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Edgar, Brian
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Publications (10 of 29) Show all publications
Edgar, B., Bradley, M. & Piedade Machado Ramos, M. (2014). Symmetry analysis of radiative spacetimes with a null isotropy using GHP formalism. General Relativity and Gravitation, 46(10), 1797
Open this publication in new window or tab >>Symmetry analysis of radiative spacetimes with a null isotropy using GHP formalism
2014 (English)In: General Relativity and Gravitation, ISSN 0001-7701, E-ISSN 1572-9532, Vol. 46, no 10, p. 1797-Article in journal (Refereed) Published
Abstract [en]

A complete and simple invariant classification of the conformally flat pure radiation metrics with a negative cosmological constant that were obtained by integration using the generalised invariant formalism is presented. We show equivalence between these metrics and the corresponding type O subclass of the more general spacetime studied by Siklos. The classification procedure indicates that the metrics possess a one degree of null isotropy freedom which has very interesting repercussions in the symmetry analysis. The Killing and homothetic vector analysis in GHP formalism is then generalised to this case were there is only one null direction defined geometrically. We determine the existing Killing vectors for the different subclasses that arise in the classification and compare these results to those obtained in the symmetry analysis performed by Siklos for a larger class of metrics with Ricci tensor representing a pure radiation field and a negative cosmological constant. It is also shown that there are no homothetic Killing vectors present.

Place, publisher, year, edition, pages
Springer Verlag (Germany), 2014
Keywords
Generalised invariant formalism; Pure radiation spacetimes; Karlhede classification; Symmetries
National Category
Mathematics
Identifiers
urn:nbn:se:liu:diva-112313 (URN)10.1007/s10714-014-1797-9 (DOI)000343646500008 ()
Note

Funding Agencies|Research Center of Mathematics of the University of Minho through the FEDER Funds Programa Operacional Factores de Competitividade COMPETE; Portuguese Funds through FCT-Fundacao para a Ciencia e Tecnologia [Est-C/MAT/UI0013/2011]

Available from: 2014-11-24 Created: 2014-11-24 Last updated: 2017-12-05
Bradley, M., Edgar, B. & M.P. MacHado, R. (2011). Classification of a class of conformally flat pure radiation metrics with cosmological constant. In: AIP Conference Proceedings: vol 1458. Paper presented at SPANISH RELATIVITY MEETING 2011 Madrid, Spain (pp. 331-334). AIP American Institute of Physics, 1458
Open this publication in new window or tab >>Classification of a class of conformally flat pure radiation metrics with cosmological constant
2011 (English)In: AIP Conference Proceedings: vol 1458, AIP American Institute of Physics , 2011, Vol. 1458, p. 331-334Conference paper, Published paper (Refereed)
Abstract [en]

A comparison between the Cartan-Karlhede classification of the conformally flat pure radiation metrics with a negative cosmological constant, satisfying Λ+ττ=0, and the construction of them in terms of the Generalised Invariant Formalism (GIF) is made. © 2012 American Institute of Physics.

Place, publisher, year, edition, pages
AIP American Institute of Physics, 2011
Series
AIP Conference Proceedings, ISSN 0094-243X
Keywords
Generalised invariant formalism; Pure radiation spacetimes
National Category
Engineering and Technology
Identifiers
urn:nbn:se:liu:diva-100717 (URN)10.1063/1.4734427 (DOI)
Conference
SPANISH RELATIVITY MEETING 2011 Madrid, Spain
Available from: 2013-11-12 Created: 2013-11-11 Last updated: 2013-11-12
Bradley, M., Edgar, B. & Machado Ramos, M. P. (2010). Invariant classification and the generalised invariant formalism: conformally flat pure radiation metrics. General Relativity and Gravitation, 42(1), 155-182
Open this publication in new window or tab >>Invariant classification and the generalised invariant formalism: conformally flat pure radiation metrics
2010 (English)In: General Relativity and Gravitation, ISSN 0001-7701, E-ISSN 1572-9532, Vol. 42, no 1, p. 155-182Article in journal (Refereed) Published
Abstract [en]

Metrics obtained by integrating within the generalised invariant formalism are structured around their intrinsic coordinates, and this considerably simplifies their invariant classification and symmetry analysis. We illustrate this by presenting a simple and transparent complete invariant classification of the conformally flat pure radiation metrics (except plane waves) in such intrinsic coordinates; in particular we confirm that the three apparently non-redundant functions of one variable are genuinely non-redundant, and easily identify the subclasses which admit a Killing and/or a homothetic Killing vector. Most of our results agree with the earlier classification carried out by Skea in the different Koutras-McIntosh coordinates, which required much more involved calculations; but there are some subtle differences. Therefore, we also rework the classification in the Koutras-McIntosh coordinates, and by paying attention to some of the subtleties involving arbitrary functions, we obtain complete agreement with the results obtained in intrinsic coordinates. We have corrected and completed statements and results by Edgar and Vickers, and by Skea, about the orders of Cartan invariants at which particular information becomes available.

