Quasi-local photon surfaces in general spherically symmetric spacetimes

Li-Ming Cao; Yong Song

RECORD

Quasi-local photon surfaces in general spherically symmetric spacetimes

Li-Ming Cao, Yong Song

General Relativity and Quantum Cosmology · Submitted 30 Oct 2019

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

The authors' main claim Based on this key investigation, we find an analytic photon surface solution in the Oppenheimer-Snyder (OS) model and reasonable numerical solutions for the marginally bounded collapse in the LTB model.

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-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 5,682 input tokens.

What the abstract itself states, as probabilities: claims first 0.07 · states limitation 0.21 · human participants 0.01 · controlled comparison 0.05 · randomized assignment 0.01 · states quantitative result 0.10 · compares with prior results 0.88 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v3. Results and the main claim are underlined; show every role.

Based on the geometry of the codimension-2 surface in a general spherically symmetric spacetime, we give a quasi-local definition of a photon sphere as well as a photon surface. This new definition is the generalization of the one by Claudel, Virbhadra, and Ellis but without reference to any umbilical hypersurface in the spacetime. The new definition effectively rules out the photon surface which has noting to do with gravity. The application of the definition to the Lemaitre-Tolman-Bondi (LTB) model of gravitational collapse reduces to a problem of a second order differential equation. We find that the energy balance on the boundary of the dust ball can provide one appropriate boundary condition to this equation. Based on this key investigation, we find an analytic photon surface solution in the Oppenheimer-Snyder (OS) model and reasonable numerical solutions for the marginally bounded collapse in the LTB model. Interestingly, in the OS model, we find that the time difference between the occurrence of the photon surface and the event horizon is mainly determined by the total mass of the system but not the size or the strength of gravitational field of the system.

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	Based on the geometry of the codimension-2 surface in a general spherically symmetric spacetime, we give a quasi-local definition of a photon sphere as well as a photon surface.	contribution 0.99	0.94	0.13	asserted 1.00
s1	This new definition is the generalization of the one by Claudel, Virbhadra, and Ellis but without reference to any umbilical hypersurface in the spacetime.	contribution 0.85	0.69	0.08	asserted 1.00
s2	The new definition effectively rules out the photon surface which has noting to do with gravity.	interpretation 0.61	0.71	0.11	asserted 1.00
s3	The application of the definition to the Lemaitre-Tolman-Bondi (LTB) model of gravitational collapse reduces to a problem of a second order differential equation.	method 0.93	0.83	0.06	asserted 1.00
s4	We find that the energy balance on the boundary of the dust ball can provide one appropriate boundary condition to this equation.	method 0.86	0.89	0.06	asserted 0.71
s5	Based on this key investigation, we find an analytic photon surface solution in the Oppenheimer-Snyder (OS) model and reasonable numerical solutions for the marginally bounded collapse in the LTB model.	result 0.99	0.97	0.42	asserted 1.00
s6	Interestingly, in the OS model, we find that the time difference between the occurrence of the photon surface and the event horizon is mainly determined by the total mass of the system but not the size or the strength of gravitational field of the system.	result 0.94	0.97	0.25	asserted 0.99

What kind of paper the classifier reports this is: theoretical result 0.94 · evidence from proof or derivation 0.99.

What was examined, and what was not

sources read

arXiv listing abstract v3

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

Based on the geometry of the codimension-2 surface in a general spherically symmetric spacetime, we give a quasi-local definition of a photon sphere as well as a photon surface. This new definition is the generalization of the one by Claudel, Virbhadra, and Ellis but without reference to any umbilical hypersurface in the spacetime. The new definition effectively rules out the photon surface which has noting to do with gravity. The application of the definition to the Lemaitre-Tolman-Bondi (LTB) model of gravitational collapse reduces to a problem of a second order differential equation. We find that the energy balance on the boundary of the dust ball can provide one appropriate boundary condition to this equation. Based on this key investigation, we find an analytic photon surface solution in the Oppenheimer-Snyder (OS) model and reasonable numerical solutions for the marginally bounded collapse in the LTB model. Interestingly, in the OS model, we find that the time difference between the occurrence of the photon surface and the event horizon is mainly determined by the total mass of the system but not the size or the strength of gravitational field of the system.

Human review

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

How the literature uses it

16 arXiv papers cite this in 25 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 · 14 sentences without a confident label

Contests it 1 paper

However, there are some problems in this definition [ref] : (i).

The particle surface of spinning test particles · Introduction · contest 0.75

Builds on it 1 paper

Enlightened by the quasi-local definition of the photon sphere and photon surface [ref] , we generalized the photon surface to the particle surface.

Quasi-local studies of the particle surfaces and their stability in general spacetimes · Introduction · 0.93

Compares with it 1 paper

The third point is a little bit different from [ref] which is based on a codimension-2 surface, and our definition is based on a hypersurface.

Quasi-local studies of the particle surfaces and their stability in general spacetimes · Discussion and conclusion · 0.96

Cites it as background 8 papers

The most important role in the mathematical understanding of shadows is played by the concept of characteristic photon surfaces [ref] – timelike hypersurfaces, where bounded photon trajectories are lined up.

The geometry of massive particle surfaces · Introduction · 0.91
Furthermore, we investigate relationship between the resulting slice structure and the structure of fundamental photon surfaces introduced in [ref] , which are a natural generalization of photon spheres [ref] .

Killing tensors and photon surfaces in foliated spacetimes · Introduction · 0.80
Black holes and the other compact objects which can be black hole mimickers have unstable (stable) light circular orbits called photon sphere (antiphoton sphere) [ref] or its alternatives and generalized surfaces [ref] .

Gravitational lensing by a photon sphere in a Reissner-Nordstr\"{o}m naked singularity spacetime in strong deflection limits · Introduction · 0.99

What it cites · 35 sentences without a confident label

Builds on 3 papers

The analysis for deriving the equation of the photon sphere with a metric of the form ([ref]) is hence a slight generalization of a recent result by Cederbaum and Galloway where $h(x) = f(x)$ and the traditional definition of photon spheres is used [ref] .

Uniqueness of photon spheres via positive mass rigidity · Static spacetimes · 0.95
The analysis for deriving the equation of the photon sphere with a metric of the form ([ref]) is hence a slight generalization of a recent result by Cederbaum and Galloway where $h(x) = f(x)$ and the traditional definition of photon spheres is used [ref] .

Uniqueness of photon spheres in electro-vacuum spacetimes · Static spacetimes · 0.95
The analysis for deriving the equation of the photon sphere with a metric of the form ([ref]) is hence a slight generalization of a recent result by Cederbaum and Galloway where $h(x) = f(x)$ and the traditional definition of photon spheres is used [ref] .

Photon surfaces with equipotential time-slices · Static spacetimes · 0.95

Cites as background 7 papers

For general spherically symmetric spacetimes, the shift vectors can be set to be vanishing, then, ${u,v}$ and ${∂/∂ξ,∂/∂η}$ have the relation that [equation] where ${∂/∂ξ,∂/∂η}$ are the coordinate basis, and ${N_u,N_v}$ are the so-called lapse functions [ref] .

Gravitational dynamics in s+1+1 dimensions II. Hamiltonian theory · the definition of a photon sphere and a photon surface · 0.83
Up to date, there are many studies on the black hole shadow and photon sphere (see [ref] ).

Shadows and strong gravitational lensing: a brief review · Introduction · 1.00
Recently, there are some generalizations to the stationary rotating space-times [ref] .

Fundamental photon orbits: black hole shadows and spacetime instabilities · Conclusion and discussion · 0.93

Discussion

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