty principle
• Spacetime discreteness via consistent microscopic measurement
• Spontaneous Lorentz symmetry violation from infrared gravity
• Decoherence limit of quantum systems obeying generalized uncertainty principle: new paradigm for Tsallis thermostatistics
• Uncertainty Principles and Maximum Entropic Force
• Probing the Quantum Nature of Gravity in the Microgravity of Space
• A rotating GUP black hole: metric, shadow, and bounds on quantum parameters
• Tidal Deformation Bounds and Perturbation Transfer in Bounded Curvature Spacetimes
• Topics in Noncommutative Gauge Theories and Deformed Relativistic Theories
• A note on scattering in deformed space with minimal length
• Exact continuity equation in a space with minimal length
• One-dimension quantum systems in the framework of the most general deformation GUP form
• From MOND entropy to extended uncertainty principles: A unified framework
• GUP/BEB correspondence
• Mixmaster chaos in a quantum scenario:a Deformed Algebra approach
• Generalized uncertainty principle for a Dirac fermion in a torsion field
• The instability of a black hole with $f(R)$ global monopole under extended uncertainty principle
• Minimal-Length Corrections to Hyperon Polarization in Rotating Quark Gluon Plasma
• Compactification, T-Duality and Quantum Erasers
• Snyder Like Modified Gravity in Newton's Spacetime
• Quantum gravity phenomenology and the blackbody radiation
• Two Approaches to Measurability Concept and Quantum Theory
• Refining Bounds for Snyder and GUP Models through Seismic Wave Analysis
• Aharonov-Bohm-Like Scattering in the Generalized Uncertainty Principle-corrected Quantum Mechanics
• On the Heisenberg principle at macroscopic scales: understanding classical negative information. Towards a general physical theory of information
• Thermomagnetic Ettingshausen-Nernst effect in tachocline, magnetic reconnection phenomenon in lower layers, axion mechanism of solar luminosity variations, coronal heating problem solution and mechanism of ADM variations around BH
• Maximally localized states and quantum corrections of black hole thermodynamics in the extreme case with an improved exponential GUP
• Quantum Gravity Effect on The Time History of The Universe
• Hilbert space representation for quasi-Hermitian position-deformed Heisenberg algebra and Path integral formulation
• UV Effects and Short-Lived Hawking Radiation: Alternative Resolution of Information Paradox
• Probable Entropic Nature of Gravity in Ultraviolet and Infrared Limits, Part I. An Ultraviolet Case
• Equations for fields with additional fundamental physical constants
• Optical and Thermodynamic Signatures of Lorentz Symmetry Breaking in Bumblebee AdS Black Holes
• An algebraic approach to gravitational quantum mechanics