Black Holes as Exact Solutions of the Einstein-Maxwell Equations of Petrov Type D

It is shown that the complex recurrent space-times are of Petrov type D or N. The spaces of type D are non-empty and decomposable into the product of two 2-dimensional spaces of arbitrary curvature, the recurrence vector being necessarily real. It is established that the problem of determining the type N complex recurrent spaces is equivalent to that of determining the spaces of type N admitting a recurrent null vector field. A coordinate system is given in which the metric of such spaces is determined up to three arbitrary functions and a constant. The spaces fall into four invariant classes according to the permitted algebraic form of the Ricci tensor. The Einstein-Maxwell equations are solved, the solutions obtained providing examples for three of the classes. It seems that the remaining class cannot contain any physically reasonable solutions of Einstein’s equations. The general metric of the complex recurrent space of Petrov type N with recurrence vector proportional to the principal null vector of the Weyl tensor is also given and some of its properties are discussed. The space of plane gravitational waves admitting a singular electromagnetic field is the only physically significant space-time of this class. The conformally recurrent spaces and the conformal symmetric spaces are also determined.

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Cosmological exact solutions set of a perfect fluid in an anisotropic space-time in Petrov type D

Advanced Studies in Theoretical Physics ◽

10.12988/astp.2016.6311 ◽

2016 ◽

Vol 10 ◽

pp. 267-295

Author(s):

R. Alvarado

Keyword(s):

Exact Solutions ◽

Perfect Fluid ◽

Space Time ◽

Petrov Type ◽

Anisotropic Space ◽

Type D ◽

Petrov Type D

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Cylindrically Symmetric, Asymptotically Flat, Petrov Type D Spacetime with a Naked Curvature Singularity and Matter Collapse

Advances in High Energy Physics ◽

10.1155/2017/7943649 ◽

2017 ◽

Vol 2017 ◽

pp. 1-6 ◽

Cited By ~ 8

Author(s):

Faizuddin Ahmed

Keyword(s):

Cosmic Time ◽

Petrov Type ◽

Energy Conditions ◽

Anisotropic Fluid ◽

Curvature Singularity ◽

Field Equations ◽

Asymptotically Flat ◽

Type D ◽

Cylindrically Symmetric ◽

Petrov Type D

We present a cylindrically symmetric, Petrov type D, nonexpanding, shear-free, and vorticity-free solution of Einstein’s field equations. The spacetime is asymptotically flat radially and regular everywhere except on the symmetry axis where it possesses a naked curvature singularity. The energy-momentum tensor of the spacetime is that for an anisotropic fluid which satisfies the different energy conditions. This spacetime is used to generate a rotating spacetime which admits closed timelike curves and may represent a Cosmic Time Machine.

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