Projective symmetry in null Einstein–Maxwell space-times

The flux integral for axisymmetric polar perturbations of static vacuum space-times, derived in an earlier paper directly from the relevant linearized Einstein equations, is rederived with the aid of the Einstein pseudo-tensor by a simple algorism. A similar earlier effort with the aid of the Landau–Lifshitz pseudo-tensor failed. The success with the Einstein pseudo-tensor is due to its special distinguishing feature that its second variation retains its divergence-free property provided only the equations governing the static space-time and its linear perturbations are satisfied. When one seeks the corresponding flux integral for Einstein‒Maxwell space-times, the common procedure of including, together with the pseudo-tensor, the energy‒momentum tensor of the prevailing electromagnetic field fails. But, a prescription due to R. Sorkin, of including instead a suitably defined ‘Noether operator’, succeeds.

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Study of charged compact stars with class 1 metric under general relativity

Canadian Journal of Physics ◽

10.1139/cjp-2018-0560 ◽

2019 ◽

Vol 97 (12) ◽

pp. 1323-1331 ◽

Cited By ~ 1

Author(s):

S.K. Maurya ◽

S. Roy Chowdhury ◽

Saibal Ray ◽

B. Dayanandan

Keyword(s):

General Relativity ◽

Compact Star ◽

Space Time ◽

Electron Cloud ◽

Compact Stars ◽

Stellar Structure ◽

Spherically Symmetric ◽

Class 1 ◽

Maxwell Space ◽

Physical Tests

In the present paper we study compact stars under the background of Einstein–Maxwell space–time, where the 4-dimensional spherically symmetric space–time of class 1 along with the Karmarkar condition has been adopted. The investigations, via the set of exact solutions, show several important results, such as (i) the value of density on the surface is finite; (ii) due to the presence of the electric field, the outer surface or the crust region can be considered to be made of electron cloud; (iii) the charge increases rapidly after crossing a certain cutoff region (r/R ≈ 0.3); and (iv) the avalanche of charge has a possible interaction with the particles that are away from the center. As the stellar structure supports all the physical tests performed on it, therefore the overall observation is that the model provides a physically viable and stable compact star.

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Infinitesimal holonomy groups of Einstein-Maxwell space-times

General Relativity and Gravitation ◽

10.1007/bf01119813 ◽

1987 ◽

Vol 19 (1) ◽

pp. 95-107 ◽

Cited By ~ 4

Author(s):

C. D. Collinson ◽

P. N. Smith

Keyword(s):

Holonomy Groups ◽

Maxwell Space

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The infinitesimal holonomy group structure of EEnstein-Maxwell space-times

Il Nuovo Cimento B ◽

10.1007/bf02739891 ◽

1979 ◽

Vol 53 (2) ◽

pp. 209-232 ◽

Cited By ~ 7

Author(s):

L. K. Norris ◽

W. R. Davis

Keyword(s):

Group Structure ◽

Holonomy Group ◽

Maxwell Space

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The flux integral for axisymmetric perturbations of static space-times

Proceedings of the Royal Society of London Series A - Mathematical and Physical Sciences ◽

10.1098/rspa.1990.0038 ◽

1990 ◽

Vol 428 (1875) ◽

pp. 325-349 ◽

Cited By ~ 19

Keyword(s):

Black Holes ◽

Perfect Fluid ◽

Gravitational Radiation ◽

Scattering Theory ◽

Scattering Matrix ◽

Conservation Of Energy ◽

Fluid Source ◽

Maxwell Space ◽

Static Space ◽

Axisymmetric Perturbations

The axisymmetric perturbations of static space-times with prevailing sources (a Maxwell field or a perfect fluid) are considered; and it is shown how a flux integral can be derived directly from the relevant linearized equations. The flux integral ensures the conservation of energy in the attendant scattering of radiation and the sometimes accompanying transformation of one kind of radiation into another. The flux integral derived for perturbed Einstein-Maxwell space-times will be particularly useful in this latter context (as in the scattering of radiation by two extreme Reissner-Nordström black-holes) and in the setting up of a scattering matrix. And the flux integral derived for a space-time with a perfect-fluid source will be directly applicable to the problem of the non-radial oscillations of a star with accompanying emission of gravitational radiation and enable its reformulation as a problem in scattering theory.

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