On the Meaning of General Covariance and the Relevance of Observers in General Relativity

Herrera, L.

doi:10.1142/s0218271811020676

Cited by 19 publications

(14 citation statements)

References 16 publications

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“…On the basis of the orthogonal splitting approach of the Riemann tensor studied by Bel [ 47 ] and followed by [ 48 , 49 , 50 , 51 , 52 , 53 ], we shall calculate structure scalars in metric

gravity. We shall use terminologies with minor changes as that utilized in [ 48 ].…”

Section: Orthogonal Splitting Of Curvature Tensorsmentioning

confidence: 99%

A Comprehensive Analysis of Hyperbolical Fluids in Modified Gravity

Yousaf

Bhatti

Khlopov

et al. 2022

Entropy

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This paper is devoted to understanding a few characteristics of static irrotational matter content that assumes hyperbolical symmetry. For this purpose, we use metric f(R) gravity to carry out our analysis. It is noticed that the matter distribution cannot fill the region close to the center of symmetry, thereby implying the existence of an empty core. Moreover, the evaluation of the effective energy density reveals that it is inevitably negative, which could have utmost relevance in understanding various quantum field events. To derive the structure scalars, we perform the orthogonal splitting of the Riemann tensor in this modified gravity. Few relationships among matter variables and both Tolman and Misner Sharp are determined. Through two generating functions, some hyperbolically symmetric cosmological models, as well as their physical interpretations, are studied. To delve deeply into the role of f(R) terms, the model of the less-complex relativistic system of Einstein gravity is presented.

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“…On the basis of the orthogonal splitting approach of the Riemann tensor studied by Bel [ 47 ] and followed by [ 48 , 49 , 50 , 51 , 52 , 53 ], we shall calculate structure scalars in metric

gravity. We shall use terminologies with minor changes as that utilized in [ 48 ].…”

Section: Orthogonal Splitting Of Curvature Tensorsmentioning

confidence: 99%

A Comprehensive Analysis of Hyperbolical Fluids in Modified Gravity

Yousaf

Bhatti

Khlopov

et al. 2022

Entropy

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“…This equation has directly relate Y T to the effective matter variables and Tolman mass function. It is well-known from the working of Herrera et al [54,55] and Yousaf et al [56][57][58] that Y T has been involved in the evolutionary equation of the expansion scalar which is widely known as Raychaudhuri equation. Equation (57) suggests that m T could be used to define the Raychaudhuri equation even in f (R, T, Q) gravity.…”

Section: The Orthogonal Splitting Of the Riemann Tensormentioning

confidence: 99%

Influence of Modification of Gravity on the Complexity Factor of Static Spherical Structures

Yousaf,

Khlopov,

Bhatti

et al. 2020

Preprint

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The aim of this paper is to generalize the definition of complexity for the static selfgravitating structure in f (R, T, Q) gravitational theory, where R is the Ricci scalar, T is the trace part of energy momentum tensor and Q ≡ R αβ T αβ . In this context, we have considered locally anisotropic spherical matter distribution and calculated field equations and conservation laws. After the orthogonal splitting of the Riemann curvature tensor, we found the corresponding complexity factor with the help of structure scalars. It is seen that the system may have zero complexity factor if the effects of energy density inhomogeneity and pressure anisotropy cancel the effects of each other. All of our results reduce to general relativity on assuming f (R, T, Q) = R condition.

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“…This expression explicitly relates Y T to the matter variables with modified corrections and Tolman mass function in f (R, T, Q) theory. Herrera et al [63,64] and Yousaf et al [65][66][67] shown the involvement of Y T in the evolutionary equation for the expansion scalar, commonly known as Raychaudhuri equation. Thus, Eq.…”

Section: The Mass Functionmentioning

confidence: 99%

New Definition of Complexity Factor in $f(R,T,R_{μν}T^{μν})$ Gravity

Yousaf,

Bhatti,

Naseer

2020

Preprint

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This paper is devoted to present new definition of complexity factor for static cylindrically symmetric matter configurations in f (R, T, R µν T µν ) gravity. For this purpose, we have considered irrotational static cylindrical spacetime coupled with a locally anisotropic relativistic fluid. After formulating gravitational field and conservation equations, we have performed orthogonal splitting of the Riemann curvature tensor. Unlike GR (for spherical case) the one of the structure scalars X T F , has been identified to be a complexity factor. This factor contains effective forms of the energy density, and anisotropic pressure components. Few peculiar relations among complexity factor, Tolman mass and Weyl scalar are also analyzed with the modified f (R, T, R µν T µν ) corrections.

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On the Meaning of General Covariance and the Relevance of Observers in General Relativity

Cited by 19 publications

References 16 publications

A Comprehensive Analysis of Hyperbolical Fluids in Modified Gravity

A Comprehensive Analysis of Hyperbolical Fluids in Modified Gravity

Influence of Modification of Gravity on the Complexity Factor of Static Spherical Structures

New Definition of Complexity Factor in $f(R,T,R_{μν}T^{μν})$ Gravity

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