Mechanical laws of the Rindler horizon

Alejandro Satz; Eugenio Bianchi

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Mechanical laws of the Rindler horizon

Eugenio Bianchi, Alejandro Satz

General Relativity and Quantum Cosmology · Submitted 21 May 2013

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

The authors' main claim Gravitational perturbations of flat Minkowski space make the Rindler horizon dynamical: the horizon satisfies mechanical laws analogous to the ones followed by black holes.

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What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.56 · human participants 0.01 · controlled comparison 0.17 · randomized assignment 0.01 · states quantitative result 0.05 · compares with prior results 0.92 · mentions code or data availability 0.02.

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Gravitational perturbations of flat Minkowski space make the Rindler horizon dynamical: the horizon satisfies mechanical laws analogous to the ones followed by black holes. We describe the gravitational perturbation of Minkowski space using perturbative field-theoretical methods. The change in the area of the Rindler horizon is described in terms of the deflection of light rays by the gravitational field. The difference between the area of the perturbed and the unperturbed horizon is related to the energy of matter crossing the horizon. We derive consistency conditions for the validity of our approximations, and compare our results to similar ones present in the literature. Finally, we discuss how this setting can be used in perturbative quantum gravity to extend the classical mechanical laws to thermodynamic laws, with the entanglement of field modes across the Rindler horizon providing a notion of thermodynamic entropy.

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	Gravitational perturbations of flat Minkowski space make the Rindler horizon dynamical: the horizon satisfies mechanical laws analogous to the ones followed by black holes.	result 0.85	0.55	0.90	asserted 1.00
s1	We describe the gravitational perturbation of Minkowski space using perturbative field-theoretical methods.	method 0.99	0.92	0.03	asserted 0.98
s2	The change in the area of the Rindler horizon is described in terms of the deflection of light rays by the gravitational field.	method 0.44	0.77	0.05	asserted 1.00
s3	The difference between the area of the perturbed and the unperturbed horizon is related to the energy of matter crossing the horizon.	result 0.99	0.80	0.15	asserted 1.00
s4	We derive consistency conditions for the validity of our approximations, and compare our results to similar ones present in the literature.	contribution 0.42	0.94	0.04	asserted 0.95
s5	Finally, we discuss how this setting can be used in perturbative quantum gravity to extend the classical mechanical laws to thermodynamic laws, with the entanglement of field modes across the Rindler horizon providing a notion of thermodynamic entropy.	interpretation 0.55	0.62	0.27	hedged possibility 0.54

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

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The paper

Original abstract

Gravitational perturbations of flat Minkowski space make the Rindler horizon dynamical: the horizon satisfies mechanical laws analogous to the ones followed by black holes. We describe the gravitational perturbation of Minkowski space using perturbative field-theoretical methods. The change in the area of the Rindler horizon is described in terms of the deflection of light rays by the gravitational field. The difference between the area of the perturbed and the unperturbed horizon is related to the energy of matter crossing the horizon. We derive consistency conditions for the validity of our approximations, and compare our results to similar ones present in the literature. Finally, we discuss how this setting can be used in perturbative quantum gravity to extend the classical mechanical laws to thermodynamic laws, with the entanglement of field modes across the Rindler horizon providing a notion of thermodynamic entropy.

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References

Forward citations

Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Gravitational Thermodynamics of Causal Diamonds in (A)dS
hep-th 2018-12 conditional novelty 6.0 of 10

Every spherical causal diamond in a maximally symmetric spacetime obeys a Smarr formula and a first law, and the diamond's gravitational temperature comes out negative.
Thermodynamics of Charged, Rotating, and Accelerating Black Holes
hep-th 2018-11 accept novelty 6.0 of 10

Charged, rotating, accelerating AdS black holes satisfy a first law of full cohomogeneity and the Smarr relation once the string tensions producing the acceleration are treated as independent thermodynamic variables.
Emergent Gravity in a Holographic Universe
hep-th 2019-08 conditional novelty 3.0 of 10

Causal diamonds in symmetric spacetimes obey a thermodynamic first law with negative temperature, and the Einstein equations can be recast as an entropy equilibrium condition, with a long-string CFT picture for non-Ad...
Black Holes in Loop Quantum Gravity
gr-qc 2017-03 conditional novelty 2.0 of 10

Loop quantum gravity's discrete quantum geometry can reproduce the Bekenstein-Hawking area law and frame black hole evaporation as information degradation rather than loss, though the program remains incomplete.

How the literature uses it

11 arXiv papers cite this in 18 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 · 12 sentences without a confident label

Uses its method or tool 1 paper

More quantitative calculations in this direction can be done by the linearized horizon formalism described in [ref] .

Holography in a background-independent effective theory · Discussion and conclusions · 0.93

Compares with it 1 paper

In order to satisfy both boundary conditions, the generators must be initially expanding and hence the area of the horizon cross-section increases towards the future.[Ref. [ref] also interpreted this in terms of an equilibrium variation version of the first law, which refers to the variation of the asymptotic horizon area rather than the variation of the bifurcation surface as in our version.]

Emergent Gravity in a Holographic Universe · Rindler space · 0.96

Cites it as support 2 papers

Since horizons encode information on the curvature of geometry [ref] (including infinitesimal perturbations [ref] ), and the strong EP implies gravity to be geometric, the EP requires no observable can be constructed sensitive to degrees of freedom beyond the horizon (the horizon must indeed be a “true” one) and hence the tracing over needs to be exact. this suggests either the equivalence principle, or quantum mechanics or at least observer-specific unitarity have to be abandoned.

Holography in a background-independent effective theory · Introduction: the equivalence principle and quantum field theory · 0.97
On the other hand, in quantum gravity the finite Planck area coefficient $L_P^2/2π$ is expected, as supported by various lines of evidence from the renormalization of the gravitational coupling in black hole backgrounds [ref] , from the thermodynamics of space-time geometry [ref] , from the holographic entanglement entropy [ref] , and from the entanglement entropy of the Rindler horizon in perturbative quantum gravity [ref] .

Loop Quantum Gravity and Quantum Information · Area-law states and the architecture of spacetime geometry · 0.99

Cites it as background 2 papers

Thermodynamics offers a surprisingly simple technique to examine the properties of both black holes as well as Rindler horizons [ref] .

Experimental observation of a Rindler horizon · Rindler horizon thermodynamics · 0.80
In the literature, on the other hand, a physical process version of the first law for Rindler space was stated for the first time in [ref] , and subsequently proven using the Einstein equation in [ref] .

Emergent Gravity in a Holographic Universe · Rindler space · 0.82

What it cites · 35 sentences without a confident label

Compares with 2 papers

While the methods used in its proof are very similar to the ones discussed here and in [ref] , there is a key difference: for the Rindler horizon, the initial configuration of the beam is not stationary.

The Physical Process First Law for Bifurcate Killing Horizons · V. Physical interpretation · 0.97
While the methods used in its proof are very similar to the ones discussed here and in [ref] , there is a key difference: for the Rindler horizon, the initial configuration of the beam is not stationary.

Horizon Entropy · V. Physical interpretation · 0.97

Cites as background 2 papers

The entanglement entropy is the Von Neumann entropy of this reduced density matrix, $S[ρ]=-Tr[ρlogρ]$, [ref] .

Entropy and Area · VIII. Horizon entropy · 0.82
The second version of the first law of black hole mechanics is an “equilibrium state comparison” [ref] .

The First Law of Black Hole Mechanics · V. Physical interpretation · 0.95

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