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Register a new userExpansion-Free Cavity Evolution: Some exact Analytical Models
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We consider spherically symmetric distributions of anisotropic fluids with a central vacuum cavity, evolving under the condition of vanishing expansion scalar. Some analytical solutions are found satisfying Darmois junction conditions on both delimiting boundary surfaces, while some others require the presence of thin shells on either (or both) boundary surfaces. The solutions here obtained model the evolution of the vacuum cavity and the surrounding fluid distribution, emerging after a central explosion. This study complements a previously published work where modeling of the evolution of such kind of systems was achieved through a different kinematical condition.
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We study the dynamical instability of a spherically symmetric anisotropic fluid which collapses adiabatically under the condition of vanishing expansion scalar. The Newtonian and post Newtonian regimes are considered in detail. It is shown that within those two approximations the adiabatic index $Gamma_1$, measuring the fluid stiffness, does not play any role. Instead, the range of instability is determined by the anisotropy of the fluid pressures and the radial profile of the energy density, independently of its stiffness, in a way which is fully consistent with results previously obtained from the study on the Tolman mass.
Scalar-tensor gravitational theories are important extensions of standard general relativity, which can explain both the initial inflationary evolution, as well as the late accelerating expansion of the Universe. In the present paper we investigate the cosmological solution of a scalar-tensor gravitational theory, in which the scalar field $phi $ couples to the geometry via an arbitrary function $F(phi $). The kinetic energy of the scalar field as well as its self-interaction potential $V(phi )$ are also included in the gravitational action. By using a standard mathematical procedure, the Lie group approach, and Noether symmetry techniques, we obtain several exact solutions of the gravitational field equations describing the time evolutions of a flat Friedman-Robertson-Walker Universe in the framework of the scalar-tensor gravity. The obtained solutions can describe both accelerating and decelerating phases during the cosmological expansion of the Universe.
We consider spherically symmetric inhomogeneous pressure Stephani universes, the center of symmetry being our location. The main feature of these models is that comoving observers do not follow geodesics. In particular, comoving perfect fluids have necessarily a radially dependent pressure. We consider a subclass of these models characterized by some inhomogeneity parameter $beta$. We show that also the velocity of sound, like the (effective) equation of state parameter, of comoving perfect fluids acquire away from the origin a time and radial dependent change proportional to $beta$. In order to produce a realistic universe accelerating at late times without dark energy component one must take $beta < 0$. The redshift gets a modified dependence on the scale factor $a(t)$ with a relative modification of $-9%$ peaking at $zsim 4$ and vanishing at the big-bang and today on our past lightcone. The equation of state parameter and the speed of sound of dustlike matter (corresponding to a vanishing pressure at the center of symmetry $r=0$) behave in a similar way and away from the center of symmetry they become negative -- a property usually encountered for the dark energy component only. In order to mimic the observed late-time accelerated expansion, the matter component must significantly depart from standard dust, presumably ruling this subclass of Stephani models out as a realistic cosmology. The only way to accept these models is to keep all standard matter components of the universe including dark energy and take an inhomogeneity parameter $beta$ small enough.
In this paper we consider spherically symmetric general fluids with heat flux, motivated by causal thermodynamics, and give the appropriate set of conditions that define separating shells defining the divide between expansion and collapse. To do so we add the new requirement that heat flux and its evolution vanish at the separating surface. We extend previous works with a fully nonlinear analysis in the 1+3 splitting, and present gauge-invariant results. The definition of the separating surface is inspired by the conservation of the Misner-Sharp mass, and is obtained by generalizing the Tolman-Oppenheimer-Volkoff equilibrium and turnaround conditions. We emphasize the nonlocal character of these conditions as found in previous works and discuss connections to the phenomena of spacetime cracking and thermal peeling.
Ghost-free bimetric gravity is an extension of general relativity, featuring a massive spin-2 field coupled to gravity. We parameterize the theory with a set of observables having specific physical interpretations. For the background cosmology and the static, spherically symmetric solutions (for example approximating the gravitational potential of the solar system), there are four directions in the parameter space in which general relativity is approached. Requiring that there is a working screening mechanism and a nonsingular evolution of the Universe, we place analytical constraints on the parameter space which rule out many of the models studied in the literature. Cosmological solutions where the accelerated expansion of the Universe is explained by the dynamical interaction of the massive spin-2 field rather than by a cosmological constant, are still viable.
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