Universality and constant scalar curvature invariants

Coley, A. A.; Hervik, Sigbjørn

doi:10.48550/arxiv.1105.2356

Cited by 5 publications

(8 citation statements)

References 1 publication

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“…For every scalar S that appears in the action (gravitational Lagrangian) we obtain by variation (since these geometric tensors are automatically conserved due to the invariance of the actions under spacetime diffeomorphisms) a symmetric conserved rank-2 tensor, e.g., S ab with S ;b ab = 0 (from which syzygys can be obtained, such as S ;b ab S a ;c c = 0). As above, to refer to the n th equation in [79]…”

Section: Conserved Tensor Quantitiesmentioning

confidence: 99%

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Identification of black hole horizons using scalar curvature invariants

Coley¹,

McNutt²

2017

Class. Quantum Grav.

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We introduce the concept of a geometric horizon, which is a surface distinguished by the vanishing of certain curvature invariants which characterize its special algebraic character. We motivate its use for the detection of the event horizon of a stationary black hole by providing a set of appropriate scalar polynomial curvature invariants that vanish on this surface. We extend this result by proving that a non-expanding horizon, which generalizes a Killing horizon, coincides with the geometric horizon. Finally, we consider the imploding spherically symmetric metrics and show that the geometric horizon identifies a unique quasi-local surface corresponding to the unique spherically symmetric marginally trapped tube, implying that the spherically symmetric dynamical black holes admit a geometric horizon. Based on these results, we propose a suite of conjectures concerning the application of geometric horizons to more general dynamical black hole scenarios.

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Section: Conserved Tensor Quantitiesmentioning

confidence: 99%

“…Bases for scalar Riemann polynomials of order eight or less in the derivatives of the metric tensor and for tensorial Riemann polynomials of order six or less were presented. The FKWC-bases were modified to be dimensionally independent [78], allowing for irreducible expressions [79].…”

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confidence: 99%

Identification of black hole horizons using scalar curvature invariants

Coley¹,

McNutt²

2017

Class. Quantum Grav.

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“…It is of interest to compare the set of exact solutions of quadratic gravity (QG) with other overlapping classes of spacetimes, such as pp-waves (pp-waves of a particular Weyl type will be denoted as ppN, ppIII etc. ), spacetimes with vanishing curvature invariants (VSI) [26], spacetimes with constant curvature invariants (CSI) [15], Kundt subclass of CSI (KCSI) and universal metrics (U) for which quantum correction is a multiple of the metric [27,28]. In this discussion we will often consider Einstein or Ricci-flat subsets of these sets.…”

Section: Comparison With Other Classes Of Spacetimesmentioning

confidence: 99%

“…Recently it was conjectured in [28] that U ⊂ KCSI. ppIII RF are examples of spacetimes which are KCSI (and VSI) but not U.…”

Section: Comparison With Other Classes Of Spacetimesmentioning

confidence: 99%

Type III and N solutions to quadratic gravity

Málek,

Pravda

2011

Preprint

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We study exact vacuum solutions to quadratic gravity (QG) of the Weyl types N and III. We show that in an arbitrary dimension all Einstein spacetimes of the Weyl type N with an appropriately chosen effective cosmological constant Λ are exact solutions to QG and we refer to explicitly known metrics within this class.For type III Einstein spacetimes, an additional constraint follows from the field equations of QG and examples of spacetimes obeying such constraint are given. However, type III pp-waves do not satisfy this constraint and thus do not solve QG.For type N, we also study a wider class of spacetimes admitting a pure radiation term in the Ricci tensor. In contrast to the Einstein case, the field equations of generic QG determine optical properties of the geometry and restrict such exact solutions to the Kundt class. We provide examples of these metrics.

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“…Of particular interest are those spacetimes where all elements of I vanish or are constant, such spacetimes are known as vanishing scalar invariant (V SI) or constant scalar invariant (CSI) spacetimes respectively [9]. The class of CSI spacetimes are applicable to many theories of gravity, as they contain a subset of spacetimes that are universal, and hence solve the vacuum equations of all gravitational theories with a Lagrangian constructed from SPIs [10,11].…”

Section: Introductionmentioning

confidence: 99%

I -preserving diffeomorphisms of Lorentzian manifolds

McNutt

Aadne

2019

Journal of Mathematical Physics

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We examine the existence of one parameter groups of diffeomorphisms whose infinitesimal generators annihilate all scalar polynomial curvature invariants through the application of the Lie derivative, known as Ipreserving diffeomorphisms. Such mappings are a generalization of isometries and appear to be related to nil-Killing vector fields, for which the associated Lie derivative of the metric yields a nilpotent rank two tensor. We show that the set of nil-Killing vector fields contains Lie algebras, although the Lie algebras may be infinite and can contain elements which are not I-preserving diffeomorphisms. We then study the curvature structure of a general Lorenztian manifold, or spacetime to show that I-preserving diffeomorphism will only exists for I-degenerate spacetimes and to determine when the I-preserving diffeomorphisms are generated by nil-Killing vector fields. We identify necessary and sufficient conditions for the degenerate Kundt spacetimes to admit an additional I-preserving diffeomorphism and conclude with an application to the class of Kundt spacetimes with constant scalar polynomial curvature invariants to show that a finite transitive Lie algebra of nil-Killing vector fields always exists for these spacetimes.

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Universality and constant scalar curvature invariants

Cited by 5 publications

References 1 publication

Identification of black hole horizons using scalar curvature invariants

Identification of black hole horizons using scalar curvature invariants

Type III and N solutions to quadratic gravity

I -preserving diffeomorphisms of Lorentzian manifolds

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