Reduced Hamiltonian for intersecting shells and Hawking radiation

Pietro Menotti

RECORD

Reduced Hamiltonian for intersecting shells and Hawking radiation

Pietro Menotti

General Relativity and Quantum Cosmology · Submitted 19 Dec 2009

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

The authors' main claim We give the reduced hamiltonian for two intersecting shells, both massless and massive.

how it is stated · asserted 1.00 read the record →

Comment (0) Read on arXiv ↗

Cite ▾

Claim paper

The compiled record

The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Open the compiled record

Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,537 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.07 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.04 · compares with prior results 0.16 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; show every role.

We consider the dynamics of one or more self gravitating shells of matter in a centrally symmetric gravitational field in the Painleve' family of gauges. We give the reduced hamiltonian for two intersecting shells, both massless and massive. Such a formulation is applied to the computation of the semiclassical action of two intersecting shells. The relation of the imaginary part of the space-part of the action to the computation of the Bogoliubov coefficients is revisited.

background contribution method result interpretation main claim

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	We consider the dynamics of one or more self gravitating shells of matter in a centrally symmetric gravitational field in the Painleve' family of gauges.	background 0.71	0.56	0.04	asserted 0.80
s1	We give the reduced hamiltonian for two intersecting shells, both massless and massive.	contribution 0.82	0.94	0.32	asserted 1.00
s2	Such a formulation is applied to the computation of the semiclassical action of two intersecting shells.	contribution 0.63	0.89	0.11	asserted 1.00
s3	The relation of the imaginary part of the space-part of the action to the computation of the Bogoliubov coefficients is revisited.	contribution 0.72	0.56	0.12	asserted 0.63

What kind of paper the classifier reports this is: theoretical result 0.99 · evidence from proof or derivation 1.00.

What was examined, and what was not

sources read

arXiv listing abstract v1

not examined

full text
figures and tables
references and citing sentences
relations to other papers

levels run

P abstract

not run

S sections
T body sentences
C citations
R cross-paper relations

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 consider the dynamics of one or more self gravitating shells of matter in a centrally symmetric gravitational field in the Painleve' family of gauges. We give the reduced hamiltonian for two intersecting shells, both massless and massive. Such a formulation is applied to the computation of the semiclassical action of two intersecting shells. The relation of the imaginary part of the space-part of the action to the computation of the Bogoliubov coefficients is revisited.

Human review

How Pith checks papers → · Full audit of this paper →

How the literature uses it

1 arXiv paper cite this in 2 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

Papers citing it

Cites it as background 1 paper

The shell dynamics was studied in detail in many papers (see [ref] where also a more complete list of references is found).

Late-time expansion in the semiclassical theory of the Hawking radiation · Introduction · 0.98

What it cites · 40 sentences without a confident label

Builds on 3 papers

The main results we shall report here are the extension of the treatment to one massive shell of matter and also the extension to two or more massive shells of matter which in the time development can also intersect [ref] .

Reduced Hamiltonian for intersecting shells · Introduction · 0.85
We extended the treatment of [ref] to more than one shell [ref] proving on the way the universality of the reduced conjugate momentum within the family of Painlevé gauges [ref] .

On the semiclassical treatment of Hawking radiation · Concluding remarks · 1.00
We extended the treatment of [ref] to more than one shell [ref] proving on the way the universality of the reduced conjugate momentum within the family of Painlevé gauges [ref] .

Self-Interaction Correction to Black Hole Radiance · Concluding remarks · 1.00

Uses the method or tool of 5 papers

We shall keep the formalism for more that one shell as close as possible to the original formalism of [ref] which can be summarized in words that we shall adopt a Painlevé gauge.

Self-Interaction Correction to Black Hole Radiance · Introduction · 0.85
As usual we write the metric for a spherically symmetric configuration in the ADM form [equation] were following [ref] we shall choose the functions $N, N^r, L, R$ as continuous functions of the coordinates.

Reduced phase space formalism for spherically symmetric geometry with a massive dust shell · The reduced action · 0.94
As usual we write the metric for a spherically symmetric configuration in the ADM form [equation] were following [ref] we shall choose the functions $N, N^r, L, R$ as continuous functions of the coordinates.

Hamiltonian spacetime dynamics with a spherical null-dust shell · The reduced action · 0.94

Compares with 1 paper

In deriving eq.([ref]) we used the consequences of the constraints ([ref],[ref]) [equation] In the outer gauge we find [equation] with $p̂$ given implicitly by [equation] This is the result obtained by Friedman, Louko, Winters-Hilt [ref] through a limit procedure in which the support of the deformation function goes to zero but actually it is independent of the deformation.

Reduced phase space formalism for spherically symmetric geometry with a massive dust shell · The reduced action · 0.93

Cites as support 1 paper

One can consider also the more general gauges depicted in Fig.3 and it can be proven [ref] that $p_c$ is always the same.

On the semiclassical treatment of Hawking radiation · The reduced action · 0.97

Cites as background 2 papers

Such field of research was started by the papers by Kraus and Wilczek [ref] .

Self-Interaction Correction to Black Hole Radiance · Introduction · 0.95
Such field of research was started by the papers by Kraus and Wilczek [ref] .

Effect of Self-Interaction on Charged Black Hole Radiance · Introduction · 0.95

Discussion

Know something about this paper? Leave a comment, or highlight any passage above to comment on it.