scholarly journals Curvature Properties of Generalized pp-Wave Metrics

2021 ◽  
Vol 45 (02) ◽  
pp. 237-258
Author(s):  
ABSOS ALI SHAIKH ◽  
TRAN QUOC BINH ◽  
HARADHAN KUNDU
Keyword(s):  
Energy Momentum Tensor ◽  
Momentum Tensor ◽  
Sufficient Condition ◽  
Type Condition ◽  
Pure Radiation ◽  
Projective Curvature ◽  
Pp Wave ◽  
Codazzi Type ◽  
Curvature Tensors ◽  
Special Case

The main objective of the present paper is to investigate the curvature properties of generalized pp-wave metrics. It is shown that a generalized pp-wave spacetime is Ricci generalized pseudosymmetric, 2-quasi-Einstein and generalized quasi-Einstein in the sense of Chaki. As a special case it is shown that pp-wave spacetime is semisymmetric, semisymmetric due to conformal and projective curvature tensors, R-space by Venzi and satisfies the pseudosymmetric type condition P ⋅ P = −13Q(S,P). Again we investigate the sufficient condition for which a generalized pp-wave spacetime turns into pp-wave spacetime, pure radiation spacetime, locally symmetric and recurrent. Finally, it is shown that the energy-momentum tensor of pp-wave spacetime is parallel if and only if it is cyclic parallel. Again the energy momentum tensor is Codazzi type if it is cyclic parallel but the converse is not true as shown by an example. Finally, we make a comparison between the curvature properties of the Robinson-Trautman metric and generalized pp-wave metric.

scholarly journals A geometrical model for the evolution of spherical planetary nebulae based on thin-shell formalism

2021 ◽  
pp. 2150191
Author(s):  
Ibrahim Gullu ◽  
S. Habib Mazharimousavi ◽  
S. Danial Forghani
Keyword(s):  
Energy Density ◽  
Planetary Nebula ◽  
Thin Shell ◽  
Energy Momentum Tensor ◽  
Geometric Model ◽  
Geometrical Model ◽  
Momentum Tensor ◽  
Evolution Pattern ◽  
Simple Power Function ◽  
Curvature Tensors

A spherical planetary nebula is described as a geometric model. The nebula itself is considered as a thin-shell, which is visualized as a boundary of two spacetimes. The inner and outer curvature tensors of the thin-shell are found in order to get an expression of the energy-momentum tensor on the thin-shell. The energy density and pressure expressions are derived using the energy-momentum tensor. The time evolution of the radius of the thin-shell is obtained in terms of the energy density. The model is tested by using a simple power function for decreasing energy density and the evolution pattern of the planetary nebula is attained.

On the origin of black hole evaporation radiation

1976 ◽  
Vol 351 (1664) ◽  
pp. 129-139 ◽  
Keyword(s):  
Black Hole ◽  
Energy Momentum Tensor ◽  
Momentum Tensor ◽  
Massless Scalar ◽  
Massless Scalar Field ◽  
Static Vacuum ◽  
Black Hole Evaporation ◽  
A Value ◽  
Special Case ◽  
Collapse Process

The physical basis underlying the black hole evaporation process is clarified by a calculation of the expectation value of the energy-momentum tensor for a massless scalar field in a completely general two dimensional collapse scenario. It is found that radiation is produced inside the collapsing matter which propagates both inwards and outwards. The ingoing com­ponent eventually emerges from the star after travelling through the centre. The outgoing energy flux appears at infinity as the evaporation radiation discovered by Hawking. At late times, outside the star, the former component fades out exponentially, and the latter component approaches a value which is independent of the details of the collapse process. In the special case of a collapsing hollow, thin shell of matter, all the radiation is produced at the shell. These results are independent of regularization ambiguities, which enter only the static vacuum polariza­tion terms in the energy-momentum tensor. The significance of an earlier remark about black hole explosions is discussed in the light of these results.

