Related papers: A new solution of the star-triangle relation
Ursell functions $U_n$ are higher-order generalizations of the covariance function, which capture the interactions between $n$ random variables. In the classical Ising model, as shown by Shlosman, when considering the spins at some…
We consider static spherically symmetric stellar configurations in Palatini theories of gravity in which the Lagrangian is an unspecified function of the form $f(R,R_{\mu\nu}R^{\mu\nu})$. We obtain the Tolman-Oppenheimer-Volkov equations…
We consider steady state solutions of the massive, asymptotically flat, spherically symmetric Einstein-Vlasov system, i.e., relativistic models of galaxies or globular clusters, and steady state solutions of the Einstein-Euler system, i.e.,…
In this paper we present a new family of identities for Euler sums and integrals of polylogarithms by using the methods of generating function and integral representations of series. Then we apply it to obtain the closed forms of all…
A four-parameter class of exact asymptotically flat solutions of the Einstein-Maxwell equations involving only rational functions is presented. It is able to describe the exterior field of a slowly or rapidly rotating neutron star with…
The linear Einstein-Boltzmann equations describe the evolution of perturbations in the universe and its numerical solutions play a central role in cosmology. We revisit this system of differential equations and present a detailed…
We explore static spherically symmetric stars in the Gauss-Bonnet gravity without cosmological constant, and present an exact internal solution which attaches to the exterior vacuum solution outside stars. It turns out that the presence of…
In this manuscript the three types of late-time behavior of spherically symmetric Boson Stars are presented, these are: stable configurations, unstable bounded that collapse to form black holes and unstable unbounded that explode. The…
We review a series of recent results on global dynamic properties of radially symmetric self-gravitating compressible Euler flows, which naturally arise in the mathematical description of stars. We focus on the role of scaling invariances…
In the Bona-Masso formulation, Einstein equations are written as a set of flux conservative first order hyperbolic equations that resemble fluid dynamics equations. Based on this formulation, we construct a lattice Boltzmann model for…
In this article, we investigate the stationary, soliton-like solutions in the model of the Einstein gravity coupled to a free and complex scalar field, and extend chains of mini-boson stars to the rotating case. These solutions manifest as…
A new class of solutions of Einstein field equations has been investigated for inhomogeneous cylindrically symmetric space-time with string source. To get the deterministic solution, it has been assumed that the expansion ($\theta$) in the…
This paper presents a systematic study of the properties of non-rotating stellar models governed by the Euler-Poisson system under general equations of state, including the case of polytropic gaseous stars. We revisit and extend existence…
We study static cosmic string solutions in the context of Bekenstein-type models. We show that there is a class of models of this type for which the classical Nielsen-Olesen vortex is still a valid solution. However, in general static…
A new class of solutions describing analytical solutions for compact stellar structures has been developed within the tenets of General Relativity. Considering the inherent anisotropy in compact stars, a stable and causal model for…
We perform a duality transformation that allows one to express the partition function of the d-dimensional Ising model with random nearest neighbor coupling in terms of new spin variables defined on the square plaquettes of the lattice. The…
Two classes of stationary axisymmetric solutions of Einstein's equations for isolated differentially rotating matter sources are presented. The asymptotic regime is extracted, with attention to quasilocal gravitational energy, shear and…
The first exact interior solution to Einstein's field equations for a static and non-uniform braneworld star with local and non-local bulk terms is presented. It is shown that the bulk Weyl scalar ${\cal U}(r)$ is always negative inside the…
We find exact static solutions of the Einstein equations in the spacetime with plane symmetry, where an infinite slab with finite thickness and homogeneous energy (mass) density is present. In the first solution the pressure is isotropic,…
In this paper we are interested in Euler-type sums with products of harmonic numbers, Stirling numbers and Bell numbers. We discuss the analytic representations of Euler sums through values of polylogarithm function and Riemann zeta…