Review of some classical gravitational superenergy tensors using computational techniques

Balfagon, Alberto C.; Jaén, Xavier

doi:10.1088/0264-9381/17/13/302

Cited by 15 publications

(27 citation statements)

References 10 publications

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“…Balfagón and Jaén ( 2000 ) used the indicial capabilities of TTC to check and correct earlier work finding all possible superenergy tensors, i.e. four-index divergence-free tensors quadratic in the Riemann tensor: a uniqueness property of the Bel–Robinson tensor is proved.…”

Section: Applicationsmentioning

confidence: 98%

Computer algebra in gravity research

MacCallum

2018

Living Rev Relativ

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The complicated nature of calculations in general relativity was one of the driving forces in the early development of computer algebra (CA). CA has become widely used in gravity research (GR) and its use can be expected to grow further. Here the general nature of computer algebra is discussed, along with some aspects of CA system design; features particular to GR’s requirements are considered; information on packages for CA in GR is provided, both for those packages currently available and for their predecessors; and applications of CA in GR are outlined.

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Section: Applicationsmentioning

confidence: 98%

Computer algebra in gravity research

MacCallum

2018

Living Rev Relativ

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“…This relation was derived in [13]. Now, since H ab is divergence-free, symmetric and trace-free, and since it is a combination of the Einstein tensor, a term that is quadratic in the Riemann tensor, and a double derivative of the Riemann tensor, H ab should be a linear combination of the completely known tensors with these properties [1,4,10]. We will show that H ab is related to the conformally well-behaved Bach tensor, which is defined by [22]…”

Section: Relation To the Bach Tensormentioning

confidence: 99%

“…The Chevreton tensor was introduced in 1964 [9] as an electromagnetic counterpart to the Bel-Robinson superenergy tensor for the gravitational field [2,3]. It is given by H abcd {∇ [1] F [2] } = 1 2 (T abcd {∇ [1] F [2] } + T cdab {∇ [1] F [2] }),…”

Section: Introductionmentioning

confidence: 99%

The Chevreton tensor and Einstein–Maxwell spacetimes conformal to Einstein spaces

Bergqvist¹,

Eriksson²

2007

Class. Quantum Grav.

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In this paper we characterize the source-free Einstein-Maxwell spacetimes which have a trace-free Chevreton tensor. We show that this is equivalent to the Chevreton tensor being of pure-radiation type and that it restricts the spacetimes to Petrov types N or O. We prove that the trace of the Chevreton tensor is related to the Bach tensor and use this to find all Einstein-Maxwell spacetimes with a zero cosmological constant that have a vanishing Bach tensor. Among these spacetimes we then look for those which are conformal to Einstein spaces. We find that the electromagnetic field and the Weyl tensor must be aligned, and in the case that the electromagnetic field is null, the spacetime must be conformally Ricci-flat and all such solutions are known. In the non-null case, since the general solution is not known on closed form, we settle with giving the integrability conditions in the general case, but we do give new explicit examples of Einstein-Maxwell spacetimes that are conformal to Einstein spaces, and we also find examples where the vanishing of the Bach tensor does not imply that the spacetime is conformal to a C-space. The non-aligned Einstein-Maxwell spacetimes with vanishing Bach tensor are conformally C-spaces, but none of them are conformal to Einstein spaces.

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“…Another way to remove the ghost stae is the following. Let us add to the action ( 19) a term of the form cw µν E ab µν w ab (27) with…”

Section: Pos(corfu2019)152mentioning

confidence: 99%

Higher Curvature Supergravity

Dalianis¹,

Taskas²

2020

Proceedings of Corfu Summer Institute 2019 "School and Workshops on Elementary Particle Physics and Gravity" — PoS(CORFU2019)

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Review of some classical gravitational superenergy tensors using computational techniques

Abstract: We use computational algorithms recently developed by us to study completely four index divergence free quadratic in Riemann tensor polynomials in GR. Some results are new and some other reproduce and/or correct known ones. The algorithms are part of a Mathematica package called

Cited by 15 publications

References 10 publications

Computer algebra in gravity research

Computer algebra in gravity research

The Chevreton tensor and Einstein–Maxwell spacetimes conformal to Einstein spaces

Higher Curvature Supergravity

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