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The Quantum States and the Statistical Entropy of the Charged Black Hole

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Cenalo Vaz, Louis Witten

General Relativity and Quantum Cosmology · Submitted 12 Jun 2000

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We also compute the entropy in the microcanonical ensemble and show that the entropy of the Reissner-Nordstr\"om black hole is proportional to this quantized difference in horizon areas.

how it is stated · asserted 1.00 read the record →

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arXiv IDgr-qc/0006039 (version 2)
Pith IDKVNQ7RNI, Pith's permanent record of this paper and its review
CitationCenalo Vaz, Louis Witten. "The Quantum States and the Statistical Entropy of the Charged Black Hole." arXiv:gr-qc/0006039 (2000). https://pith.science/paper/KVNQ7RNI
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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 5,021 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.84 · human participants 0.01 · controlled comparison 0.03 · randomized assignment 0.01 · states quantitative result 0.51 · compares with prior results 0.94 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; .

We quantize the Reissner-Nordstr\"om black hole using an adaptation of Kucha\v{r}'s canonical decomposition of the Kruskal extension of the Schwarzschild black hole. The Wheeler-DeWitt equation turns into a functional Schroedinger equation in Gaussian time by coupling the gravitational field to a reference fluid or dust. The physical phase space of the theory is spanned by the mass, $M$, the charge, $Q$, the physical radius, $R$, the dust proper time, $\tau$, and their canonical momenta. The exact solutions of the functional Schroedinger equation imply that the difference in the areas of the outer and inner horizons is quantized in integer units. This agrees in spirit, but not precisely, with Bekenstein's proposal on the discrete horizon area spectrum of black holes. We also compute the entropy in the microcanonical ensemble and show that the entropy of the Reissner-Nordstr\"om black hole is proportional to this quantized difference in horizon areas.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 We quantize the Reissner-Nordstr\"om black hole using an adaptation of Kucha\v{r}'s canonical decomposition of the Kruskal extension of the Schwarzschild black hole. method 0.79 0.93 0.04 asserted 1.00
s1 The Wheeler-DeWitt equation turns into a functional Schroedinger equation in Gaussian time by coupling the gravitational field to a reference fluid or dust. method 0.97 0.64 0.04 asserted 1.00
s2 The physical phase space of the theory is spanned by the mass, $M$, the charge, $Q$, the physical radius, $R$, the dust proper time, $\tau$, and their canonical momenta. method 0.84 0.73 0.05 asserted 1.00
s3 The exact solutions of the functional Schroedinger equation imply that the difference in the areas of the outer and inner horizons is quantized in integer units. result 0.98 0.92 0.50 asserted 1.00
s4 This agrees in spirit, but not precisely, with Bekenstein's proposal on the discrete horizon area spectrum of black holes. interpretation 0.92 0.36 0.10 asserted 0.86
s5 We also compute the entropy in the microcanonical ensemble and show that the entropy of the Reissner-Nordstr\"om black hole is proportional to this quantized difference in horizon areas. result 0.98 0.96 0.49 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

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  • references and citing sentences
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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

We quantize the Reissner-Nordstr\"om black hole using an adaptation of Kucha\v{r}'s canonical decomposition of the Kruskal extension of the Schwarzschild black hole. The Wheeler-DeWitt equation turns into a functional Schroedinger equation in Gaussian time by coupling the gravitational field to a reference fluid or dust. The physical phase space of the theory is spanned by the mass, $M$, the charge, $Q$, the physical radius, $R$, the dust proper time, $\tau$, and their canonical momenta. The exact solutions of the functional Schroedinger equation imply that the difference in the areas of the outer and inner horizons is quantized in integer units. This agrees in spirit, but not precisely, with Bekenstein's proposal on the discrete horizon area spectrum of black holes. We also compute the entropy in the microcanonical ensemble and show that the entropy of the Reissner-Nordstr\"om black hole is proportional to this quantized difference in horizon areas.

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Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it

Builds on it 1 paper
  • Partially successful extensions of the methods used in [ref] to the study of other types of black holes appear in [ref] .

    Quantization of Midisuperspace Models · Quantization of spherically symmetric midisuperspaces · 0.95

Cites it as background 1 paper
  • A series of papers [ref] dealing with the quantization of spherically symmetric models coupled to matter is due to Kiefer, Louko, Vaz, L.

    Quantization of Midisuperspace Models · Quantization of spherically symmetric midisuperspaces · 0.95

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