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Energy spectrum of black holes : a new view
General Relativity and Quantum Cosmology · Submitted 20 Mar 2013
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim The energy spectrum that we obtain, explicitly reveals the correspondence between asymptotic and local observations through the presence of the surface gravity of the horizon as a parameter in the spectrum, rather than being expressed as a function of area and consequently getting quantized in the usual approach.
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The abstract, sentence by sentence
Energy of a black hole is usually quantized by invoking some area quantization scheme after expressing the energy in terms of the horizon area. However, in this approach one has to quantize the local and asymptotic energy of the black hole separately and the two results do not manifest any physical correspondence with each other. Here, as opposed to this practice, we find the unique energy spectrum of black holes by adopting a top-down approach. The physical links among the underlying quantum theory, statistical mechanics and thermodynamics of the black hole horizon play the central role in determining the energy spectrum. The energy spectrum that we obtain, explicitly reveals the correspondence between asymptotic and local observations through the presence of the surface gravity of the horizon as a parameter in the spectrum, rather than being expressed as a function of area and consequently getting quantized in the usual approach. Thus, our result presents a new view as far as black hole energy quantization is concerned. The calculations are performed using the quantum geometric description of black hole horizons as laid down by loop quantum gravity.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | Energy of a black hole is usually quantized by invoking some area quantization scheme after expressing the energy in terms of the horizon area. | background 1.00 | 0.04 | 0.03 | asserted 0.99 |
| s1 | However, in this approach one has to quantize the local and asymptotic energy of the black hole separately and the two results do not manifest any physical correspondence with each other. | gap 0.51 | 0.07 | 0.04 | asserted 1.00 |
| s2 | Here, as opposed to this practice, we find the unique energy spectrum of black holes by adopting a top-down approach. | contribution 0.95 | 0.95 | 0.22 | asserted 1.00 |
| s3 | The physical links among the underlying quantum theory, statistical mechanics and thermodynamics of the black hole horizon play the central role in determining the energy spectrum. | method 0.72 | 0.59 | 0.14 | asserted 1.00 |
| s4 | The energy spectrum that we obtain, explicitly reveals the correspondence between asymptotic and local observations through the presence of the surface gravity of the horizon as a parameter in the spectrum, rather than being expressed as a function of area and consequently getting quantized in the usual approach. | result 0.76 | 0.94 | 0.69 | asserted 1.00 |
| s5 | Thus, our result presents a new view as far as black hole energy quantization is concerned. | interpretation 0.96 | 0.65 | 0.33 | asserted 0.95 |
| s6 | The calculations are performed using the quantum geometric description of black hole horizons as laid down by loop quantum gravity. | method 1.00 | 0.71 | 0.03 | asserted 1.00 |
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The paper
Original abstract
Energy of a black hole is usually quantized by invoking some area quantization scheme after expressing the energy in terms of the horizon area. However, in this approach one has to quantize the local and asymptotic energy of the black hole separately and the two results do not manifest any physical correspondence with each other. Here, as opposed to this practice, we find the unique energy spectrum of black holes by adopting a top-down approach. The physical links among the underlying quantum theory, statistical mechanics and thermodynamics of the black hole horizon play the central role in determining the energy spectrum. The energy spectrum that we obtain, explicitly reveals the correspondence between asymptotic and local observations through the presence of the surface gravity of the horizon as a parameter in the spectrum, rather than being expressed as a function of area and consequently getting quantized in the usual approach. Thus, our result presents a new view as far as black hole energy quantization is concerned. The calculations are performed using the quantum geometric description of black hole horizons as laid down by loop quantum gravity.
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How the literature uses it
4 arXiv papers cite this in 14 sentences
What it cites · 43 sentences without a confident label
Cites as support 2 papers
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Furthermore, one can show [ref] that the expectation values of the proposed Hamiltonian and area operators for the QIH are proportional for a given $Ł$.
Thermodynamics of Quantum Isolated Horizons with model Hamiltonians · Introduction · 0.99
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In [ref] , taking the Schwarzschild spacetime as an example, it has been explicitly shown that the equations of motion of the connection fields on the event horizon (a special case of IH) are that of a source coupled CS theory !
Schwarzschild horizon dynamics and SU(2) Chern-Simons theory · Introduction · 0.98
Cites as background 10 papers
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A quantum black hole spacetime is effectively described by a quantum isolated horizon(QIH) coupled to the bulk spin network graphs at specific points called punctures, which carry the SU(2) spin representations of the corresponding intersecting edges of the graph [ref] .
Quantum Geometry of Isolated Horizons and Black Hole Entropy · Introduction · 0.97
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A quantum black hole spacetime is effectively described by a quantum isolated horizon(QIH) coupled to the bulk spin network graphs at specific points called punctures, which carry the SU(2) spin representations of the corresponding intersecting edges of the graph [ref] .
Quantum Geometry and Black Hole Entropy · Introduction · 0.97
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The area operator is a gauge invariant, self-adjoint observable in loop quantum gravity(LQG) defined for any arbitrary two dimensional surface $(S)$ embedded in the three dimensional spatial manifold $(Σ)$ obtained from a specific foliation of the four dimensional spacetime manifold $(M≡R⊗Σ)$ by some preferred time evolution vector field $(t)$ [ref] .
Discreteness of area and volume in quantum gravity · Introduction · 0.93
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