Thermodynamics of Quantum Isolated Horizons with model Hamiltonians

Abhishek Majhi

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Thermodynamics of Quantum Isolated Horizons with model Hamiltonians

Abhishek Majhi

General Relativity and Quantum Cosmology · Submitted 20 Mar 2013

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

The authors' main claim Arguing that the known classical results must follow in the correspondence limit (viz. the equilibrium temperature as observed by a local observer) the model is fixed, yielding the energy spectrum of the QIH.

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What the abstract itself states, as probabilities: claims first 0.06 · states limitation 0.22 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.07 · compares with prior results 0.44 · mentions code or data availability 0.02.

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Following a recent proposal, we consider the most general structure possible for the Hamiltonian operator associated with the Quantum Isolated Horizon(QIH) with explanations of the underlying physical motivations. An extensive thermodynamic analysis with this model Hamiltonian is presented. Considering {\it fixed} number of punctures, the canonical partition function can now be written in the usual energy ensemble. Arguing that the known classical results must follow in the correspondence limit (viz. the equilibrium temperature as observed by a local observer) the model is fixed, yielding the energy spectrum of the QIH.

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What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	Following a recent proposal, we consider the most general structure possible for the Hamiltonian operator associated with the Quantum Isolated Horizon(QIH) with explanations of the underlying physical motivations.	contribution 0.87	0.84	0.06	asserted 0.92
s1	An extensive thermodynamic analysis with this model Hamiltonian is presented.	contribution 0.86	0.91	0.08	asserted 0.99
s2	Considering {\it fixed} number of punctures, the canonical partition function can now be written in the usual energy ensemble.	method 0.91	0.76	0.07	asserted 0.85
s3	Arguing that the known classical results must follow in the correspondence limit (viz. the equilibrium temperature as observed by a local observer) the model is fixed, yielding the energy spectrum of the QIH.	method 0.45	0.84	0.46	asserted 0.94

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.93.

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Original abstract

Following a recent proposal, we consider the most general structure possible for the Hamiltonian operator associated with the Quantum Isolated Horizon(QIH) with explanations of the underlying physical motivations. An extensive thermodynamic analysis with this model Hamiltonian is presented. Considering {\it fixed} number of punctures, the canonical partition function can now be written in the usual energy ensemble. Arguing that the known classical results must follow in the correspondence limit (viz. the equilibrium temperature as observed by a local observer) the model is fixed, yielding the energy spectrum of the QIH.

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2 arXiv papers cite this in 7 sentences

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

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Cites it as support 1 paper

Furthermore, one can show [ref] that the expectation values of the proposed Hamiltonian and area operators for the QIH are proportional for a given $Ł$.

Energy spectrum of black holes : a new view · Introduction · 0.99

What it cites · 102 sentences without a confident label

Contests 1 paper

But, the proposal was based on some ad hoc arguments and semiclassical approximations and above all, QIHs with such energy spectrum has been shown to be thermodynamically unstable [ref] .

Stability of Quantum Isolated Horizon : A Local Observer's View · Model Hamiltonian and Energy spectrum of QIH · contest 0.82

Uses the method or tool of 2 papers

Now, to get more insight about the thermodynamical properties of QIH we shall switch over to the canonical ensemble and follow the arguments made in [ref] .

Charged Quantum Black Holes : Thermal Stability Criterion · Canonical Ensemble · 0.89
Now, to get more insight about the thermodynamical properties of QIH we shall switch over to the canonical ensemble and follow the arguments made in [ref] .

Generalized Hawking-Page Phase Transition · Canonical Ensemble · 0.89

Compares with 3 papers

Since, we have $=2π$, the above expression for specific heat reduces to $C=N^2d^2/d^2$, which is the expression for specific heat obtained in [ref] (correct expression to be found in the erratum).

Black hole entropy and isolated horizons thermodynamics · A Specific Case : $E_j ∝A_j$ · 0.89
Now, as far as the thermodynamic aspect of this paper is concerned, it is worth mentioning that unlike [ref] we deal with usual canonical energy ensemble as we have an explicit structure of the Hamiltonian.

The thermodynamic limit and black hole entropy in the area ensemble · Discussion · 0.92
Now, as far as the thermodynamic aspect of this paper is concerned, it is worth mentioning that unlike [ref] we deal with usual canonical energy ensemble as we have an explicit structure of the Hamiltonian.

On Quantum Statistical Mechanics of a Schwarzschild Black Hole · Discussion · 0.92

Cites as background 9 papers

As we begin with the quantum theory, the available knowledge at our disposal and relevant in this context are the quantum geometric area operators and area spectrum in LQG [ref] and the theory of QIH [ref] .

Quantum Theory of Gravity I: Area Operators · Model Hamiltonian and Energy spectrum of QIH · 1.00
As we begin with the quantum theory, the available knowledge at our disposal and relevant in this context are the quantum geometric area operators and area spectrum in LQG [ref] and the theory of QIH [ref] .

Quantum Geometry and Black Hole Entropy · Model Hamiltonian and Energy spectrum of QIH · 1.00
As we begin with the quantum theory, the available knowledge at our disposal and relevant in this context are the quantum geometric area operators and area spectrum in LQG [ref] and the theory of QIH [ref] .

Quantum Geometry of Isolated Horizons and Black Hole Entropy · Model Hamiltonian and Energy spectrum of QIH · 1.00

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