Related papers: Solution generating theorems for the TOV equation
The thesis concentrates on two problems in discrete geometry, whose solutions are obtained by analytic, probabilistic and combinatoric tools. The first chapter deals with the strong polarization problem. This states that for any sequence…
The problem of deforming geometries is particularly important in the context of constructing new exact solutions of Einstein's equation. This issue often appears when extensions of the general relativity are treated, for instance in brane…
A crucial issue in fluid dynamics is related to the knowledge of the fluid pressure. A new general pressure equation is derived from compressible Navier-Stokes equation. It is argued that this new pressure equation allows unifying…
Liquid state theories such as integral equations and classical density functional theory often overestimate the bulk pressure of fluids because they require closure relations or truncations of functionals. Consequently, the cost to create a…
A thermodynamic analysis of weakly nonlocal non-relativistic fluids is presented under the assumption that an additional scalar field also contributes to the dynamics. The most general evolution of this field and the constitutive relations…
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…
The topos theory is a theory which is used for deciding a number of problems of theory of relativity, gravitation and quantum physics. In the article spherically symmetric solution of the vacuum Einstein equations in the Intuitionistic…
The equations of state for a characteristic spacetime are studied in the context of the spherically symmetric interior exact and analytical solutions in Horava gravity and Einstein-aether theory in which anisotropic fluids are considered.…
We take up the investigation we left in the future-work stack in Giordano \textit{et al.} [``Fluid statics of a self-gravitational isothermal sphere of van der Waals' gas,'' Phys. Fluids \textbf{36}, 056127 (2024)], in which we pointed out…
We consider cosmological solutions to general relativity with a single barotropic fluid, where the pressure is a general function of the density, $p = f(\rho)$. We derive conditions for static and oscillating solutions and provide examples,…
There is an ever-growing need for predictive models for the elasto-viscoplastic deformation of solids. Our goal in this paper is to incorporate recently developed out-of-equilibrium statistical concepts into a thermodynamically consistent,…
The macroscopic model for a neutron star (NS) as a liquid drop at the equilibrium is used to extend the Tolman-Oppenheimer-Volkoff (TOV) equations taking into account the gradient terms responsible for the system surface. The parameters of…
We investigate spherically symmetric cosmological models in Einstein-aether theory with a tilted (non-comoving) perfect fluid source. We use a 1+3 frame formalism and adopt the comoving aether gauge to derive the evolution equations, which…
A classical 3-D thermoviscoelastic system of Kelvin-Voigt type is considered. The existence and uniqueness of a global regular solution is proved without small data assumption. The existence proof is based on the successive approximation…
The torsion models have stood out among the proposals for an alternative description of gravity. The simplest of them, the Teleparallel theory, is equivalent to General Relativity and there are many studies that seek to study its extension…
We develop an analytic method of inverting the Tolman-Oppenheimer-Volkoff (TOV) relations to high accuracy. In principle, a specified $\mathcal{E}\mbox{-}P$ relation gives a unique $M\mbox{-}R$ relation, and vice-versa. Our method is…
In this paper, starting from the Bogoliubov-Born-Green-Yvon equations of the liquid-state theory, we formulate two equivalent approaches for the calculation of the total density profile and of the charge density profile of ionic fluids near…
We show by explicit construction that for every solution of the incompressible Navier-Stokes equation in $p+1$ dimensions, there is a uniquely associated "dual" solution of the vacuum Einstein equations in $p+2$ dimensions. The dual…
A relativistic self-gravitating equilibrium system with steady flow as well as spherical symmetry is discovered. The energy-momentum tensor contains the contribution of a current related to the flow and the metric tensor does an…
The topos theory is a theory which is used for deciding a number of problems of theory of relativity, gravitation and quantum physics. It is known that topos-theoretic geometry can be successfully developed within the framework of Synthetic…