| 1. |
- Edgar, Brian, 1945-, et al.
(författare)
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A local potential for the Weyl tensor in all dimensions
- 2004
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Ingår i: Classical and quantum gravity. - 0264-9381 .- 1361-6382. ; 21:22
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Tidskriftsartikel (refereegranskat)abstract
- In all dimensions n ≥ 4 and arbitrary signature, we demonstrate the existence of a new local potential - a double (2, 3)-form, Pabcde - for the Weyl curvature tensor Cabcd, and more generally for all tensors Wabcd with the symmetry properties of the Weyl tensor. The classical four-dimensional Lanczos potential for a Weyl tensor - a double (2, 1)-form, Habc - is proven to be a particular case of the new potential: its double dual.
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| 2. |
- Edgar, Brian, 1945-, et al.
(författare)
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Obtaining a class of type N pure radiation metrics using invariant operators
- 2005
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Ingår i: Classical and quantum gravity. - : IOP Publishing. - 0264-9381 .- 1361-6382. ; 22:5, s. 791-802
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Tidskriftsartikel (refereegranskat)abstract
- We develop further the integration procedure in the generalized invariant formalism, and demonstrate its efficiency by obtaining a class of Petrov type N pure radiation metrics without any explicit integration, and with comparatively little detailed calculations. The method is similar to the one exploited by Edgar and Vickers when deriving the general conformally flat pure radiation metric. A major addition to the technique is the introduction of non-intrinsic elements in the generalized invariant formalism, which can be exploited to keep calculations manageable.
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| 3. |
- Edgar, Brian, et al.
(författare)
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Petrov D vacuum spaces revisited : identities and invariant classification
- 2009
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Ingår i: CLASSICAL AND QUANTUM GRAVITY. - : IOP Publishing. - 0264-9381 .- 1361-6382. ; 26:10, s. 105022-
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Tidskriftsartikel (refereegranskat)abstract
- For Petrov D vacuum spaces, two simple identities are rederived and some new identities are obtained, in a manageable form, by a systematic and transparent analysis using the GHP formalism. This gives a complete involutive set of tables for the four GHP derivatives on each of the four GHP spin coefficients and the one Weyl tensor component. It follows directly from these results that the theoretical upper bound on the order of covariant differentiation of the Riemann tensor required for a Karlhede classification of these spaces is reduced to two.
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| 4. |
- Andersson, Fredrik, et al.
(författare)
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Existence of Lanczos potentials and superpotentials for the Weyl spinor/tensor
- 2001
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Ingår i: Classical and quantum gravity. - : IOP Publishing. - 0264-9381 .- 1361-6382. ; 18:12, s. 2297-2304
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Tidskriftsartikel (refereegranskat)abstract
- A new and concise proof of existence - emphasizing the very natural and simple structure - is given for the Lanczos spinor potential LABCA' of an arbitrary symmetric spinor WABCD defined by WABCD = 2?(AA' LBCD)A', this proof is easily translated into tensors in such a way that it is valid in four-dimensional spaces of any signature. In particular, this means that the Weyl spinor ?ABCD has Lanczos potentials in all spacetimes, and furthermore that the Weyl tensor has Lanczos potentials on all four-dimensional spaces, irrespective of signature. In addition, two superpotentials for WABCD are identified: the first TABCD (= T(ABC)D) is given by LABCA' = ?A'DTABCD, while the second HABA'B' (= H(AB)(A'B')) (which is restricted to Einstein spacetimes) is given by LABCA' = ? (AB' HBC)A'B'. The superpotential TABCD is used to describe the gauge freedom in the Lanczos potential.
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| 5. |
- Bergqvist, Göran, et al.
