Bilocal geodesic operators as a tool of investigating the optical properties of spacetimes

Julius Serbenta

RECORD

Bilocal geodesic operators as a tool of investigating the optical properties of spacetimes

Julius Serbenta

General Relativity and Quantum Cosmology · Submitted 30 May 2023

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

The authors' main claim Furthermore, it provides a more unified picture of relativistic geometrical optics and imposes a number of consistency requirements between the optical observables.

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, 5,658 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.17 · human participants 0.02 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.03 · compares with prior results 0.23 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

In my thesis, I present one particular example of the formalism capable of describing the propagation of a family of light rays in a curved spacetime. It is based on the resolvent operator of the geodesic deviation equation for null geodesics which is known as the bilocal geodesic operator (BGO) formalism. The BGO formalism generalizes the standard treatment of light ray bundles by allowing observations extended in time or performed by a family of neighbouring observers. Furthermore, it provides a more unified picture of relativistic geometrical optics and imposes a number of consistency requirements between the optical observables. The thesis begins with a brief introduction of the transfer matrix and its relativistic versions known as the Jacobi propagators and the bilocal geodesic operators. Then the basics of differential geometry are reviewed, with an emphasis on the geometry of the tangent bundle and the geodesic flow, which later provide the foundation for the BGO formalism. The mathematical introduction is then followed by two articles about the applications of the BGO formalism in the studies of optical distance measures and the conclusion.

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	In my thesis, I present one particular example of the formalism capable of describing the propagation of a family of light rays in a curved spacetime.	contribution 0.99	0.81	0.07	asserted 0.99
s1	It is based on the resolvent operator of the geodesic deviation equation for null geodesics which is known as the bilocal geodesic operator (BGO) formalism.	method 0.82	0.20	0.05	asserted 1.00
s2	The BGO formalism generalizes the standard treatment of light ray bundles by allowing observations extended in time or performed by a family of neighbouring observers.	contribution 0.74	0.29	0.12	asserted 1.00
s3	Furthermore, it provides a more unified picture of relativistic geometrical optics and imposes a number of consistency requirements between the optical observables.	contribution 0.77	0.50	0.19	asserted 1.00
s4	The thesis begins with a brief introduction of the transfer matrix and its relativistic versions known as the Jacobi propagators and the bilocal geodesic operators.	background 0.57	0.43	0.02	asserted 0.99
s5	Then the basics of differential geometry are reviewed, with an emphasis on the geometry of the tangent bundle and the geodesic flow, which later provide the foundation for the BGO formalism.	background 0.73	0.38	0.02	asserted 0.99
s6	The mathematical introduction is then followed by two articles about the applications of the BGO formalism in the studies of optical distance measures and the conclusion.	contribution 0.68	0.47	0.07	asserted 0.98

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

What was examined, and what was not

sources read

arXiv listing abstract v2

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

In my thesis, I present one particular example of the formalism capable of describing the propagation of a family of light rays in a curved spacetime. It is based on the resolvent operator of the geodesic deviation equation for null geodesics which is known as the bilocal geodesic operator (BGO) formalism. The BGO formalism generalizes the standard treatment of light ray bundles by allowing observations extended in time or performed by a family of neighbouring observers. Furthermore, it provides a more unified picture of relativistic geometrical optics and imposes a number of consistency requirements between the optical observables. The thesis begins with a brief introduction of the transfer matrix and its relativistic versions known as the Jacobi propagators and the bilocal geodesic operators. Then the basics of differential geometry are reviewed, with an emphasis on the geometry of the tangent bundle and the geodesic flow, which later provide the foundation for the BGO formalism. The mathematical introduction is then followed by two articles about the applications of the BGO formalism in the studies of optical distance measures and the conclusion.

Human review

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

How the literature uses it

What this paper does with the arXiv papers it cites

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

What it cites · 56 sentences without a confident label

Uses data or values from 12 papers

For example, in an FLRW model, $μ(z = 1) = 0.22$ [ref] .

Geometric optics in relativistic cosmology: new formulation and a new observable · Distance slip · 0.93
* (from drift of gravitational lens system parameters): for a multiply-lensed quasar at $z = 1.4$ with a lensing cluster at $z = 0.36$ we get angular drift of 0.1 nas/year and time delay drift of 1 ms/year [ref] - not measurable * (from differences of redshifts of gravitationally lensed images): for a galaxy cluster with velocity dispersion $σ_v = 1500 km/s$, eccentricity $ϵ= 0.6$, redshifts of the lens and the source $z_l = 0.5$, $z_s = 4$ respectively, we can reach $δz ≈10^-8$ [ref]

The Instantaneous Redshift Difference of Gravitationally Lensed Images: Theory and Observational Prospects · Redshift drift · 0.87
* (from drift of gravitational lens system parameters): for a multiply-lensed quasar at $z = 1.4$ with a lensing cluster at $z = 0.36$ we get angular drift of 0.1 nas/year and time delay drift of 1 ms/year [ref] - not measurable * (from differences of redshifts of gravitationally lensed images): for a galaxy cluster with velocity dispersion $σ_v = 1500 km/s$, eccentricity $ϵ= 0.6$, redshifts of the lens and the source $z_l = 0.5$, $z_s = 4$ respectively, we can reach $δz ≈10^-8$ [ref]

Redshift drift of gravitational lensing · Redshift drift · 0.87

Cites as support 5 papers

Recent studies suggest that redshift drift cosmography admits a metric-independent cosmological data analysis [ref] .

Multipole decomposition of redshift drift -- model independent mapping of the expansion history of the Universe · Future directions · 0.98
Recent studies suggest that redshift drift cosmography admits a metric-independent cosmological data analysis [ref] .

Redshift drift as a model independent probe of dark energy · Future directions · 0.98
Recent studies suggest that redshift drift cosmography admits a metric-independent cosmological data analysis [ref] .

Redshift drift cosmography for model-independent cosmological inference · Future directions · 0.98

Cites as background 24 papers

We note that the notion of the cosmic parallax varies between authors [ref] , and sometimes the cosmic parallax includes all of the aforementioned effects.

Geometric optics in general relativity using bilocal operators · Parallax and position drift · 0.87
Physical aspects of drift effects [ref] , general relativistic parallax [ref] , times of arrivals [ref] , and BGOs [ref] have been discussed previously, along with some geometrical remarks.

Testing the null energy condition with precise distance measurements · Introduction · 1.00
Physical aspects of drift effects [ref] , general relativistic parallax [ref] , times of arrivals [ref] , and BGOs [ref] have been discussed previously, along with some geometrical remarks.

Weighing the spacetime along the line of sight using times of arrival of electromagnetic signals · Introduction · 1.00

Discussion

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