Embedding FLRW geometries in pseudo-Euclidean and anti–de Sitter spaces

Akbar, M.

doi:10.1103/physrevd.95.064058

Cited by 11 publications

(7 citation statements)

References 19 publications

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“…for any (s, p) ∈ I × f S n , is an isometric embedding, [1], that allows us contemplate I × f S n as a rotation Lorentzian hypersurface in L n+2 .…”

Section: Introductionmentioning

confidence: 99%

A new approach to the study of spacelike submanifolds in a spherical Friedmann–Lemaître–Robertson–Walker spacetime: characterization of the stationary spacelike submanifolds as an application

Ferreira

Lima

Palomo

et al. 2023

J. Phys. A: Math. Theor.

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A natural codimension one isometric embedding of each $(n+1)$-dimensional spherical Friedmann-Lema\^{\i}tre-Robertson-Walker (FLRW) spacetime $I\times_f \mathbb{S}^n$ in the $(n+2)$-dimensional Lorentz-Minkowski spacetime $\mathbb{L}^{n+2}$ permits to contemplate $I\times_f \mathbb{S}^n$ as a rotation Lorentzian hypersurface in $\mathbb{L}^{n+2}$. After a detailed study of such Lorentzian hypersurfaces, any $k$-dimensional spacelike submanifold of such an FLRW spacetime can be contemplated as a spacelike submanifold of  $\mathbb{L}^{n+2}$. Then, we use that situation to study $k$-dimensional stationary (i.e., of zero mean curvature vector field) spacelike submanifolds of the FLRW spacetime. In particular, we prove a wide extension of the Lorentzian version of the classical Takahashi theorem, giving a characterization of stationary spacelike submanifolds of $I\times_f \mathbb{S}^n$ when contemplating them as spacelike submanifolds of $\mathbb{L}^{n+2}$.

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“…for any (s, p) ∈ I × f S n , is an isometric embedding, [1], that allows us contemplate I × f S n as a rotation Lorentzian hypersurface in L n+2 .…”

Section: Introductionmentioning

confidence: 99%

A new approach to the study of spacelike submanifolds in a spherical Friedmann–Lemaître–Robertson–Walker spacetime: characterization of the stationary spacelike submanifolds as an application

Ferreira

Lima

Palomo

et al. 2023

J. Phys. A: Math. Theor.

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“…The solutions fulfilling the Karmarkar conditions alongside the condition suggested by Pandey & Sharma [121] are well-known as embedding class-one solutions. It is intriguing to observe that Schwarzschild's internal solution [122] is the only structure of bounded neutral matter with a disappearing anisotropy parameter fulfilling the Kar-markar condition. For a further in-depth survey, one may refer to the literature [123,[124][125], where the authors have clearly examined the impacts of the procedure of embedding four-dimensional Riemannian spatiotemporal variety into five-dimensional pseudo-Euclidean spatiotemporal variety in the scenario of GR and alternative gravity.…”

Section: Introductionmentioning

confidence: 99%

Exploring physical properties of compact stars in f(R,T)-gravity: An embedding approach

et al. 2020

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Solving field equations exactly in gravity is a challenging task. To do so, many authors have adopted different methods such as assuming both the metric functions and an equation of state (EoS) and a metric function. However, such methods may not always lead to well-behaved solutions, and the solutions may even be rejected after complete calculations. Nevertheless, very recent studies on embedding class-one methods suggest that the chances of arriving at a well-behaved solution are very high, which is inspiring. In the class-one approach, one of the metric potentials is estimated and the other can be obtained using the Karmarkar condition. In this study, a new class-one solution is proposed that is well-behaved from all physical points of view. The nature of the solution is analyzed by tuning the coupling parameter , and it is found that the solution leads to a stiffer EoS for than that for . This is because for small values of , the velocity of sound is higher, leading to higher values of in the curve and the EoS parameter . The solution satisfies the causality condition and energy conditions and remains stable and static under radial perturbations (static stability criterion) and in equilibrium (modified TOV equation). The resulting diagram is well-fitted with observed values from a few compact stars such as PSR J1614-2230, Vela X-1, Cen X-3, and SAX J1808.4-3658. Therefore, for different values of , the corresponding radii and their respective moments of inertia have been predicted from the curve.

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“…It is intriguing to observe that the internal solution of [117] is the only structure of bounded neutral matter with a disappearing anisotropy parameter fulfilling the Karmarkar condition. For a more in-depth survey, one may seek advice from alluded literature [61,118,119] where authors have clearly involved and examined the impacts of the procedure of embedding of 4-dimensional Riemannian spatio-temporal variety into the 5-dimensional pseudo-Euclidean spatio-temporal variety in the scenario of GR and alternative gravity.…”

Section: Introductionmentioning

confidence: 99%

Exploring physical properties of compact stars in $f(R,T)-$gravity: An embedding approach

Singh¹,

Errehymy²,

Rahaman³

et al. 2020

Preprint

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Solving field equations exactly in f (R, T ) gravity is one of the difficult task. To do so, many authors have adopted different methods such as assuming both the metric functions, an equation of state (EoS) and a metric function etc. However, such methods may not always lead to well-behaved solutions and thereby rejection of the solutions may happen after complete calculations. Indeed, very recent works on embedding class one methods suggested that the chances of arriving at the well behaved-solution is very high thereby inspired us to used it. In class one approach, we have to ansatz one of the metric potentials and the other can be obtain from the Karmarkar condition. In this paper, we are proposing new class one solution which is well-behaved in all physical points of view.We have analyzed the nature of the solution by tuning the f (R, T )−coupling parameter χ and found that the solution results into stiffer EoS for χ = −1 than χ = 1. This is because for lesser values of χ, velocity of sound is more, higher M max in M − R curve and the EoS parameter ω is larger. The solution satisfy the causality condition, energy conditions, stable and static under radial perturbations (static stability criterion) and in equilibrium (modified TOV-equation). The resulting M − R diagram from this solution is well fitted with observed values of few compact stars such as PSR J1614-2230, Vela X-1, Cen X-3 and SAX J1808.4-3658. Therefore, for different values of χ, we have predicted the corresponding radii and their respective moment of inertia from the M − I curve.

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Embedding FLRW geometries in pseudo-Euclidean and anti–de Sitter spaces

Cited by 11 publications

References 19 publications

A new approach to the study of spacelike submanifolds in a spherical Friedmann–Lemaître–Robertson–Walker spacetime: characterization of the stationary spacelike submanifolds as an application

A new approach to the study of spacelike submanifolds in a spherical Friedmann–Lemaître–Robertson–Walker spacetime: characterization of the stationary spacelike submanifolds as an application

Exploring physical properties of compact stars in f(R,T)-gravity: An embedding approach

Exploring physical properties of compact stars in $f(R,T)-$gravity: An embedding approach

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