Gauss-Codazzi thermodynamics on the timelike screen

Federico Piazza

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Gauss-Codazzi thermodynamics on the timelike screen

Federico Piazza

General Relativity and Quantum Cosmology · Submitted 27 May 2010

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

The authors' main claim We extend such a result to a timelike screen of observers with finite acceleration.

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What the abstract itself states, as probabilities: claims first 0.10 · states limitation 0.87 · human participants 0.01 · controlled comparison 0.04 · randomized assignment 0.01 · states quantitative result 0.04 · 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; show every role.

It is a known result by Jacobson that the flux of energy-matter through a local Rindler horizon is related with the expansion of the null generators in a way that mirrors the first law of thermodynamics. We extend such a result to a timelike screen of observers with finite acceleration. Since timelike curves have more freedom than null geodesics, the construction is more involved than Jacobson's and few geometrical constraints need to be imposed: the observers' acceleration has to be constant in time and everywhere orthogonal to the screen. Moreover, at any given time, the extrinsic curvature of the screen has to be flat. The latter requirement can be weakened by asking that the extrinsic curvature, if present at the beginning, evolves in time like on a cone and just rescales proportionally to the expansion.

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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	It is a known result by Jacobson that the flux of energy-matter through a local Rindler horizon is related with the expansion of the null generators in a way that mirrors the first law of thermodynamics.	background 1.00	0.02	0.04	asserted 1.00
s1	We extend such a result to a timelike screen of observers with finite acceleration.	contribution 1.00	0.92	0.46	asserted 1.00
s2	Since timelike curves have more freedom than null geodesics, the construction is more involved than Jacobson's and few geometrical constraints need to be imposed: the observers' acceleration has to be constant in time and everywhere orthogonal to the screen.	method 0.64	0.47	0.08	asserted 1.00
s3	Moreover, at any given time, the extrinsic curvature of the screen has to be flat.	limitation 0.41	0.70	0.08	asserted 1.00
s4	The latter requirement can be weakened by asking that the extrinsic curvature, if present at the beginning, evolves in time like on a cone and just rescales proportionally to the expansion.	result 0.47	0.77	0.11	asserted 0.49

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.97.

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arXiv listing abstract v2

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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

It is a known result by Jacobson that the flux of energy-matter through a local Rindler horizon is related with the expansion of the null generators in a way that mirrors the first law of thermodynamics. We extend such a result to a timelike screen of observers with finite acceleration. Since timelike curves have more freedom than null geodesics, the construction is more involved than Jacobson's and few geometrical constraints need to be imposed: the observers' acceleration has to be constant in time and everywhere orthogonal to the screen. Moreover, at any given time, the extrinsic curvature of the screen has to be flat. The latter requirement can be weakened by asking that the extrinsic curvature, if present at the beginning, evolves in time like on a cone and just rescales proportionally to the expansion.

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9 arXiv papers cite this in 10 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 · 6 sentences without a confident label

Uses its method or tool 1 paper

Along the lines of [ref] , we can formally construct a congruence of radially accelerating observers, work out its expansion $θ$ and, via an application of the Gauss-Codazzi equations, establish the second law.

Emergence of Spacetime: From Entanglement to Einstein · Summary and Future Work · 0.90

Cites it as background 3 papers

The holographic approach [ref] within the thermodynamical formulation of gravity [ref] became logically accomplished in papers by E.Verlinde [ref] and T.Padmanabhan [ref] as well as in further developments, modifications and applications of their ideas in various aspects [ref] .

The holographic screen at low temperatures · Introduction · 1.00
Moreover, certain timelike screen is also proposed to repeat the local Rindler horizon thermodynamics [ref] .

First and second laws of modified gravity theories on dynamical holographic screens · Introduction · 0.87
An incomplete list of thermodynamics topics in entropic force frame is [ref] .

Thermodynamics for Kodama observer in general spherically symmetric spacetimes · Introduction · 0.99

What it cites · 11 sentences without a confident label

Builds on 1 paper

We have enquired under which conditions the result of Jacobson [ref] can be extended to a timelike screen of observers of finite acceleration.

Thermodynamics of Spacetime: The Einstein Equation of State · Conclusions · 0.98

Compares with 1 paper

Also, we should mention the work [ref] , as it shares some similarities with the present approach.

Dynamical Horizons and their Properties · Introduction · 0.84

Cites as background 5 papers

Such a point of view has been deepened by Padmanabhan in a series of works (see e.g. [ref] ), where the thermodynamics of horizons has been studied in great detail and other analogies explored.

Gravity and the Thermodynamics of Horizons · Introduction · 0.93
I also thank Badri Krishnan for making me aware of Ref. [ref] .

Dynamical Horizons and their Properties · Conclusions · 0.84
The analogies between gravity and thermodynamics are sometimes taken as hints that gravity is an emergent phenomenon, possibly together with spacetime itself [ref] .

Glimmers of a pre-geometric perspective · Conclusions · 0.90

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