scholarly journals THE SCATTERING MATRIX APPROACH FOR THE QUANTUM BLACK HOLE: AN OVERVIEW

1996 ◽  
Vol 11 (26) ◽  
pp. 4623-4688 ◽  
Author(s):  
G. 'T HOOFT
Keyword(s):  
Black Hole ◽  
Degrees Of Freedom ◽  
Flat Space ◽  
Scattering Matrix ◽  
Quantum Mechanical ◽  
Quantum Field ◽  
Quantum Black Hole ◽  
Quantum Mechanical Description ◽  
Starting Point ◽  
Alternative Approaches

If one assumes the validity of conventional quantum field theory in the vicinity of the horizon of a black hole, one does not find a quantum-mechanical description of the entire black hole that even remotely resembles that of conventional forms of matter; in contrast with matter made out of ordinary particles one finds that, even if embedded in a finite volume, a black hole would be predicted to have a strictly continuous spectrum. Dissatisfied with such a result, which indeed hinges on assumptions concerning the horizon that may well be wrong, various investigators have now tried to formulate alternative approaches to the problem of “quantizing” the black hole. We here review the approach based on the assumption of quantum-mechanical purity and unitarity as a starting point, as has been advocated by the present author for some time, concentrating on the physics of the states that should live on a black hole horizon. The approach is shown to be powerful in producing not only promising models for the quantum black hole, but also new insights concerning the dynamics of physical degrees of freedom in ordinary flat space–time.

TOPOLOGICAL QUANTUM MECHANICS IN 2+1 DIMENSIONS

1990 ◽  
Vol 05 (08) ◽  
pp. 1575-1595 ◽  
Author(s):  
B.-S. SKAGERSTAM ◽  
A. STERN
Keyword(s):  
Quantum Mechanics ◽  
Degrees Of Freedom ◽  
Flat Space ◽  
Noncommutative Space ◽  
Quantum Mechanical ◽  
De Sitter ◽  
Spinning Particles ◽  
Topological Quantum ◽  
Quantum Mechanical Description ◽  
Adjoint Orbits

We show that the classical and quantum covariant dynamics of spinning particles in flat space in 2+1 dimensions are derived from a pure Wess-Zumino term written on the space of adjoint orbits of the ISO(2, 1) group. Similarly, the dynamics of spinning particles in 2+1 de Sitter [anti-de Sitter] space are derived from a Wess-Zumino term on the space of adjoint orbits of SO(3, 1) [SO(2, 2)]. It is shown that a quantum mechanical description of spin is possible in 2+1 dimensions without introducing explicit spin degrees of freedom, but at the expense of having a noncommutative space-time geometry.

scholarly journals Black hole hair removal for N = 4 CHL models

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Subhroneel Chakrabarti ◽  
Suresh Govindarajan ◽  
P. Shanmugapriya ◽  
Yogesh K. Srivastava ◽  
Amitabh Virmani
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Degrees Of Freedom ◽  
Microscopic Analysis ◽  
Flat Space ◽  
Special Care ◽  
Hair Removal ◽  
Partition Functions ◽  
Rotating Black Holes

Abstract Although BMPV black holes in flat space and in Taub-NUT space have identical near-horizon geometries, they have different indices from the microscopic analysis. For K3 compactification of type IIB theory, Sen et al. in a series of papers identified that the key to resolving this puzzle is the black hole hair modes: smooth, normalisable, bosonic and fermionic degrees of freedom living outside the horizon. In this paper, we extend their study to N = 4 CHL orbifold models. For these models, the puzzle is more challenging due to the presence of the twisted sectors. We identify hair modes in the untwisted as well as twisted sectors. We show that after removing the contributions of the hair modes from the microscopic partition functions, the 4d and 5d horizon partition functions agree. Special care is taken to present details on the smoothness analysis of hair modes for rotating black holes, thereby filling an essential gap in the literature.

scholarly journals BLACK HOLE EVAPORATION BASED UPON A q-DEFORMATION DESCRIPTION

2005 ◽  
Vol 20 (26) ◽  
pp. 6039-6049 ◽  
Author(s):  
XIN ZHANG
Keyword(s):  
Black Hole ◽  
Degrees Of Freedom ◽  
Radiation Spectrum ◽  
Correlation Effect ◽  
Space Time ◽  
Noncommutative Space ◽  
Schwarzschild Black Hole ◽  
Black Hole Evaporation ◽  
Starting Point ◽  
New Distribution

