Related papers: Series solutions to the TOV equations
In this paper, we introduce a method of converting implicit equations to the usual forms of functions locally without differentiability. For a system of implicit equations which are equipped with continuous functions, if there are unique…
In this paper we present several set of solutions of static and spherically symmetric solitonic boson stars. Each set is characterized by the value of {\sigma} that defines the solitonic potential in the complex scalar field theory. The…
In the quest for describing massive neutron stars with radii compatible with recent expectations, we take a different approach in the present paper and, instead of tuning the equations of state, we use an appropriate parameterization of the…
We derive global analytic representations of fundamental solutions for a class of linear parabolic systems with full coupling of first order derivative terms where coefficient may depend on space and time. Pointwise convergence of the…
We introduce a new type of generating theorems in General Relativity for anisotropic, static, spherically symmetric solutions of the Einstein field equations. The results are used to derive a class of solutions that can serve as new models…
The Thomas - Fermi equation describing the screening of the Coulomb potential inside heavy neutral atoms is reconsidered. An accurate representation for its numerical solution was obtained by means of the variational principle. The proposed…
The aim of this review is to provide a concise overview of some of the generic approaches that have been developed to deal with the statistical description of large systems of interacting dissipative 'units'. The latter notion includes,…
A spectral parameter power series (SPPS) representation for solutions of Sturm-Liouville equations of the form $$(pu')'+qu=u\sum_{k=1}^{N}\lambda^{k}r_{k}$$ is obtained. It allows one to write a general solution of the equation as a power…
We derive the general relativistic linear tidal response of a neutron star modeled as a barotropic perfect fluid. From the covariant fluid effective action, we linearize about equilibrium and obtain the action for fluid displacements…
For the natural initial conditions $L^1$ in the density field (more generally a positive bounded Radon measure) and $L^\infty$ in the velocity field we obtain global approximate solutions to the Cauchy problem for the 3-D systems of…
We present algorithms to solve coupled systems of linear differential equations, arising in the calculation of massive Feynman diagrams with local operator insertions at 3-loop order, which do {\it not} request special choices of bases.…
The Tolman VII solution (an exact static spherically symmetric perfect fluid solution) to the Einstein equations is reexamined, and a closed form equation of state (EOS) is deduced for the first time. This EOS allows further analysis…
Generic approximation of entire functions by their Pad\'{e} approximants has been achieved in the past (\cite{3}). In the present article we obtain generic approximation of holomorphic functions on arbitrary open sets by sequences of their…
We consider the extension of the method of Gauss-Newton from complex floating-point arithmetic to the field of truncated power series with complex floating-point coefficients. With linearization we formulate a linear system where the…
A class of general relativistic solutions in isotropic spherical polar coordinates are discussed which describe compact stars in hydrostatic equilibrium. The stellar models obtained here are characterized by four parameters, namely,…
We consider a spherically symmetric internal solution within the context of Einstein-Chern-Simons gravity and derive a generalized five-dimensional Tolman-Oppenheimer-Volkoff (TOV) equation. It is shown that the generalized TOV equation…
Wave equations for some curved spacetimes may involve functions that prevent a solution in a closed form. In some cases, these functions can be eliminated by transformations and the solutions can be found analytically. In the cases where…
In this article we prove three obstruction results on the existence of equations of state in clusters of stellar systems fulfilling mass-radius relationships and some additional bound (on the mass, on the radius or a causal bound). The…
We show that there exists a family of analytic convex global rotating solutions for the vortex patch equations, bifurcating from ellipses. As a byproduct, the analyticity proof can also be adapted to the rotating patch solutions bifurcating…
In a holographic model, which was used to investigate the color superconducting phase of QCD, a dilute gas of instantons is introduced to study the nuclear matter. The free energy of the nuclear matter is computed as a function of the…