Related papers: Series solutions to the TOV equations
In this manuscript, we present analytical external spherical solutions of entangled relativity, which we compare to numerical solutions obtained in a Tolman-Oppenheimer-Volkoff framework. Analytical and numerical solutions match perfectly…
By means of a variational approach we find new series representations both for well known mathematical constants, such as $\pi$ and the Catalan constant, and for mathematical functions, such as the Riemann zeta function. The series that we…
We present a method for constructing global analytical expressions that approximate a function over its entire range. These approximations not only mirror the original function as accurately as desired, but are purposefully created to…
We numerically examine the exterior solution of spherically symmetric and static configuration in scalar-tensor theories by using the nonminimally coupled scalar field with zero potential as our sample model. Our main purpose in this work…
We present analytical solutions to the steady state injection-condensation-coagulation equation of aerosols in the atmosphere. These solutions are appropriate under different limits but more general than previously derived analytical…
Mixtures of hard hyperspheres in odd space dimensionalities are studied with an analytical approximation method. This technique is based on the so-called Rational Function Approximation and provides a procedure for evaluating equations of…
We report several new transformation theorems that map perfect fluid spheres into perfect fluid spheres. In addition, we report new ``solution generating'' theorems for the TOV, whereby any given solution can be ``deformed'' to a new…
Spherical collapse has turned out to be a successful semi-analytic model to study structure formation in different DE models and theories of gravity. Nevertheless, the process of virialization is commonly studied on the basis of the virial…
In this paper we study a class of Hausdorff--transformed power series whose convergence is extremely slow for large values of the argument. We perform a Watson-type resummation of these expansions, and obtain, by the use of the Pollaczek…
Perfect fluid spheres, both Newtonian and relativistic, have attracted considerable attention as the first step in developing realistic stellar models (or models for fluid planets). Whereas there have been some early hints on how one might…
We consider an application of variational-wavelet approach to nonlinear collective models of beam/plasma physics: Vlasov/Boltzmann-like reduction from general BBGKY hierachy. We obtain fast convergent multiresolution representations for…
We introduce and study a family of integral operators in the Kantorovich sense for functions acting on locally compact topological groups. We obtain convergence results for the above operators with respect to the pointwise and uniform…
There are many ways to probe alternative theories of gravity, namely, via: experimental tests at solar system scale, cosmological data and models, gravitational waves and compact objects. In the present paper we consider a model of gravity…
We develop a method for computing series expansions for solutions to ordinary differential equations when the asymptotic form contains both linear and logarithmic terms. Such situations are common in primordial cosmology when considering…
In this work, we construct stellar models ba-\break sed on the complexity factor as a supplementary condition which allows to close the system of differential equations arising from the Gravitational Decoupling. The assumed complexity is a…
Power series in which the summand satisfies a linear recurrence relation with polynomial coefficients are shown to be the solution of a linear differential or algebraic equation. Solving the associated differential or algebraic equation…
The relativistic equations of hydrostatic equilibrium for a spherically symmetric star, or the Tolman-Oppenheimer-Volkoff equations are known in higher dimensions. In this paper, these equations have been expressed in terms of parameters of…
This work introduces a new functional series for expanding an analytic function in terms of an arbitrary analytic function. It is generally applicable and straightforward to use. It is also suitable for approximating the behavior of a…
In this work, we use rational approximation to improve the accuracy of spectral solutions of differential equations. When working in the vicinity of solutions with singularities, spectral methods may fail their propagated spectral rate of…
Cool giant and supergiant star atmospheres are characterized by complex velocity fields originating from convection and pulsation processes which are not fully understood yet. The velocity fields impact the formation of spectral lines,…