A toy model based upon the q-deformation description for studying the radiation spectrum of black hole is proposed. The starting point is to make an attempt to consider the space–time noncommutativity in the vicinity of black hole horizon. We use a trick that all the space–time noncommutative effects are ascribed to the modification of the behavior of the radiation field of black hole and a kind of q-deformed degrees of freedom are postulated to mimic the radiation particles that live on the noncommutative space–time, meanwhile the background metric is preserved as usual. We calculate the radiation spectrum of Schwarzschild black hole in this framework. The new distribution deviates from the standard thermal spectrum evidently. The result indicates that some correlation effect will be introduced to the system if the noncommutativity is taken into account. In addition, an infrared cutoff of the spectrum is the prediction of the model.

scholarly journals FROM BRICKS TO QUASINORMAL MODES: A NEW PERSPECTIVE ON BLACK HOLE ENTROPY

2013 ◽  
Vol 22 (12) ◽  
pp. 1342027 ◽  
Author(s):  
MICHELE ARZANO ◽  
STEFANO BIANCO ◽  
OLAF DREYER
Keyword(s):  
Black Hole ◽  
Short Distance ◽  
Degrees Of Freedom ◽  
Quasinormal Modes ◽  
Black Hole Entropy ◽  
Quantum Field ◽  
Extended Region ◽  
New Perspective ◽  
The Right ◽  
Dynamical Degrees

Calculations of black hole entropy based on the counting of modes of a quantum field propagating in a Schwarzschild background need to be regularized in the vicinity of the horizon. To obtain the Bekenstein–Hawking result, the short distance cut-off needs to be fixed by hand. In this note, we give an argument for obtaining this cut-off in a natural fashion. We do this by modeling the black hole by its set of quasinormal modes (QNMs). The horizon then becomes a extended region: the quantum ergosphere. The interaction of the quantum ergosphere and the quantum field provides a natural regularization mechanism. The width of the quantum ergosphere provides the right cut-off for the entropy calculation. We arrive at a dual picture of black hole entropy. The entropy of the black hole is given both by the entropy of the quantum field in the bulk and the dynamical degrees of freedom on the horizon.

scholarly journals Where are the degrees of freedom responsible for black-hole entropy?

2008 ◽  
Vol 86 (4) ◽  
pp. 653-658 ◽  
Author(s):  
S Das ◽  
S Shankaranarayanan ◽  
S Sur
Keyword(s):  
Black Hole ◽  
Excited State ◽  
Power Law ◽  
Ground State ◽  
Degrees Of Freedom ◽  
Black Hole Entropy ◽  
Quantum Field ◽  
Hole Area ◽  
Area Law ◽  
03.65 Ud

Considering the entanglement between quantum field degrees of freedom inside and outside the horizon as a plausible source of black-hole entropy, we address the question: where are the degrees of freedom that give rise to this entropy located? When the field is in ground state, the black-hole area law is obeyed and the degrees of freedom near the horizon contribute most to the entropy. However, for excited state, or a superposition of ground state and excited state, power-law corrections to the area law are obtained, and more significant contributions from the degrees of freedom far from the horizon are shown.PACS Nos.: 04.60.–m, 04.62., 04.70.–s, 03.65.Ud

scholarly journals Charged quantum fields in AdS$_2$

2019 ◽  
Vol 7 (4) ◽  
Author(s):  
Dionysios Anninos ◽  
Diego Hofman ◽  
Jorrit Kruthoff
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Black Hole ◽  
Kerr Black Hole ◽  
Principal Series ◽  
Flat Space ◽  
Quantum Field ◽  
Quantum Fields ◽  
Electrically Charged ◽  
Large Charge

We consider quantum field theory near the horizon of an extreme Kerr black hole. In this limit, the dynamics is well approximated by a tower of electrically charged fields propagating in an SL(2,\mathbb{R})SL(2,ℝ) invariant AdS_22 geometry endowed with a constant, symmetry preserving background electric field. At large charge the fields oscillate near the AdS_22 boundary and no longer admit a standard Dirichlet treatment. From the Kerr black hole perspective, this phenomenon is related to the presence of an ergosphere. We discuss a definition for the quantum field theory whereby we ‘UV’ complete AdS_22 by appending an asymptotically two dimensional Minkowski region. This allows the construction of a novel observable for the flux-carrying modes that resembles the standard flat space SS-matrix. We relate various features displayed by the highly charged particles to the principal series representations of SL(2,\mathbb{R})SL(2,ℝ). These representations are unitary and also appear for massive quantum fields in dS_22.

