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Kerr-Schild Symmetries
General Relativity and Quantum Cosmology · Submitted 13 Jun 2000
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim We prove that all these vector fields can be intrinsically characterized and that they constitute a Lie algebra if the null deformation direction is fixed.
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The abstract, sentence by sentence
We study continuous groups of generalized Kerr-Schild transformations and the vector fields that generate them in any n-dimensional manifold with a Lorentzian metric. We prove that all these vector fields can be intrinsically characterized and that they constitute a Lie algebra if the null deformation direction is fixed. The properties of these Lie algebras are briefly analyzed and we show that they are generically finite-dimensional but that they may have infinite dimension in some relevant situations. The most general vector fields of the above type are explicitly constructed for the following cases: any two-dimensional metric, the general spherically symmetric metric and deformation direction, and the flat metric with parallel or cylindrical deformation directions.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We study continuous groups of generalized Kerr-Schild transformations and the vector fields that generate them in any n-dimensional manifold with a Lorentzian metric. | contribution 0.99 | 0.91 | 0.06 | asserted 0.85 |
| s1 | We prove that all these vector fields can be intrinsically characterized and that they constitute a Lie algebra if the null deformation direction is fixed. | result 0.96 | 0.95 | 0.52 | asserted 1.00 |
| s2 | The properties of these Lie algebras are briefly analyzed and we show that they are generically finite-dimensional but that they may have infinite dimension in some relevant situations. | result 0.99 | 0.94 | 0.26 | asserted 0.84 |
| s3 | The most general vector fields of the above type are explicitly constructed for the following cases: any two-dimensional metric, the general spherically symmetric metric and deformation direction, and the flat metric with parallel or cylindrical deformation directions. | contribution 0.64 | 0.94 | 0.10 | asserted 1.00 |
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The paper
Original abstract
We study continuous groups of generalized Kerr-Schild transformations and the vector fields that generate them in any n-dimensional manifold with a Lorentzian metric. We prove that all these vector fields can be intrinsically characterized and that they constitute a Lie algebra if the null deformation direction is fixed. The properties of these Lie algebras are briefly analyzed and we show that they are generically finite-dimensional but that they may have infinite dimension in some relevant situations. The most general vector fields of the above type are explicitly constructed for the following cases: any two-dimensional metric, the general spherically symmetric metric and deformation direction, and the flat metric with parallel or cylindrical deformation directions.
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References
How the literature uses it
3 arXiv papers cite this in 7 sentences
Papers citing it · 3 sentences without a confident label
Cites it as background 3 papers
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In the literature, a specialization of the nil-Killing vector fields known as the Kerr-Schild vector fields, has been discussed [ref] these are defined as nil-Killing vector fields with respect to $$ for which $ℒ_ g = T$ is nilpotent of order two, $T^2 = 0$ with the additional condition: [, ] ∝.
$\mathcal{I}$-Preserving Diffeomorphisms of Lorentzian Manifolds · Introduction · 0.92
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For further discussion of the Kerr-Schild transformation as a diffeomorphism on the manifold, the interested reader is referred to the papers [ref] ; in particular, the last reference which acts as a mathematically detailed review for the topic.
Aspects of the Classical Double Copy · Kerr-Schild flow · 0.98
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Further investigations and examples concerning Kerr–Schild perturbations can found in [ref] .
Kerr-Schild perturbations of coset CFTs as scale invariant integrable $\sigma$-models · Essentials of Kerr–Schild perturbations · 1.00
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