Near-Horizon Conformal Structure of Black Holes

Abstract

The near-horizon properties of a black hole are studied within an algebraic framework, using a scalar field as a simple probe to analyze the geometry. The operator H governing the near-horizon dynamics of the scalar field contains an inverse square interaction term. It is shown that the operators appearing in the corresponding algebraic description belong to the representation space of the Virasoro algebra. The operator H is studied using the representation theory of the Virasoro algebra. We observe that the wave functions exhibit scaling behaviour in a band-like region near the horizon of the black hole.

9 pages, Latex

Cited by in corpus (101)

• Conformal Field Theory, (2+1)-Dimensional Gravity, and the BTZ Black Hole
• Anomaly in conformal quantum mechanics: From molecular physics to black holes
• Further Evidence for the Conformal Structure of a Schwarzschild Black Hole in an Algebraic Approach
• Conformal structure of the Schwarzschild black hole
• Singular inverse square potential in arbitrary dimensions with a minimal length: Application to the motion of a dipole in a cosmic string background
• Inequivalent Quantizations of the Rational Calogero Model
• Horizon Constraints and Black Hole Entropy
• Horizon constraints and black hole entropy
• Black Hole Thermodynamics from Near-Horizon Conformal Quantum Mechanics
• Novel Quantum States of the Rational Calogero Models Without the Confining Interaction
• Symmetries, Horizons, and Black Hole Entropy
• Near-horizon aspects of acceleration radiation by free fall of an atom into a black hole
• On the Universality of Hawking Radiation
• On the resolvent and spectral functions of a second order differential operator with a regular singularity
• CFT/Gravity Correspondence on the Isolated Horizon
• Black Hole Thermodynamics and Statistical Mechanics
• Electron Capture and Scaling Anomaly in Polar Molecules
• Bound States in One-Dimensional Quantum N-Body Systems with Inverse Square Interaction
• Singular inverse square potential in coordinate space with a minimal length
• Quasinormal modes for single horizon black holes in generic 2-d dilaton gravity
• Unusual poles of the $\zeta$-functions for some regular singular differential operators
• Renormalization in conformal quantum mechanics
• Acceleration radiation of an atom freely falling into a Kerr black hole and near-horizon conformal quantum mechanics
• Effects of Noncommutativity on the Black Hole Entropy
• Semiclassical Methods in Curved Spacetime and Black Hole Thermodynamics
• Aspects of hidden and manifest SL(2,R) symmetry in 2D near-horizon black-hole background
• A multispecies Calogero model
• Hidden conformal symmetry on the black hole photon sphere
• Bound States in Gapped Graphene with Impurities : Effective Low-Energy Description of Short-Range Interactions
• Quantization and Conformal Properties of a Generalized Calogero Model
• The Exact String Black-Hole behind the hadronic Rindler horizon?
• Singular inverse-square potential: renormalization and self-adjoint extensions for medium to weak coupling
• Black Hole Thermodynamics from Euclidean Horizon Constraints
• Quantum statistics and noncommutative black holes
• Quantum Tunneling and Caustics under Inverse Square Potential
• Calogero model, deformed oscillators and the collapse
• Black Hole Entropy and the Problem of Universality
• Generalized Calogero model in arbitrary dimensions
• Universal canonical entropy for gravitating systems
• Horizons, Constraints, and Black Hole Entropy
• Dipole binding in a cosmic string background due to quantum anomalies
• Atom capture by nanotube and scaling anomaly
• Critical scalar field collapse in AdS_3: an analytic approach
• Universal near-horizon conformal structure and black hole entropy
• On the Inequivalence of Renormalization and Self-Adjoint Extensions for Quantum Singular Interactions
• Explanatory Depth in Primordial Cosmology: A Comparative Study of Inflationary and Bouncing Paradigms
• Scalar Field Probes of Power-Law Space-Time Singularities
• 2D Black Holes, Conformal Vacua and CFTs on the Cylinder
• Functional determinants for general self-adjoint extensions of Laplace-type operators resulting from the generalized cone
• Conformal Tightness of Holographic Scaling in Black Hole Thermodynamics
• Observables in Quantum Mechanics and the Importance of Self-adjointness
• Black Hole Entropy and the Problem of Universality
• Black Holes as Conformal Field Theories on Horizons
• Scalar field dynamics in warped AdS_3 black hole background
• Time of falling of a quantum particle into an inverse square potential
• Universal properties of conformal quantum many-body systems
• A Unified Algebraic Approach to Few and Many-Body Correlated Systems
• Matrix oscillator and Calogero-type models
• Novel black hole bound states and entropy
• Solitons in the Calogero model for distinguishable particles
• A Dirac type xp-Model and the Riemann Zeros
• A note on the hidden conformal structure of non-extremal black holes
• Collective Field Formulation of the Multispecies Calogero Model and its Duality Symmetries
• Horizon Conformal Field Theories from $Ad{S}_2$ Black Holes
• Inequivalent Quantizations of the N = 3 Calogero model with Scale and Mirror-S_3 Symmetry
• Orthogonality catastrophe and fractional exclusion statistics
• Conformal Quantum Mechanics in Two Black Hole Moduli Space
• Liouville Theory on Horizons: Towards a Quantum Theory of Black Holes
• AdS segment and hidden conformal symmetry in general non-extremal black holes
• Duality between the quantum inverted harmonic oscillator and inverse square potentials
• Hidden Degeneracy in the Brick Wall Model of Black Holes
• Quantum space and quantum completeness
• Near-Horizon States of Black Holes and Calogero Models
• Normal mode analysis for scalar fields in BTZ black hole background
• Extremal Black Hole Entropy from Horizon Conformal Field Theories
• SUSY shields the scaling symmetry of conformal quantum mechanics
• Duality and interacting families in models with the inverse-squared interaction
• Conformal quantum mechanics and holography in noncommutative space-time
• Conformal quantum mechanics of causal diamonds: Time evolution, thermality, and instability via path integral functionals
• Conformal anomaly in non-hermitian quantum mechanics
• Inequivalent quantization of the rational Calogero model with a Coulomb type interaction
• Hidden conformal symmetries for black holes in modified gravity
• Quantum aspects of spacetime: A quantum optics view of acceleration radiation and black holes
• Black Holes, Holography and Moduli Space Metric
• Black Hole Decay as Geodesic Motion
• Near-Horizon Geometry and the Entropy of a Minimally Coupled Scalar Field in the Schwarzschild Black Hole
• Dirac spinors in solenoidal field and self adjoint extensions of its Hamiltonian
• Fall-to-the-centre as a $\mathcal{P}\mathcal{T}$ symmetry breaking transition
• Inequivalent quantization in the field of a ferromagnetic wire
• Hidden scale in quantum mechanics
• Anomalies and Renormalization of Impure States in Quantum Theories
• Multichannel Framework for Singular Quantum Mechanics
• Effects of external field and potential on non-relativistic quantum particles in disclinations background
• Spectral Functions of Singular Operators
• Krein's Formula And Heat-Kernel Expansion For Some Differential Operators With A Regular Singularity
• Inverse square problem and so(2,1) symmetry in noncommutative space
• Symmetries of the near horizon of a Black Hole by Group Theoretic methods
• The Cardy-Verlinde equation in a spherical symmetric gravitational collapse
• Quantum optics meets black hole thermodynamics via conformal quantum mechanics: I. Master equation for acceleration radiation
• Quantization of exciton in magnetic field background
• Totally classical Calogero model