scholarly journals Improved effective dynamics of loop-quantum-gravity black hole and Nariai limit

2021 ◽  
Author(s):  
Muxin Han ◽  
Hongguang Liu
Keyword(s):  
Black Hole ◽  
Quantum Gravity ◽  
Degrees Of Freedom ◽  
Loop Quantum Gravity ◽  
Late Time ◽  
White Hole ◽  
Quantum Black Hole ◽  
Effective Dynamics ◽  
Symmetric Quantum ◽  
Space Formulation

Abstract We propose a new model of the spherical symmetric quantum black hole in the reduced phase space formulation. We deparametrize gravity by coupling to the Gaussian dust which provides the material coordinates. The foliation by dust coordinates covers both the interior and exterior of the black hole. After the spherical symmetry reduction, our model is a 1+1 dimensional field theory containing infinitely many degrees of freedom. The effective dynamics of the quantum black hole is generated by an improved physical Hamiltonian ${\bf H}_\Delta$. The holonomy correction in ${\bf H}_\Delta$ is implemented by the $\bar{\mu}$-scheme regularization with a Planckian area scale $\Delta$ (which often chosen as the minimal area gap in Loop Quantum Gravity). The effective dynamics recovers the semiclassical Schwarzschild geometry at low curvature regime and resolves the black hole singularity with Planckian curvature, e.g. $R_{\mu\nu\rho\sigma}R^{\mu\nu\rho\sigma}\sim 1/{\Delta}^2$. Our model predicts that the evolution of the black hole at late time reaches the charged Nariai geometry ${\rm dS}_2\times S^2$ with Planckian radii $\sim \sqrt{\Delta}$. The Nariai geometry is stable under linear perturbations but may be unstable by nonperturbative quantum effects. Our model suggests the existence of quantum tunneling of the Nariai geometry and a scenario of black-hole-to-white-hole transition.

scholarly journals Anti-Newtonian Expansions and the Functional Renormalization Group

Universe ◽  
2019 ◽  
Vol 5 (3) ◽  
pp. 85 ◽  
Author(s):  
Max Niedermaier
Keyword(s):  
Renormalization Group ◽  
Degrees Of Freedom ◽  
World Line ◽  
Newtonian Limit ◽  
Field Theories ◽  
Quantum Mechanical ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Functional Renormalization Group ◽  
Scalar Quantum

Anti-Newtonian expansions are introduced for scalar quantum field theories and classical gravity. They expand around a limiting theory that evolves only in time while the spatial points are dynamically decoupled. Higher orders of the expansion re-introduce spatial interactions and produce overlapping lightcones from the limiting isolated world line evolution. In scalar quantum field theories, the limiting system consists of copies of a self-interacting quantum mechanical system. In a spatially discretized setting, a nonlinear “graph transform” arises that produces an in principle exact solution of the Functional Renormalization Group for the Legendre effective action. The quantum mechanical input data can be prepared from its 1 + 0 dimensional counterpart. In Einstein gravity, the anti-Newtonian limit has no dynamical spatial gradients, yet remains fully diffeomorphism invariant and propagates the original number of degrees of freedom. A canonical transformation (trivialization map) is constructed, in powers of a fractional inverse of Newton’s constant, that maps the ADM action into its anti-Newtonian limit. We outline the prospects of an associated trivializing flow in the quantum theory.

scholarly journals THE GAUGE SYMMETRY OF THE THIRD KIND AND QUANTUM MECHANICS AS AN INFRARED LIMIT

2007 ◽  
Vol 05 (01n02) ◽  
pp. 215-222 ◽  
Author(s):  
HANS-THOMAS ELZE
Keyword(s):  
Field Theory ◽  
Degrees Of Freedom ◽  
Quantum Mechanical ◽  
Dynamical Structure ◽  
Quantum Field ◽  
The Third ◽  
Gauge Principle ◽  
Fundamental Length ◽  
Infrared Limit ◽  
Quantum Mechanical Systems

We introduce functional degrees of freedom by a new gauge principle related to the phase of the wave functional. Thus, quantum mechanical systems are dissipatively embedded into a nonlinear classical dynamical structure. There is a necessary fundamental length, besides an entropy/area parameter, and standard couplings. For states that are sufficiently spread over configuration space, quantum field theory is recovered.

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