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In the metric approach of $f(R)$ theories of gravity, the fourth-order field equations are often recast as effective Einstein equations in the presence of standard matter and a curvature fluid (which gathers all the extra terms), always in…
In this article we study the hydrostatic equilibrium configuration of neutron stars and strange stars, whose fluid pressure is computed from the equations of state $p=\omega\rho^{5/3}$ and $p=0.28(\rho-4{\cal B})$, respectively, with…
Given an Equation of State (EOS) for neutron star (NS) matter, there is a unique mass-radius sequence characterized by a maximum mass $M_{\rm{NS}}^{\max}$ at radius $R_{\max}$. We first show analytically that the $M_{\rm{NS}}^{\max}$ and…
We study gravitational instabilities in disks, with special attention to the most massive clumps that form because they are expected to be the progenitors of globular-type clusters. The maximum unstable mass is set by rotation and depends…
The dynamical stability of differentially rotating neutron stars, including hypermassive neutron stars, is of paramount importance in understanding the fate of the post-merger remnant of binary neutron stars mergers and the formation of a…
Recently, zero-point length cosmology has shown some positive insights into some non-singular aspects of the early Universe. In addition, topological defects are known to play a significant role by its presence as a part of the total energy…
Observationally, it has been reported that the densest stellar system in the Universe does not exceed a maximum stellar surface density, $\Sigma^{\max}_{*}$ = $3\times10^5$M$_{\odot}$pc$^{-2}$, throughout a wide physical scale ranging from…
The orbits of stars in galaxies are generically chaotic: the chaotic behavior arises in part from the intrinsically grainy nature of a potential that is composed of point masses. Even if the potential is assumed to be smooth, however,…
It is still a matter of debate to understand the equation of state of cold supra-nuclear matter in compact stars because of unknown on-perturbative strong interaction between quarks. Nevertheless, it is speculated from an astrophysical view…
We derive the equation for pressure within a neutron star, taking into account a non-zero cosmological constant ($\Lambda$). We then examine the stability of the neutron star's equilibrium state in the presence of cosmological constant. Our…
As discussed in a number of recent papers, cosmological stasis is a phenomenon wherein the abundances of multiple cosmological energy components with different equations of state remain constant for an extended period despite the expansion…
Understanding the origin of stellar masses is a key problem in astrophysics. In the solar neighborhood, the mass distribution of stars follows a seemingly universal pattern. In the centre of the Milky Way, however, there are indications for…
We provide a set of general tools to study the problem of stellar equilibrium in any gravitational theory in which spherically symmetric spacetimes satisfy master field equations taking the form of an equality between an identically…
A rotating continuum of particles attracted to each other by gravity may be modeled by the Euler-Poisson system. The existence of solutions is a very classical problem. Here it is proven that a curve of solutions exists, parametrized by the…
It is shown that a first-order relativistic perturbation theory for the open, flat or closed Friedmann-Lemaitre-Robertson-Walker universe admits one, and only one, gauge-invariant quantity which describes the perturbation to the energy…
Charged stars have the potential of becoming charged black holes or even naked singularities. It is presented a set of numerical solutions of the Tolman-Oppenheimer-Volkov equations that represents spherical charged compact stars in…
We investigate relativistic spherically symmetric static perfect fluid models in the framework of the theory of dynamical systems. The field equations are recast into a regular dynamical system on a 3-dimensional compact state space,…
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…
The common attribute of all Big Bang cosmologies is that they are based on the assumption that the universe is expanding. However examination of the evidence for this expansion clearly favours a static universe. The major topics considered…
The existence of stars with a large mass of 2 solar masses means that the equation of state is stiff enough to provide high enough pressure at large central densities. Previous work shows that such a stiff equation of state is possible if…