Pseudo B-symmetric manifolds

2017 ◽  
Vol 14 (09) ◽  
pp. 1750119
Author(s):  
Young Jin Suh ◽  
Carlo Alberto Mantica ◽  
Uday Chand De ◽  
Prajjwal Pal
Keyword(s):  
Riemannian Manifold ◽  
Explicit Form ◽  
Riemannian Manifolds ◽  
Ricci Tensor ◽  
Sufficient Condition ◽  
Conformally Flat ◽  
Harmonic Curvature ◽  
Codazzi Type ◽  
Curvature Tensors

In this paper, we introduce a new tensor named [Formula: see text]-tensor which generalizes the [Formula: see text]-tensor introduced by Mantica and Suh [Pseudo [Formula: see text] symmetric Riemannian manifolds with harmonic curvature tensors, Int. J. Geom. Methods Mod. Phys. 9(1) (2012) 1250004]. Then, we study pseudo-[Formula: see text]-symmetric manifolds [Formula: see text] which generalize some known structures on pseudo-Riemannian manifolds. We provide several interesting results which generalize the results of Mantica and Suh [Pseudo [Formula: see text] symmetric Riemannian manifolds with harmonic curvature tensors, Int. J. Geom. Methods Mod. Phys. 9(1) (2012) 1250004]. At first, we prove the existence of a [Formula: see text]. Next, we prove that a pseudo-Riemannian manifold is [Formula: see text]-semisymmetric if and only if it is Ricci-semisymmetric. After this, we obtain a sufficient condition for a [Formula: see text] to be pseudo-Ricci symmetric in the sense of Deszcz. Also, we obtain the explicit form of the Ricci tensor in a [Formula: see text] if the [Formula: see text]-tensor is of Codazzi type. Finally, we consider conformally flat pseudo-[Formula: see text]-symmetric manifolds and prove that a [Formula: see text] spacetime is a [Formula: see text]-wave under certain conditions.

Propagation of hydromagnetic waves in a relativistic plasma

1982 ◽  
Vol 27 (1) ◽  
pp. 121-127 ◽  
Author(s):  
A. Granik
Keyword(s):  
Energy Momentum Tensor ◽  
Momentum Density ◽  
Momentum Tensor ◽  
Mhd Equations ◽  
Hydrodynamic Approach ◽  
Zero Momentum ◽  
Hydromagnetic Waves ◽  
Limiting Case ◽  
Special Case ◽  
Perturbation Approximation

The hydrodynamic approach to a relativistic gas is studied on the basis of methods used by Chew, Goldberger & Low and by Scargle. As the result of this study, the explicit form of the energy–momentum tensor is obtained by straight-forward application of Lorentz transformation. The term corresponding to non-zero momentum density in the plasma frame of reference is included in the energy–momentum tensor. For the limiting case of small bulk velocities compared with the speed of light in vacua, the energy flux as described by non- relativistic theory is immediately recovered. For the special case of scalar pressure, the energy–momentum tensor considered by Taub and by Harris follows directly from our expression. In a small-perturbation approximation, it is possible to close the system of MHD equations. As a result the solution describing all possible wave modes is derived. This solution coincides with the solution obtained by means of the kinetic theory.

scholarly journals THE LUKASH PLANE-WAVE ATTRACTOR AND RELATIVE ENERGY

2007 ◽  
Vol 22 (21) ◽  
pp. 1601-1609
Author(s):  
MURAT KORUNUR ◽  
MUSTAFA SALTI ◽  
OKTAY AYDOGDU
Keyword(s):  
Plane Wave ◽  
Energy Distribution ◽  
Energy Momentum Tensor ◽  
Teleparallel Gravity ◽  
Relative Energy ◽  
Momentum Tensor ◽  
Gravitational Fields ◽  
Teleparallel Theory ◽  
The Universe ◽  
Special Case

We study energy distribution in the context of teleparallel theory of gravity, due to matter and fields including gravitation, of the universe based on the plane-wave Bianchi VIIδ spacetimes described by the Lukash metric. For this calculation, we consider the teleparallel gravity analogs of the energy–momentum formulations of Einstein, Bergmann–Thomson and Landau–Lifshitz. We find that Einstein and Bergmann–Thomson prescriptions agree with each other and give the same results for the energy distribution in a given spacetime, but the Landau–Lifshitz complex does not. Energy density turns out to be nonvanishing in all of these prescriptions. It is interesting to mention that the results can be reduced to the already available results for the Milne universe when we write ω = 1 and Ξ2 = 1 in the metric of the Lukash spacetime, and for this special case, we get the same relation among the energy–momentum formulations of Einstein, Bergmann–Thomson and Landau–Lifshitz as obtained for the Lukash spacetime. Furthermore, our results support the hypothesis by Cooperstock that the energy is confined to the region of nonvanishing energy–momentum tensor of matter and all non-gravitational fields, and also sustain the importance of the energy–momentum definitions in the evaluation of the energy distribution associated with a given spacetime.