Keywords
Generalised invariant formalism; Pure radiation spacetimes; Karlhede invariant classification of spacetimes
National Category
Mathematics
Identifiers
urn:nbn:se:liu:diva-52894 (URN)10.1007/s10714-009-0823-9 (DOI)
Available from: 2010-01-13 Created: 2010-01-12 Last updated: 2017-12-12
Edgar, B., Garcia-Parrado Gomez-Lobo, A. & Maria Martin-Garcia, J. (2009). Petrov D vacuum spaces revisited: identities and invariant classification. CLASSICAL AND QUANTUM GRAVITY, 26(10), 105022
Open this publication in new window or tab >>Petrov D vacuum spaces revisited: identities and invariant classification
2009 (English)In: CLASSICAL AND QUANTUM GRAVITY, ISSN 0264-9381, Vol. 26, no 10, p. 105022-Article in journal (Refereed) Published
Abstract [en]

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.

National Category
Mathematics
Identifiers
urn:nbn:se:liu:diva-18953 (URN)10.1088/0264-9381/26/10/105022 (DOI)
Note
Original Publication: Brian Edgar, Alfonso Garcia-Parrado Gomez-Lobo and José Maria Martin-Garcia, Petrov D vacuum spaces revisited: identities and invariant classification, 2009, CLASSICAL AND QUANTUM GRAVITY, (26), 10, 105022. http://dx.doi.org/10.1088/0264-9381/26/10/105022 Copyright: Institute of Physics Publishing http://www.iop.org/ Available from: 2009-09-02 Created: 2009-06-05 Last updated: 2009-09-02Bibliographically approved
Edgar, B. & Senovilla, J. M. (2008). The new potential for the Weyl tensor in n dimensions: wave equation and gauge. In: Spanish Relativity Meeting 2007,2007: (pp. 245-248). Spain: EDR
Open this publication in new window or tab >>The new potential for the Weyl tensor in n dimensions: wave equation and gauge
2008 (English)In: Spanish Relativity Meeting 2007,2007, Spain: EDR , 2008, p. 245-248Conference paper, Published paper (Refereed)
Abstract [en]

Although the Lanczos potential (a (2,1) form, L) for the Weyl tensor does not exist in dimensions greater than four, a new potential (a (2,3) form, P, which coincides with the double dual of L in four dimensions) has recently been shown to exist in all dimensions. In this talk we discuss the structure of its wave equation which is obtained from the Bianchi identities, and the related question of gauge. 

Place, publisher, year, edition, pages
Spain: EDR, 2008
National Category
Mathematics
Identifiers
urn:nbn:se:liu:diva-39967 (URN)10.1051/eas:0830036 (DOI)51874 (Local ID)51874 (Archive number)51874 (OAI)
Available from: 2009-10-10 Created: 2009-10-10 Last updated: 2014-08-12
Edgar, B. & Ramos, M. P. (2007). Obtaining a class of Type O pure radiation metrics with a negative cosmological constant, using invariant operators. General Relativity and Gravitation, 39, 539-566
Open this publication in new window or tab >>Obtaining a class of Type O pure radiation metrics with a negative cosmological constant, using invariant operators
2007 (English)In: General Relativity and Gravitation, ISSN 0001-7701, E-ISSN 1572-9532, Vol. 39, p. 539-566Article in journal (Refereed) Published
Abstract [en]

Using the generalised invariant formalism we derive a special subclass of conformally flat spacetimes whose Ricci tensor has a pure radiation and a Ricci scalar component. The method used is a development of the methods used earlier for pure radiation spacetimes of Petrov types O and N, respectively. In this paper we demonstrate how to handle, in the generalised invariant formalism, spacetimes with isotropy freedom and rich Killing vector structure. Once the spacetimes have been constructed, it is straightforward to deduce their Karlhede classification: the Karlhede algorithm terminates at the fourth derivative order, and the spacetimes all have one degree of null isotropy and three, four or five Killing vectors.

National Category
Mathematics
Identifiers
urn:nbn:se:liu:diva-36071 (URN)10.1007/s10714-006-0392-0 (DOI)29745 (Local ID)29745 (Archive number)29745 (OAI)
Available from: 2009-10-10 Created: 2009-10-10 Last updated: 2017-12-13
Edgar, B. & Senovilla, J. (2007). The new potential for the Weyl tensor in all dimensions: gauge and wave equation. In: Britgrav7,2007.
Open this publication in new window or tab >>The new potential for the Weyl tensor in all dimensions: gauge and wave equation
2007 (English)In: Britgrav7,2007, 2007Conference paper, Published paper (Refereed)
Abstract [en]

 Although the Lanczos potential L for the Weyl tensor does not exist in dimensions greater than four, a new potential P, (which coincides with the double dual of L in four dimensions) has recently been shown to exist in all dimensions. In this talk we discuss the structure of its wave equation which is obtained from the Bianchi identities, and the related question of gauge.  

