Vacuum Einstein equations in terms of curvature forms

Obukhov, Yuri N.; Tertychniy, S. I.

doi:10.1088/0264-9381/13/6/025

Cited by 17 publications

(19 citation statements)

References 34 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…They seem to be the first who were able to show that a conformal metric structure is actually implied as a consequence of symmetry and closure. These structures were subsequently discussed by numerous people, by 't Hooft [70], Harnett [18], and Obukhov & Tertychniy [50], amongst others, see also the references given there. These structures were subsequently discussed by numerous people, by 't Hooft [70], Harnett [18], and Obukhov & Tertychniy [50], amongst others, see also the references given there.…”

Section: Dual Operators and Metricsmentioning

confidence: 99%

Linear pre-metric electrodynamics and deduction of the light cone

Rubilar

2002

Ann. Phys.

106

View full text Add to dashboard Cite

We formulate a general framework for describing the electromagnetic properties of spacetime. These properties are encoded in the 'constitutive tensor of the vacuum', a quantity analogous to that used in the description of material media. We give a generally covariant derivation of the Fresnel equation describing the local properties of the propagation of electromagnetic waves for the case of the most general possible linear constitutive tensor. We also study the particular case in which a light cone structure is induced and the circumstances under which such a structure emerges. In particular, we will study the relationship between the dual operators defined by the constitutive tensor under certain conditions and the existence of a conformal metric. Closure and symmetry of the constitutive tensor will be found as conditions which ensure the existence of a conformal metric. We will also see how the metric components can be explicitly deduced from the constitutive tensor if these two conditions are met. Finally, we will apply the same method to explore the consequences of relaxing the condition of symmetry and how this affects the emergence of the light cone. * Email: grubilar at udec dot cl.

show abstract

Section: Dual Operators and Metricsmentioning

confidence: 99%

Linear pre-metric electrodynamics and deduction of the light cone

Rubilar

2002

Ann. Phys.

106

View full text Add to dashboard Cite

show abstract

“…(5) Extracting the metric: Urbantke [7] (see also the discussions in [9,10]) was able to derive, within SU (2) Yang-Mills theory, a 4-dimensional metric g ij (with i, j, . .…”

mentioning

confidence: 99%

Spacetime metric from linear electrodynamics

Obukhov

Hehl

1999

Physics Letters B

View full text Add to dashboard Cite

show abstract

“…At the root of the methods of complex relativity [1][2][3][4][5] is the fact that the Lorentz group O(3, 1) -or rather, its Lie algebra so(3, 1) -admits various isomorphic representations. Perhaps the most studied representation is the (1-to-2) representation of the proper orthochronous Lorentz group SO 0 (3, 1) by the elements of the group SL(2; C), which leads one into the realm of Dirac spinors and relativistic wave mechanics.…”

Section: Introductionmentioning

confidence: 99%

“…Perhaps the most studied representation is the (1-to-2) representation of the proper orthochronous Lorentz group SO 0 (3, 1) by the elements of the group SL(2; C), which leads one into the realm of Dirac spinors and relativistic wave mechanics. One approach to complex relativity then involves the representation of 2-forms on spacetime by SL(2; C) spinors (see Obukhov and Tertychniy [5]). Another approach to complex relativity is based in the fact that there is also an isomorphism of SO 0 (3, 1) with the complex orthogonal group in three dimensions SO(3; C), which acts naturally on C 3 .…”

Section: Introductionmentioning

confidence: 99%

A more direct representation for complex relativity

Delphenich¹

2007

Ann. Phys.

View full text Add to dashboard Cite

An alternative to the representation of complex relativity by self-dual complex 2-forms on the spacetime manifold is presented by assuming that that the bundle of real 2-forms is given an almost-complex structure. From this, one can define a complex orthogonal structure on the bundle of 2-forms, which results in a more direct representation of the complex orthogonal group in three complex dimensions. The geometrical foundations of general relativity are then presented in terms of the bundle of oriented complex orthogonal 3-frames on the bundle of 2-forms in a manner that essentially parallels their construction in terms of self-dual complex 2-forms. It is shown that one can still discuss the Debever-Penrose classification of the Riemannian curvature tensor in terms of the representation presented here.Comment: 33 page

show abstract

Vacuum Einstein equations in terms of curvature forms

Cited by 17 publications

References 34 publications

Linear pre-metric electrodynamics and deduction of the light cone

Linear pre-metric electrodynamics and deduction of the light cone

Spacetime metric from linear electrodynamics

A more direct representation for complex relativity

Contact Info

Product

Resources

About