scholarly journals Curvature properties of Nariai spacetimes

2020 ◽  
Vol 17 (03) ◽  
pp. 2050034 ◽  
Author(s):  
Absos Ali Shaikh ◽  
Akram Ali ◽  
Ali H. Alkhaldi ◽  
Dhyanesh Chakraborty
Keyword(s):  
Covariant Derivative ◽  
Ricci Tensor ◽  
Energy Momentum Tensor ◽  
Momentum Tensor ◽  
Topological Product ◽  
Geometric Structures ◽  
Type Formula ◽  
Curvature Tensors ◽  
Recurrent Type

This paper is concerned with the study of the geometry of (charged) Nariai spacetime, a topological product spacetime, by means of covariant derivative(s) of its various curvature tensors. It is found that on this spacetime the condition [Formula: see text] is satisfied and it also admits the pseudosymmetric type curvature conditions [Formula: see text] and [Formula: see text]. Moreover, it is 4-dimensional Roter type, [Formula: see text]-quasi-Einstein and generalized quasi-Einstein spacetime. The energy–momentum tensor is expressed explicitly by some 1-forms. It is worthy to see that a generalization of such topological product spacetime proposes to exist with a class of generalized recurrent type manifolds which is semisymmetric. It is observed that the rank of [Formula: see text], [Formula: see text], of Nariai spacetime (NS) is 0 whereas in case of charged Nariai spacetime (CNS) it is 2, which exhibits that effects of charge increase the rank of Ricci tensor. Also, due to the presence of charge in CNS, it gives rise to the proper pseudosymmetric type geometric structures.

CASIMIR EFFECT FOR THE ROBIN SURFACES IN STATIC ROBERTSON–WALKER SPACE–TIME

2011 ◽  
Vol 20 (02) ◽  
pp. 161-168 ◽  
Author(s):  
MOHAMMAD R. SETARE ◽  
M. DEHGHANI
Keyword(s):  
Scalar Field ◽  
Energy Momentum Tensor ◽  
Casimir Effect ◽  
Vacuum Expectation ◽  
Robin Boundary Condition ◽  
Momentum Tensor ◽  
Space Time ◽  
Conformally Invariant ◽  
Time Space ◽  
Robin Boundary

We investigate the energy–momentum tensor for a massless conformally coupled scalar field in the region between two curved surfaces in k = -1 static Robertson–Walker space–time. We assume that the scalar field satisfies the Robin boundary condition on the surfaces. Robertson–Walker space–time space is conformally related to Rindler space; as a result we can obtain vacuum expectation values of the energy–momentum tensor for a conformally invariant field in Robertson–Walker space–time space from the corresponding Rindler counterpart by the conformal transformation.

scholarly journals Cutoff AdS3 versus $$ T\overline{T} $$ CFT2 in the large central charge sector: correlators of energy-momentum tensor

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Yi Li ◽  
Yang Zhou
Keyword(s):  
Field Theory ◽  
Euclidean Plane ◽  
Energy Momentum Tensor ◽  
Central Charge ◽  
Momentum Tensor ◽  
Two Dimensional ◽  
Conformal Field ◽  
Operator Identity ◽  
Pure Gravity ◽  
Charge Sector

Abstract In this article we probe the proposed holographic duality between $$ T\overline{T} $$ T T ¯ deformed two dimensional conformal field theory and the gravity theory of AdS3 with a Dirichlet cutoff by computing correlators of energy-momentum tensor. We focus on the large central charge sector of the $$ T\overline{T} $$ T T ¯ CFT in a Euclidean plane and a sphere, and compute the correlators of energy-momentum tensor using an operator identity promoted from the classical trace relation. The result agrees with a computation of classical pure gravity in Euclidean AdS3 with the corresponding cutoff surface, given a holographic dictionary which identifies gravity parameters with $$ T\overline{T} $$ T T ¯ CFT parameters.

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