Related papers: Hyperbolic polytrope
We prove local polyhomogeneity of asymptotically real or complex hyperbolic Einstein metrics, with application to unique continuation problems.
We consider the model Poisson problem $-\Delta u = f \in \Omega$, $u = g$ on $\pa \Omega$, where $ \Omega $ is a bounded polyhedral domain in $\RR^n$. The objective of the paper is twofold. The first objective is to review the well…
We investigate the plausibility of some models emerging from an algorithm devised to generate a one-parameter family of interior solutions for the Einstein equations. It is explored how their physical variables change as the…
In this paper we study the asymptotic behavior of solutions to systems of strongly coupled integral equations with oscillatory coefficients. The system of equations is motivated by a peridynamic model of the deformation of heterogeneous…
Results on the behaviour in the past time direction of cosmological models with collisionless matter and a cosmological constant $\Lambda$ are presented. It is shown that under the assumption of non-positive $\Lambda$ and spherical or plane…
The equation of state inside very compact objects like neutron stars is still largely unkown. Even though a lot progress has been made in recent years to develop the so-called realistic equations of state, a lot of insight can be gained by…
We consider the wave and Klein-Gordon equations on the real hyperbolic space $\mathbb{H}^{n}$ ($n \geq2$) in a framework based on weak-$L^{p}$ spaces. First, we establish dispersive estimates on Lorentz spaces in the context of…
During the last stage of collapse of a compact object into the horizon of events, the potential energy of its surface layer decreases to a negative value below all limits. The energy-conservation law requires an appearance of a…
The possibility of an inhomogeneous charge density wave phase is investigated in a system of two coupled electron and hole monolayers separated by a hexagonal boron nitride insulating layer. The charge density wave state is induced through…
Incompressibility is established for three-dimensional and two-dimensional deformations of an anisotropic linearly elastic material, as conditions to be satisfied by the elastic compliances. These conditions make it straightforward to…
We discuss the connection between logotropes and polytropes in astrophysics and cosmology. The logotropic equation of state $P=A\ln(\rho/\rho_P)$ may be seen as a degenerate form of the polytropic equation of state $P=K\rho^{\gamma}$ in the…
In this thesis we investigate cosmological models more general than the isotropic and homogeneous Friedmann-Lemaitre models. We focus on cosmologies with one spatial degree of freedom, whose matter content consists of a perfect fluid and…
This research develops a well-established analytical solution of the Einstein-Maxwell field equations. We analyze the behavior of a spherically symmetric and static interior driven by a charged anisotropic matter distribution. The class I…
We investigate the behavior of the asymptotic late-times effective equation of state for a class of nonlocal theories of gravity. These theories modify the Einstein-Hilbert Lagrangian introducing terms containing negative powers of the…
The condition for pressure isotropy, for spherically symmetric gravitational fields with charged and uncharged matter, is reduced to a recurrence equation with variable, rational coefficients. This difference equation is solved in general…
We consider a self-consistent system of Bianchi type-I (BI) gravitational field and a binary mixture of perfect fluid and dark energy. The perfect fluid is taken to be the one obeying the usual equation of state, i.e., $p = \zeta \ve$, with…
The Lane-Emden system is written as \begin{equation*} \begin{cases} -\Delta u = v^p &\text{in } \Omega,\\ -\Delta v = u^q &\text{in } \Omega,\\ u, v > 0 &\text{in } \Omega,\\ u = v = 0 &\text{on } \partial \Omega \end{cases} \end{equation*}…
We extract new classes of anisotropic solutions in the framework of mimetic gravity, by applying the Tolman-Finch-Skea metric and a specific anisotropy not directly depending on it, and by matching smoothly the interior anisotropic solution…
We consider static charged fluid spheres with a cosmological constant. We assume a polytropic equation of state, $p \propto \rho^\Gamma$, and a power law charge distribution, $q\propto r^n$. Using this, we convert the generalised…
We study anisotropic geometric energy functionals defined on a class of k-dimensional surfaces in a Euclidean space. The classical notion of ellipticity, coming from Almgren, for such functionals is investigated. We prove a variant of a…