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The $D\to 2$ Limit of General Relativity
General Relativity and Quantum Cosmology · Submitted 13 Aug 1992
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim A method for taking the $D\to 2$ limit of D-dimensional general relativity is constructed, yielding a two-dimensional theory which couples gravitation to conserved stress-energy.
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The abstract, sentence by sentence
A method for taking the $D\to 2$ limit of D-dimensional general relativity is constructed, yielding a two-dimensional theory which couples gravitation to conserved stress-energy. We show how this theory is related to those obtained via an alternative dimensional reduction approach.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | A method for taking the $D\to 2$ limit of D-dimensional general relativity is constructed, yielding a two-dimensional theory which couples gravitation to conserved stress-energy. | contribution 0.86 | 0.94 | 0.78 | asserted 1.00 |
| s1 | We show how this theory is related to those obtained via an alternative dimensional reduction approach. | contribution 0.72 | 0.88 | 0.12 | asserted 1.00 |
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The paper
Original abstract
A method for taking the $D\to 2$ limit of D-dimensional general relativity is constructed, yielding a two-dimensional theory which couples gravitation to conserved stress-energy. We show how this theory is related to those obtained via an alternative dimensional reduction approach.
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References
How the literature uses it
47 arXiv papers cite this in 71 sentences
Papers citing it · 54 sentences without a confident label
Builds on it 1 paper
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Ref. [ref] extends the method for obtaining the $D→2$ limit of general relativity [ref] to the $D→4$ limit of EGB gravity.
Strong gravitational lensing of a 4-dimensional Einstein-Gauss-Bonnet black hole in homogeneous plasma · Introduction · 0.89
Uses its method or tool 2 papers
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Evaluating this for a conformally rescaled metric $g̃=e^ψ g$, we consider the difference [ref] S_D^ = κ̂(∫d^Dx √(-g̃)R̃ - ∫d^Dx √(-g)R) = κ̂∫d^Dx [e^ϵψ/2[(R-(ϵ+1)ψ)-1/4ϵ(ϵ+1)(∂ψ)^2] - R ] , where $ϵ=D-2$.
On Taking the $D\to 4$ limit of Gauss-Bonnet Gravity: Theory and Solutions · The $D→2$ limit of General Relativity · 0.84
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The second, used first by Mann and Ross [ref] , involves first conformally transforming the term of interest followed by coupling rescalings and the addition of counterterms to eliminate total derivatives.
Lower-dimensional Gauss-Bonnet Gravity and BTZ Black Holes · Conclusions · 0.89
Compares with it 4 papers
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For $m=0$ our action [ref] coincides with the one proposed by Mann and Ross [ref] as the $D→2$ limit of General Relativity (cf. also [ref] ).
Liouville gravity from Einstein gravity · Constructing the limiting action · 0.87
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In contrast to [ref] , for example, these equations do not decouple in the following sense.
A new 2D formulation of modified General Relativity · The model and its key properties · 0.97
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Lastly, the comparison between ([ref]) and the action in [ref] is really a comparison between the two methods of writing down a novel theory: dimensional reduction versus the Ross-Mann dimensional regularization [ref] .
The Stringy Origins of Galileons and their Novel Limit · Novel $α'$-Corrected String Theory? · 0.98
Cites it as support 2 papers
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A strength of this model – and hence the rationale for its use in this study – is that it is the best classical and semiclassical approximation for general relativity in the 2-D limit [ref] [Reference [ref] also notes the favorability of Liouville gravity, whose solutions and metric structure are virtually identical.].
Primordial Black Hole Evaporation and Spontaneous Dimensional Reduction · Lower dimensional black hole thermodynamics · 1.00
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This result was also confirmed from another perspective [ref] through adding counter terms in $D$ dimensions [ref] .
Cosmology and gravitational waves in consistent $D\to 4$ Einstein-Gauss-Bonnet gravity · Introduction · 0.96
Cites it as background 7 papers
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In the former this is done via a conformal rescaling trick (analogous to an earlier procedure wherein the $D→2$ limit of GR was obtained [ref] ), and in the latter a Kaluza-Klein dimensional reduction technique [ref] .
Neutron stars in 4D Einstein-Gauss-Bonnet gravity · Introduction · 0.81
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The theory was first constructed in [ref] , by taking the conformal transformation of Einstein gravity in general $D$ dimensions that introduces a scalar field.
General Solutions of Einstein Gravity at $D\rightarrow 2$ · Introduction · 0.81
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This approach leads to the appearance of a scalar Kaluza-Klein mode, which introduces additional contributions to the gravitational field equations also in 4 dimensions, which then reproduce the proposed contribution from the Gauss-Bonnet term [ref] Another approach that yields a supplementary scalar mode is by introducing a counter-term in the gravitational action, which is constructed from a conformally rescaled metric [ref] , in analogy to a similar procedure for \(D = 2\) Einstein gravity [ref] .
Canonical variational completion and 4D Gauss-Bonnet gravity · Introduction · 0.92
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