Erratum: “A condition for a perfect-fluid space-time to be a generalized Robertson-Walker space-time” [J. Math. Phys. 57, 022508 (2016)]
About: This article is published in Journal of Mathematical Physics.The article was published on 2016-04-08 and is currently open access. It has received 20 citations till now. The article focuses on the topics: Space time & Perfect fluid.
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TL;DR: In this article, the behavior of spacetime with content of matter having magnetism was examined and the curvature properties of relativistic magneto-fluid spacetime were investigated.
3 citations
TL;DR: For the Friedmann-Lemaitre-Robertson-Walker metric, the field equations of any generic gravity theory in arbitrary dimensions are of the perfect fluid type as discussed by the authors.
Abstract: We prove that for the Friedmann–Lemaitre–Robertson–Walker metric, the field equations of any generic gravity theory in arbitrary dimensions are of the perfect fluid type. The cases of general Lovelock and $${\mathcal {F}}(R, {\mathcal {G}})$$
theories are given as examples.
2 citations
TL;DR: In this paper , the authors studied how a spacetime manifold evolves when thermal flux, thermal energy density and thermal stress are involved; such spacetime is called a thermodynamical fluid spacetime (TFS).
Abstract: The goal of the present research paper is to study how a spacetime manifold evolves when thermal flux, thermal energy density and thermal stress are involved; such spacetime is called a thermodynamical fluid spacetime (TFS). We deal with some geometrical characteristics of TFS and obtain the value of cosmological constant Λ. The next step is to demonstrate that a relativistic TFS is a generalized Ricci recurrent TFS. Moreover, we use TFS with thermodynamic matter tensors of Codazzi type and Ricci cyclic type. In addition, we discover the solitonic significance of TFS in terms of the Ricci metric (i.e., Ricci soliton RS).
1 citations
TL;DR: For the Friedmann-Lemaitre-Robertson-Walker metric, the field equations of any generic gravity theory in arbitrary dimensions are of the perfect fluid type.
Abstract: We prove that for the Friedmann-Lemaitre-Robertson-Walker metric, the field equations of any generic gravity theory in arbitrary dimensions are of the perfect fluid type. The cases of general Lovelock and $\mathcal{F}(R, \mathcal{G})$ theories are given as examples.
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TL;DR: In this paper, it was shown that if the gradient of the energy density is parallel to the velocity, then either the expansion rate is zero, or the vorticity vanishes.
Abstract: We obtain expressions for the shear and the vorticity tensors of perfect-fluid spacetimes, in terms of the divergence of the Weyl tensor. For such spacetimes, we prove that if the gradient of the energy density is parallel to the velocity, then either the expansion rate is zero, or the vorticity vanishes. This statement recalls the "shear-free conjecture" for a perfect barotropic fluid: vanishing shear implies either vanishing expansion rate or vanishing vorticity. Finally, we give a new condition for a perfect fluid to be a Generalized Robinson-Walker spacetime.
Cites background from "Erratum: “A condition for a perfect..."
...2 we significantly weaken the hypotheses given in ref.[11], for a perfect fluid to be a Generalized Robinson-Walker space-time....
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...In [11] we proved that a perfect-fluid spacetime with ∇iuj = ∇jui and ∇mCjkl m = 0 is a GRW spacetime....
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TL;DR: In this paper, a generalised Robertson-Walker space-time with null divergence of the Weyl tensor is shown to be a perfect-fluid space time, and condition (1) is verified whenever pressure and energy density are related by an equation of state.
Abstract: A perfect-fluid space-time of dimension n ≥ 4, with (1) irrotational velocity vector field and (2) null divergence of the Weyl tensor, is a generalised Robertson-Walker space-time with an Einstein fiber. Condition (1) is verified whenever pressure and energy density are related by an equation of state. The contraction of the Weyl tensor with the velocity vector field is zero. Conversely, a generalized Robertson-Walker space-time with null divergence of the Weyl tensor is a perfect-fluid space-time.
56 citations