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Self-Excited Gravitational Instantons
General Relativity and Quantum Cosmology · Submitted 2 Aug 2024
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim These new self-excited instantons exhibit striking similarities to BPST instantons in Yang-Mills theory, as their action reduces to a topological Nieh-Yan term, which allows us to identify the axial torsion as a topological current and show that the gravitational action is given by a topological charge.
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The abstract, sentence by sentence
We present a novel approach to constructing gravitational instantons based on the observation that the gravitational action of general relativity in its teleparallel formulation can be expressed as a product of the torsion and excitation forms. We introduce a new class of solutions where these two forms are equal, which we term the self-excited instantons, and advocate for their use over the self-dual instantons of Eguchi and Hanson. These new self-excited instantons exhibit striking similarities to BPST instantons in Yang-Mills theory, as their action reduces to a topological Nieh-Yan term, which allows us to identify the axial torsion as a topological current and show that the gravitational action is given by a topological charge.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We present a novel approach to constructing gravitational instantons based on the observation that the gravitational action of general relativity in its teleparallel formulation can be expressed as a product of the torsion and excitation forms. | contribution 0.72 | 0.70 | 0.10 | asserted 1.00 |
| s1 | We introduce a new class of solutions where these two forms are equal, which we term the self-excited instantons, and advocate for their use over the self-dual instantons of Eguchi and Hanson. | contribution 0.99 | 0.90 | 0.40 | asserted 1.00 |
| s2 | These new self-excited instantons exhibit striking similarities to BPST instantons in Yang-Mills theory, as their action reduces to a topological Nieh-Yan term, which allows us to identify the axial torsion as a topological current and show that the gravitational action is given by a topological charge. | result 0.82 | 0.88 | 0.47 | asserted 1.00 |
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The paper
Original abstract
We present a novel approach to constructing gravitational instantons based on the observation that the gravitational action of general relativity in its teleparallel formulation can be expressed as a product of the torsion and excitation forms. We introduce a new class of solutions where these two forms are equal, which we term the self-excited instantons, and advocate for their use over the self-dual instantons of Eguchi and Hanson. These new self-excited instantons exhibit striking similarities to BPST instantons in Yang-Mills theory, as their action reduces to a topological Nieh-Yan term, which allows us to identify the axial torsion as a topological current and show that the gravitational action is given by a topological charge.
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References
How the literature uses it
1 arXiv paper cite this in 1 sentence
What it cites · 33 sentences without a confident label
Uses the method or tool of 3 papers
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The well-known solution is to consider a reference tetrad $^a=(d r,r σ_x, r σ_y, rσ_z )$ and calculate the teleparallel connection as the Riemannian connection of the reference tetrad $ω^a_b=^a_b (^a)$ [ref] .
Spin Connection and Renormalization of Teleparallel Action · Examples · 0.83
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The well-known solution is to consider a reference tetrad $^a=(d r,r σ_x, r σ_y, rσ_z )$ and calculate the teleparallel connection as the Riemannian connection of the reference tetrad $ω^a_b=^a_b (^a)$ [ref] .
Teleparallel Theories of Gravity: Illuminating a Fully Invariant Approach · Examples · 0.83
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The well-known solution is to consider a reference tetrad $^a=(d r,r σ_x, r σ_y, rσ_z )$ and calculate the teleparallel connection as the Riemannian connection of the reference tetrad $ω^a_b=^a_b (^a)$ [ref] .
Einstein gravity from the Einstein action: Counterterms and covariance · Examples · 0.83
Compares with 1 paper
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We find that the axial torsion can be written as [equation] For all functions that goes as $g→1$ at $r→∞$, and using that the volume of $S^3$ is $∫_S^3σ_x∧σ_y∧σ_z=2π^2$, we obtain the Nieh-Yan charge as [equation] which is the same result as obtained in [ref] since the axial torsion [ref] is independent of $f$.
Topological Invariants, Instantons and Chiral Anomaly on Spaces with Torsion · Examples · 0.97
Cites as support 1 paper
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This is consistent with our recent argument that the teleparallel action [ref] with a suitably chosen teleparallel connection is fully equivalent to the full general relativity action including all boundary and counterterms [ref] .
Einstein gravity from the Einstein action: Counterterms and covariance · Examples · 0.96
Cites as background 10 papers
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The Nieh-Yan term was originally discovered in Riemann-Cartan geometry [ref] , which is the underlying geometry of various metric-affine theories of gravity [ref] .
Metric-Affine Gauge Theory of Gravity: Field Equations, Noether Identities, World Spinors, and Breaking of Dilation Invariance · Discussion and Conclusions · 1.00
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The Nieh-Yan term was originally discovered in Riemann-Cartan geometry [ref] , which is the underlying geometry of various metric-affine theories of gravity [ref] .
Gauge symmetries of the teleparallel theory of gravity · Discussion and Conclusions · 1.00
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Most of the previous works discussing torsional instantons or the Nieh-Yan term were conducted either in this context [ref] , or various axion-like modified gravity theories [ref] .
Revisiting a parity violating gravity model without ghost instability: Local Lorentz covariance · Discussion and Conclusions · 0.91
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