Hyperbolically symmetric static fluids: A general study

Abstract

We carry on a comprehensive study on static fluid distributions endowed with hyperbolical symmetry. Their physical properties are analyzed in detail. The energy density appears to be necessarily negative, which suggests that any possible application of this kind of fluids requires extreme physical conditions where quantum effects are expected to play an important role. Also, it is found that the fluid distribution cannot fill the region close to the center of symmetry. Such a region may be represented by a vacuum cavity around the center. A suitable definition of mass function, as well as the Tolman mass are explicitly calculated. While the former is positive defined, the latter is negative in most cases, revealing the repulsive nature of gravitational interaction. A general approach to obtain exact solutions is presented and some exact analytical solutions are exhibited.

14 pages Revtex. Published in Phys.Rev.D

References in corpus (21)

• Quasilocal Energy and Conserved Charges Derived from the Gravitational Action
• All static spherically symmetric anisotropic solutions of Einstein's equations
• New definition of complexity for self-gravitating fluid distributions: The spherically symmetric, static case
• Structure and evolution of self-gravitating objects and the orthogonal splitting of the Riemann tensor
• Twilight for the energy conditions?
• Stability of the isotropic pressure condition
• Generalized energy conditions in Extended Theories of Gravity
• Energy conditions in general relativity and quantum field theory
• Energy conditions in modified gravity
• On the role of density inhomogeneity and local anisotropy in the fate of spherical collapse
• Conformally flat anisotropic spheres in general relativity
• Galactic Potentials
• Dynamical laws of superenergy in General Relativity
• Duality between static spherically or hyperbolically symmetric solutions and cosmological solutions in scalar-tensor gravity
• Geodesics of the hyperbolically symmetric black hole
• Dark matter effects in vacuum spacetime
• Gravity of a static massless scalar field and a limiting Schwarzschild-like geometry
• Possibility of hyperbolic tunneling
• New perspectives on the TOV equilibrium from a dual null approach
• Affine-null metric formulation of General Relativity at two intersecting null hypersurfaces
• On Negative Energies, Strings, Branes, and Braneworlds: A Review of Novel Approaches

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• Hyperbolically symmetric versions of Lemaitre-Tolman-Bondi spacetimes
• Influence of Electromagnetic Field on Hyperbolically Symmetric Source
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• Hyperbolic Casimir-like wormhole
• Characteristic initial value problems for the Einstein-Maxwell-scalar field equations in spherical symmetry
• Gaussian curvature of spherical shells: A geometric measure of complexity
• Hyperbolic polytrope