Symmetries of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"><mml:mrow><mml:mi>f</mml:mi><mml:mo>−</mml:mo></mml:mrow></mml:math>associated standard static spacetimes and applications

El-Sayied, H. K.; Shenawy, Sameh; Syied, Noha

doi:10.1016/j.joems.2017.07.002

Cited by 4 publications

(4 citation statements)

References 11 publications

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“…Spacetimes of constant curvature are known to have maximum such symmetry, that is, they admit the maximum number of linearly independent Killing vector fields. The maximum numer of linearly independent Killing vector fields in an n − dimensional spacetime is n(n+1) 2 (The reader is referred to [18][19][20][21][22] and references therein for a more discussion on this topic). This fact with the above theorem leads to the following corollary.…”

Section: Concircularly Flat Spacetimes In F(r) Gravitymentioning

confidence: 99%

Spacetimes Admitting Concircular Curvature Tensor in f(R) Gravity

Shenawy

Abu-Donia

et al. 2022

Front. Phys.

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The main object of this paper is to investigate spacetimes admitting concircular curvature tensor in f(R) gravity theory. At first, concircularly flat and concircularly flat perfect fluid spacetimes in fR gravity are studied. In this case, the forms of the isotropic pressure p and the energy density σ are obtained. Next, some energy conditions are considered. Finally, perfect fluid spacetimes with divergence free concircular curvature tensor in f(R) gravity are studied; amongst many results, it is proved that if the energy-momentum tensor of such spacetimes is recurrent or bi-recurrent, then the Ricci tensor is semi-symmetric and hence these spacetimes either represent inflation or their isotropic pressure and energy density are constants.

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Section: Concircularly Flat Spacetimes In F(r) Gravitymentioning

confidence: 99%

Spacetimes Admitting Concircular Curvature Tensor in f(R) Gravity

Shenawy

Abu-Donia

et al. 2022

Front. Phys.

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“…Let M = I ψ ×M be a standard static spacetime with the metric tensor ¯ = −ψ 2 dt 2 ⊕ . Then the Levi-Civita connection ∇ on M is given by [8]…”

Section: Preliminariesmentioning

confidence: 99%

“…In GR, Lorentzian twisted product manifolds were adapted in order to find a general solution to Einstein's field equations. Two well-known significant examples are generalized Robertson Walker spacetime (GRW) ( for more details see [9], [16]) and standard static spacetime (SSST) [8]. Basically, a normal static spacetime can be treated as a Lorentzian warped product manifold where the warping function f is defined on Riemannian manifold and acting on the negative definite metric on an open interval I of real numbers .…”

Section: Introductionmentioning

confidence: 99%

Estimation of almost Ricci-Yamabe solitons on static spacetimes

Siddiqi

Uday

Deshmukh

2022

Filomat

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This research work examines the standard static spacetime (SSST) in terms of almost Ricci-Yamabe soliton with conformal vector field. It is shown that almost Ricci-Yamabe soliton in standard static spacetime with function ? satisfies Poisson-Laplace equation. Next, we consider the function ? is harmonic and discuss the harmonic aspect of almost Ricci-Yamabe soliton on SSST. In addition, we investigate the nature of almost Ricci-Yamabe soliton on SSST with non-rotating Killing vector field. Also, we exhibit that non-steady non shrinking almost Ricci-Yamabe soliton i.e., ?? 0 on smooth, connected, and non-compact SSST with Killing vector field satisfies the Schr?dinger equation for a smooth function ?. Finally, we study almost Ricci-Yamabe soliton on static perfect fluid and vacuum static spacetime with conformal Killing vector field.

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“…Likewise, the submanifold { t }× M is isomorphic to M for each t ∈ M . The reader is referred to previous studies() for more details on warped product manifolds and to other studies() for more details on f −associated standard static spacetimes.…”

Section: An Introductionmentioning

confidence: 99%

Locally symmetric f−associated standard static spacetimes

El-Sayied

Shenawy

Syied

2017

Math Methods in App Sciences

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In this note, we study and explore locally symmetric f−associated standard static spacetimes I f × M. Necessary and sufficient conditions on f−associated standard static spacetimes to be locally symmetric are derived. Some implications for these conditions are considered. KEYWORDSlocally symmetric, standard static spacetime, second-order symmetric tensor Math Meth Appl Sci. 2018;41:5733-5736.wileyonlinelibrary.com/journal/mma

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Symmetries off−associated standard static spacetimes and applications

Cited by 4 publications

References 11 publications

Spacetimes Admitting Concircular Curvature Tensor in f(R) Gravity

Spacetimes Admitting Concircular Curvature Tensor in f(R) Gravity

Estimation of almost Ricci-Yamabe solitons on static spacetimes

Locally symmetric f−associated standard static spacetimes

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