Static plane symmetric spacetimes (original) (raw)

Classification of Plane Symmetric Static Space-Times According to Their Noether Symmetries

International Journal of Theoretical Physics, 2013

In this paper we give a classification of plane symmetric static space-times using symmetry method. For this purpose we consider the Lagrangian corresponding to the general plane symmetric static metric in the Noether symmetry equation. This provides a system of determining equations. Solutions of this system give us classification of the plane symmetric static space-times according to their Noether symmetries. During this classification we recover all the results listed in Feroze et al.

Complete classification of spherically symmetric static spacetimes via Noether symmetries

In this paper we give a complete classification of spherically symmetric static space-times by their Noether symmetries. The determining equations for Noether symmetries are obtained by using the usual Lagrangian of a general spherically symmetric static spacetime which are integrated for each case. In particular we observe that spherically symmetric static spacetimes are categorized into six distinct classes corresponding to Noether algebra of dimensions 5, 6, 7, 9, 11 and 17. Using Noether`s theorem we also write down the first integrals for each class of such spacetimes corresponding to their Noether symmetries.

Matter Symmetries of Non-Static Plane Symmetric Spacetimes

2020

The matter collineations of plane symmetric spacetimes are studied according to the degenerate energy-momentum tensor. We have found many cases where the energy-momentum tensor is degenerate but the group of matter collineations is finite. Further we obtain different constraint equations on the energy-momentum tensor. Solving these constraints may provide some new exact solutions of Einstein field equations.

Some properties of a particular static, axially symmetric space-time

Physical Review D, 1981

The behavior of the directional singularities of a family of Weyl solutions is examined. By examining the. space-time in a different coordinate system, the directional singularities are understood. The singular points are actually extended hypersurfaces which have been collapsed to a point by an improper choice of coordinates. The singular structure is examined in the new coordinate system. The coordinate system shows the space-time to be geodesically incomplete. A completion of the symmetry axis is described.

On the local form of static plane symmetric spacetimes in the presence of matter

Classical and Quantum Gravity

For any configuration of a static plane-symmetric distribution of matter along spacetime, there are coordinates where the metric can be put explicitly as a functional of the energy density and pressures. It satisfies Einstein equations as far as we require the conservation of the energy-momentum tensor, which is the single ODE for selfgravitating hydrostatic equilibrium. As a direct application, a general solution is given when the pressures are linearly related to the energy density, recovering, as special cases, most of known solutions of static plane-symmetric Einstein equations.

static spacetimes via Noether symmetries

2014

In this paper we give a complete classification of spherically symmetric static spacetimes by their Noether symmetries. The determining equations for Noether symmetries are obtained by using the usual Lagrangian of a general spherically symmetric static spacetime which are integrated for each case. In particular we observe that spherically symmetric static spacetimes are categorized into six distinct classes corresponding to Noether algebra of dimensions 5, 6, 7, 9, 11 and 17. Using Noether's theorem we also write down the first integrals for each class of such spacetimes corresponding to their Noether symmetries.

Classification of Spherically Symmetric Static Spacetimes According to Their Matter Collineations

General Relativity and Gravitation, 2003

The spherically symmetric static spacetimes are classified according to their matter collineations. These are studied when the energy-momentum tensor is degenerate and also when it is non-degenerate. We have found a case where the energy-momentum tensor is degenerate but the group of matter collineations is finite. For the non-degenerate case, we obtain either four, five, six or ten independent matter collineations in which four are isometries and the rest are proper. We conclude that the matter collineations coincide with the Ricci collineations but the constraint equations are different which on solving can provide physically interesting cosmological solutions.

Lie Symmetries of the Energy–Momentum Tensor for Plane Symmetric Static Spacetimes

International Journal of Modern Physics D, 2005

Matter collineations (MCs) are the vector fields along which the energy–momentum tensor remains invariant under Lie transport. Invariance of the metric, the Ricci and the Riemann tensors have been studied extensively and the vectors along which these tensors remain invariant are called Killing vectors (KVs), Ricci collineations (RCs) and curvature collineations (CCs), respectively. In this paper, plane symmetric static spacetimes have been studied for their MCs. Explicit form of MCs together with the Lie algebra admitted by them has been presented. Examples of spacetimes have been constructed for which MCs have been compared with their RCs and KVs. The comparison shows that neither of the sets of RCs and MCs contains the other, in general.