National Category
Mathematics
Identifiers
urn:nbn:se:liu:diva-37831 (URN)39445 (Local ID)39445 (Archive number)39445 (OAI)
Available from: 2009-10-10 Created: 2009-10-10
Edgar, B. & Machado Ramos, M. (2007). Type O pure radiation metrics with a cosmological constant. General Relativity and Gravitation, 39(11), 1749-1772
Open this publication in new window or tab >>Type O pure radiation metrics with a cosmological constant
2007 (English)In: General Relativity and Gravitation, ISSN 0001-7701, E-ISSN 1572-9532, Vol. 39, no 11, p. 1749-1772Article in journal (Refereed) Published
Abstract [en]

In this paper we complete the integration of the conformally flat pure radiation spacetimes with a non-zero cosmological constant Λ, and τ ≠ 0, by considering the case Λ +ττ ≠ 0. This is a further demonstration of the power and suitability of the generalised invariant formalism (GIF) for spacetimes where only one null direction is picked out by the Riemann tensor. For these spacetimes, the GIF picks out a second null direction (from the second derivative of the Riemann tensor) and once this spinor has been identified the calculations are transferred to the simpler GHP formalism, where the tetrad and metric are determined. The whole class of conformally flat pure radiation spacetimes with a non-zero cosmological constant (those found in this paper, together with those found earlier for the case Λ +ττ = 0) have a rich variety of subclasses with zero, one, two, three, four or five Killing vectors. © 2007 Springer Science+Business Media, LLC.

National Category
Mathematics
Identifiers
urn:nbn:se:liu:diva-39966 (URN)10.1007/s10714-007-0487-2 (DOI)51873 (Local ID)51873 (Archive number)51873 (OAI)
Available from: 2009-10-10 Created: 2009-10-10 Last updated: 2017-12-13
Edgar, B. & Ramos, M. P. (2007). Using the generalised invariant formalism: a class of conformally flat pure radiation metrics with a negative cosmological constant. In: The Spanish Relativity Meeting ERE 2006: Einsteins Legacy,2006. Paper presented at XXIXth Spanish Relativity Meeting (ERE 2006), Palma de Mallorca, Spain (pp. 012013). Institute of Physics Publishing (IOPP)
Open this publication in new window or tab >>Using the generalised invariant formalism: a class of conformally flat pure radiation metrics with a negative cosmological constant
2007 (English)In: The Spanish Relativity Meeting ERE 2006: Einsteins Legacy,2006, Institute of Physics Publishing (IOPP), 2007, p. 012013-Conference paper, Published paper (Refereed)
Abstract [en]

We demonstrate an integration procedure for the generalised invariant formalism by obtaining a subclass of conformally flat pure radiation spacetimes with a negative cosmological constant. The method used is a development of the methods used earlier for pure radiation spacetimes of Petrov types O and N respectively. This subclass of spacetimes turns out to have one degree of isotropy freedom, so in this paper we have extended the integration procedure for the generalised invariant formalism to spacetimes with isotropy freedom. 

Place, publisher, year, edition, pages
Institute of Physics Publishing (IOPP), 2007
Series
Journal of Physics: Conference Series (Print), ISSN 1742-6588
National Category
Mathematics
Identifiers
urn:nbn:se:liu:diva-36072 (URN)10.1088/1742-6596/66/1/012013 (DOI)29765 (Local ID)29765 (Archive number)29765 (OAI)
Conference
XXIXth Spanish Relativity Meeting (ERE 2006), Palma de Mallorca, Spain
Available from: 2009-10-10 Created: 2009-10-10 Last updated: 2012-08-16Bibliographically approved
Senovilla, J. M. & Edgar, B. (2006). A weighted de Rham operator acting on arbitrary tensor fields and their local potentials. Journal of Geometry and Physics, 56(10), 2135-2162
Open this publication in new window or tab >>A weighted de Rham operator acting on arbitrary tensor fields and their local potentials
2006 (English)In: Journal of Geometry and Physics, ISSN 0393-0440, E-ISSN 1879-1662, Vol. 56, no 10, p. 2135-2162Article in journal (Refereed) Published
Abstract [en]

We introduce a weighted de Rham operator which acts on arbitrary tensor fields by considering their structure as r-fold forms. We can thereby define associated superpotentials for all tensor fields in all dimensions and, from any of these superpotentials, we deduce in a straightforward and natural manner the existence of 2 r potentials for any tensor field, where r is its form-structure number. By specialising this result to symmetric double forms, we are able to obtain a pair of potentials for the Riemann tensor, and a single (2, 3)-form potential for the Weyl tensor due to its tracelessness. This latter potential is the n-dimensional version of the double dual of the classical four-dimensional (2, 1)-form Lanczos potential. We also introduce a new concept of harmonic tensor fields, and demonstrate that the new weighted de Rham operator has many other desirable properties and, in particular, is the natural operator to use in the Laplace-like equation for the Riemann tensor. © 2005 Elsevier Ltd. All rights reserved.

National Category
Mathematics
Identifiers
urn:nbn:se:liu:diva-30239 (URN)10.1016/j.geomphys.2005.11.011 (DOI)15744 (Local ID)15744 (Archive number)15744 (OAI)
Available from: 2009-10-09 Created: 2009-10-09 Last updated: 2017-12-13
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