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.
Citations
More filters
TL;DR: In this paper, the Ricci and Weyl tensors on generalized Robertson-Walker space-times of dimension n = 4 with null conformal divergence were shown to be a quasi-Einstein manifold.
Abstract: We prove theorems about the Ricci and the Weyl tensors on generalized Robertson-Walker space-times of dimension $n\ge 3$. In particular, we show that the concircular vector introduced by Chen decomposes the Ricci tensor as a perfect fluid term plus a term linear in the contracted Weyl tensor. The Weyl tensor is harmonic if and only if it is annihilated by Chen's vector, and any of the two conditions is necessary and sufficient for the GRW space-time to be a quasi-Einstein (perfect fluid) manifold. Finally, the general structure of the Riemann tensor for Robertson-Walker space-times is given, in terms of Chen's vector. A GRW space-time in n = 4 with null conformal divergence is a Robertson-Walker space-time.
12 citations
TL;DR: In this article, a method capable of producing an infinite number of solutions for Einstein's equation on static spacetimes with perfect fluid as a matter field was presented, which is the basis for our work.
Abstract: In this paper, we provide a method capable of producing an infinite number of solutions for Einstein’s equation on static spacetimes with perfect fluid as a matter field. All spacetimes of this type which are symmetric with respect to a given group of translations and whose spatial factor is conformally flat are characterized. We use this method to give some exact solutions of the referred equation.
10 citations
TL;DR: In this paper, the local structure of four-dimensional Lorentzian quasi-Einstein manifolds under conditions on the Weyl tensor was investigated, and it was shown that if the potential function preserves this harmonicity then, in the isotropic case, the manifold is necessarily a pp wave.
Abstract: We investigate the local structure of four-dimensional Lorentzian quasi-Einstein manifolds under conditions on the Weyl tensor. We show that if the Weyl tensor is harmonic and the potential function preserves this harmonicity then, in the isotropic case, the manifold is necessarily a pp-wave. Using the quasi-Einstein equation, further conclusions are obtained for pp-waves. In particular, we show that a four-dimensional pp-wave is conformally Einstein if and only if it is locally conformally flat or has harmonic Weyl tensor.
6 citations
Posted Content•
TL;DR: In this article, a method capable of producing an infinite number of solutions for Einstein's equation on static spacetimes with perfect fluid as a matter field is presented, which is used to give some exact solutions of the referred equation.
Abstract: In this paper we provide a method capable of producing an infinite number of solutions for Einstein's equation on static spacetimes with perfect fluid as a matter field. All spacetimes of this type which are symmetric with respect to a given group of translations and whose spatial factor is conformally flat, are characterized. We use this method to give some exact solutions of the referred equation.
5 citations
TL;DR: In this article, the authors investigated pseudo Q-symmetric spacetimes and showed that they are quasi-Einstein spacetime and perfect fluid Spacetimes with cyclic parallel Ricci tensors.
Abstract: In this paper, we investigate pseudo Q-symmetric spacetimes $$(PQS)_{4}$$
. At first, we prove that a $$(PQS)_{4}$$
spacetime is a quasi-Einstein spacetime. Then we investigate perfect fluid $$(PQS)_{4}$$
spacetimes and interesting properties are pointed out. From a result of Mantica and Suh (Int J Geom Methods Mod Phys 10:1350013, 2013) we have shown that $$(PQS)_{4}$$
spacetime is the Robertson-Walker spacetime. Further, it is shown that a $$(PQS)_{4}$$
spacetime with cyclic parallel Ricci tensor is an Einstein spacetime. Finally, we construct an example of a $$(PQS)_{4}$$
spacetime.
4 citations
References
More filters
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