Conformally flat anisotropic spheres in general relativity
TLDR
In this paper, the vanishing of the Weyl tensor is integrated in the spherically symmetric case, and the resulting expression is used to find new, conformally flat, interior solutions to Einstein equations for locally anisotropic fluids.Abstract:
The condition for the vanishing of the Weyl tensor is integrated in the spherically symmetric case. Then, the resulting expression is used to find new, conformally flat, interior solutions to Einstein equations for locally anisotropic fluids. The slow evolution of these models is contrasted with the evolution of models with similar energy density or radial pressure distribution but nonvanishing Weyl tensor, thereby bringing out the different role played by the Weyl tensor, the local anisotropy of pressure, and the inhomogeneity of the energy density in the collapse of relativistic spheres.read more
Citations
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Sound speeds, cracking and the stability of self-gravitating anisotropic compact objects
TL;DR: In this article, the authors explore the influence that density fluctuations and local anisotropy have on the stability of local and non-local anisotropic matter configurations in general relativity and show that potentially unstable regions within a configuration can be identified as a function of the difference of propagations of sound along tangential and radial directions.
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Anisotropic stars in general relativity
M. K. Mak,Tiberiu Harko +1 more
TL;DR: In this paper, a class of exact solutions of Einstein's gravitational field equations describing spherically symmetric and static anisotropic stellar-type configurations are presented by assuming a particular form of the anisotropy factor.
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Spherically symmetric dissipative anisotropic fluids: A General study
TL;DR: In this paper, the full set of equations governing the evolution of self-gravitating spherically symmetric dissipative fluids with anisotropic stresses is deployed and used to carry out a general study on the behavior of such systems, in the context of general relativity.
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Gravastars must have anisotropic pressures
TL;DR: In this paper, the authors consider a generalized class of similar models that exhibit continuous pressure without the presence of infinitesimally thin shells and find that anisotropic pressures in the "crust" of a gravastar-like object are unavoidable.
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Structure and evolution of self-gravitating objects and the orthogonal splitting of the Riemann tensor
TL;DR: In this article, the full set of equations governing the structure and the evolution of self-gravitating spherically symmetric dissipative fluids with anisotropic stresses is written down in terms of five scalar quantities obtained from the orthogonal splitting of the Riemann tensor, in the context of general relativity.
References
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General Relativity: an Einstein Centenary Survey
Stephen W. Hawking,Werner Israel +1 more
TL;DR: In this paper, Weinberg et al. present a survey of the history of the field of quantum physics and its application to the theory of the Kerr metric and its peturbations.
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General Relativity; an Einstein Centenary Survey
Stephen W. Hawking,Werner Israel +1 more
TL;DR: In this article, Weinberg et al. present a survey of the history of the field of quantum physics and its application to the theory of the Kerr metric and its peturbations.
Journal ArticleDOI
Local anisotropy in self-gravitating systems
L. Herrera,N. O. Santos +1 more
TL;DR: In this article, the authors review and discuss possible causes for the appearance of local anisotropy (principal stresses unequal) in self-gravitating systems and present its main consequences.
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Time functions in numerical relativity: Marginally bound dust collapse
Douglas M. Eardley,Larry Smarr +1 more
TL;DR: In this paper, the existence of global maximal and constant mean-curvature time functions in general relativity is studied. But the authors focus on the case where the curvature of the time slices is constant.