(författare)
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Algebraic Rainich theory and antisymmetrization in higher dimensions
- 2002
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Ingår i: Classical and quantum gravity. - : IOP Publishing. - 0264-9381 .- 1361-6382. ; 19:12, s. 3341-3355
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Tidskriftsartikel (refereegranskat)abstract
- The classical Rainich(-Misner-Wheeler) theory gives necessary and sufficient conditions on an energy-momentum tensor T to be that of a Maxwell field (a 2-form) in four dimensions. Via Einstein's equations, these conditions can be expressed in terms of the Ricci tensor, thus providing conditions for a spacetime geometry to be an Einstein-Maxwell spacetime. One of the conditions is that T2 is proportional to the metric, and it has previously been shown in arbitrary dimension that any tensor satisfying this condition is a superenergy tensor of a simple p-form. Here we examine algebraic Rainich conditions for general p-forms in higher dimensions and their relations to identities by antisymmetrization. Using antisymmetrization techniques we find new identities for superenergy tensors of these general (non-simple) forms, and we also prove in some cases the converse: that the identities are sufficient to determine the form. As an example we obtain the complete generalization of the classical Rainich theory to five dimensions.
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| 6. |
- Bergqvist, Göran, et al.
(författare)
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New electromagnetic conservation laws
- 2003
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Ingår i: Classical and Quantum Gravity. - : IOP Publishing. - 0264-9381 .- 1361-6382. ; 20:13, s. 2663-2668
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Tidskriftsartikel (refereegranskat)abstract
- The Chevreton superenergy tensor was introduced in 1964 as a counterpart, for electromagnetic fields, of the well-known Bel–Robinson tensor of the gravitational field. We here prove the unnoticed facts that, in the absence of electromagnetic currents, Chevreton's tensor (i) is completely symmetric, and (ii) has a trace-free divergence if the Einstein–Maxwell equations hold. It follows that the trace of the Chevreton tensor is a rank-2, symmetric, trace-free, conserved tensor, which is different from the energy–momentum tensor, and nonetheless can be constructed for any test Maxwell field or any Einstein–Maxwell spacetime.
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| 7. |
- Bergqvist, Göran, et al.
(författare)
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The Chevreton tensor and Einstein-Maxwell spacetimes conformal to Einstein spaces
- 2007
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Ingår i: Classical and Quantum Gravity. - : IOP Publishing. - 0264-9381 .- 1361-6382. ; 24:13, s. 3437-3455
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Tidskriftsartikel (refereegranskat)abstract
- 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 type 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 a closed form, we settle by 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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| 8. |
- Bergqvist, Göran, 1963-, et al.
(författare)
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Unique characterization of the Bel-Robinson tensor
- 2004
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Ingår i: Classical and quantum gravity. - : IOP Publishing. - 0264-9381 .- 1361-6382. ; 21:14, s. 3499-3503
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Tidskriftsartikel (refereegranskat)abstract
- We prove that a completely symmetric and trace-free rank-4 tensor is, up to sign, a Bel-Robinson-type tensor, i.e., the superenergy tensor of a tensor with the same algebraic symmetries as the Weyl tensor, if and only if it satisfies a certain quadratic identity. This may be seen as the first Rainich theory result for rank-4 tensors.
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| 9. |
- Bäckdahl, Thomas
(författare)
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Axisymmetric stationary solutions with arbitrary multipole moments
- 2007
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Ingår i: Classical and Quantum Gravity. - : IOP Publishing. - 0264-9381 .- 1361-6382. ; 24:9, s. 2205-2215
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Tidskriftsartikel (refereegranskat)abstract
- In this paper, the problem of finding an axisymmetric stationary spacetime from a specified set of multipole moments is studied. The condition on the multipole moments, for the existence of a solution, is formulated as a convergence condition on a power series formed from the multipole moments. The methods in this paper can also be used to give approximate solutions to any order, as well as estimates on each term of the resulting power series.
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| 10. |
- Bäckdahl, Thomas, et al.
(författare)
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Calculation of, and bounds for, the multipole moments of stationary spacetimes
- 2006
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Ingår i: Classical and Quantum Gravity. - : IOP Publishing. - 0264-9381 .- 1361-6382. ; 23:20, s. 5997-6006
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Tidskriftsartikel (refereegranskat)abstract
- In this paper, the multipole moments of stationary asymptotically flat spacetimes are considered. We show how the tensorial recursion of Geroch and Hansen can be replaced by a scalar recursion on . We also give a bound on the multipole moments. This gives a proof of the 'necessary part' of a long-standing conjecture due to Geroch.
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