Embeddings for general relativity

León, J. Ponce de

doi:10.1088/0264-9381/32/19/195018

Cited by 19 publications

(34 citation statements)

References 62 publications

(197 reference statements)

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“…This situation was also encountered by Ray et al (2007) who considered a dark energy model with Λ = 3αH 2 (see also Arbab 1997;Singh et al 1998;Ponce de Leone 2003), under the assumption that G is also time dependent, and showed that comparison with most observations requires a negative value of α.…”

Section: Discussionsupporting

confidence: 51%

Inertia in Friedmann Universes with variable G $G$ and Λ $\varLambda$

Sultana

Kazanas

2015

Astrophys Space Sci

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In light of the recent interest in dynamical dark energy models based on a cosmology with varying gravitational and cosmological parameters G and Λ, we present here a model of inertia in a type of Friedmann universe with G = G 0 (A/A 0 ) σ ; A being the dimensionless scale factor, that was recently studied by Singh et al. (Astrophys. Space Sci. 345:213, 2013). The proposed Machian model of inertia utilizes the curved space generalization of Sciama's law of inertial induction, which is based on the analogy between the retarded far fields of electrodynamics and those of gravitation, and expresses the total inertial force F = −ma on an accelerating mass m in terms of contributions from all matter in the observable Universe. We show that for a varying Friedmann model with σ = −3/2, inertial induction alone can account for the total inertial force on the accelerating mass. We then compare this cosmological model with current observational constraints for the variation of G.

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Section: Discussionsupporting

confidence: 51%

Inertia in Friedmann Universes with variable G $G$ and Λ $\varLambda$

Sultana

Kazanas

2015

Astrophys Space Sci

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“…It is worth noting that in establishing the IMT [4], or even the modified scalar-tensor theories, see, e.g., [9], an apparent vacuum 2 bulk has been considered. However, in this work, we would establish a more extended version of a reduced theory by taking a non-vanishing energy momentum tensor, L (D+1) matt = 0.…”

Section: Modified Sáez-ballester Scalar-tensor Theory In Arbitrarmentioning

confidence: 99%

“…It has been shown that the classical tests of general relativity and the experimental limits on violation of the equivalence principle do not disqualify any higher dimensional theories of gravity [5][6][7]. Concerning astrophysical/cosmological applications, such induced sectors or their extensions can play the role of either ordinary matter, dark matter or dark energy [7][8][9][10][11][12][13][14][15].…”

Section: Introductionmentioning

confidence: 99%

Late time cosmic acceleration in modified Sáez–Ballester theory

Rasouli

Pacheco

Sakellariadou

et al. 2020

Physics of the Dark Universe

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We establish an extended version of the modified Sáez-Ballester (SB) scalar-tensor theory in arbitrary dimensions whose energy momentum tensor as well as potential are pure geometrical quantities. This scenario emerges by means of two scalar fields (one is present in the SB theory and the other is associated with the extra dimension) which widens the scope of the induced-matter theory. Moreover, it bears a close resemblance to the standard Sáez-Ballester scalar-tensor theory, as well as other alternative theories to general relativity, whose construction includes either a minimally or a non-minimally coupled scalar field. However, contrary to those theories, in our framework the energy momentum tensor and the scalar potential are not added by hand, but instead are dictated from the geometry. Concerning cosmological applications, our herein contribution brings a new perspective. We firstly show that the dark energy sector can be naturally retrieved within a strictly geometric perspective, and we subsequently analyze it. Moreover, our framework may provide a hint to understand the physics of lower gravity theories.

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“…The famous Friedman-Robertson-Lemaitre space-time, is of class p = 1, while the Schwarzschilds exterior and interior solutions are of class p = 2 and class p = 1 respectively, moreover Kerr metric is class 5. In the literature [42][43][44][45][46][47][48][49], there are many interesting work concerning the effects of the technique of embedding of lower dimensional Riemannian space into the higher dimensional pseudo-Euclidean space in the framework of GR. The main consequence of embedding a Riemannian variety corresponding to a spherically symmetric and static spacetime into a pseudo Euclidean space is the so-called Eisland condition.…”

Section: Introductionmentioning

confidence: 99%

A generalized Finch–Skea class one static solution

et al. 2019

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In the present article, we discuss relativistic anisotropic solutions of the Einstein field equation for the spherically symmetric line element under the class one condition. To do so we apply the embedding class one technique using Eisland condition. Within this approach, one arrives at a particular differential equation that links the two metric components e ν and e λ . In order to obtain the full space-time description inside the stellar configuration we ansatz the generalized form of metric component grr corresponding to the Finch-Skea solution. Once the space-time geometry is specified we obtain the complete thermodynamic description i.e. the matter density ρ, the radial, and tangential pressures pr and pt, respectively. Graphical analysis shows that the obtained model respects the physical and mathematical requirements that all ultra-high dense collapsed structures must obey. These salient features concern well behaved metric potentials and thermodynamic observables i.e. free from geometrical and physical singularities within the object, preservation of causality in both radial and tangential direction, well behaved and positively defined energy-momentum tensor and , stability trough Abreu, adiabatic index and Harrison-Zeldovich-Novikov criteria, anisotropy factor, compactness factor and equilibrium via modified Tolman-Oppenheimer-Volkoff equation. The M − R diagram suggest that the solution yields stiffer EoS as parameter n increases. The M − I graph is in agreement with the concepts of Bejgar et al. [86] that the mass at Imax is lesser by few percent (for this solution ∼ 3%) from Mmax. This suggest that the EoSs is without any strong high-density softening due to hyperonization or phase transition to an exotic state.

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Embeddings for general relativity

Cited by 19 publications

References 62 publications

Inertia in Friedmann Universes with variable G $G$ and Λ $\varLambda$

Inertia in Friedmann Universes with variable G $G$ and Λ $\varLambda$

Late time cosmic acceleration in modified Sáez–Ballester theory

A generalized Finch–Skea class one static solution

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