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One of the possible applications of macroscopic Einstein equations has been considered. So, the nonsingular isotropic and uniform cosmological model is built. The cosmological consequences of this model are agree with conclusions of…
We study generating functions in the context of Rota-Baxter algebras. We show that exponential generating functions can be naturally viewed in a very special case of complete free commutative Rota-Baxter algebras. This allows us to use free…
Various interpretations of the Riemann Curvature Tensor, Ricci Tensor, and Scalar Curvature are described. Also, the physical meanings of the Einstein Tensor and Einstein's Equations are discussed. Finally a derivation of Newtonian Gravity…
We explore the intimate connection between spacetime geometry and electrodynamics. This link is already implicit in the constitutive relations between the field strengths and excitations, which are an essential part of the axiomatic…
We obtain an approximate global stationary and axisymmetric solution of Einstein's equations which can be considered as a simple star model: a self-gravitating perfect fluid ball with constant mass density rotating in rigid motion. Using…
We find new exact solutions to the Einstein-Maxwell field equations which are relevant in the description of highly compact stellar objects. The relativistic star is charged and anisotropic with a quark equation of state. Exact solutions of…
Many of the technical complications associated with the general theory of relativity ultimately stem from the nonlinearity of Einstein's equation. It is shown here that an appropriate choice of dynamical variables may be used to eliminate…
We generalize previous work by considering a novel gravitational model with an action given by an arbitrary function of the Ricci scalar, the matter Lagrangian density, a scalar field and a kinetic term constructed from the gradients of the…
Matrix Riccati equations and other nonlinear ordinary differential equations with superposition formulas are, in the case of constant coefficients, shown to have the same exact solutions as their group theoretical discretizations. Explicit…
New problem is considered that is to find nonlinear differential equations with special solutions. Method is presented to construct nonlinear ordinary differential equations with exact solution. Crucial step to the method is the assumption…
We propose a new model of gravity where the Ricci scalar (R) in Einstein-Hilbert action is replaced by an arbitrary function of R and of the norm of energy-momentum tensor i.e., $f(R,T_{\mu\nu}T^{\mu\nu})$. Field equations are derived in…
By assuming a particular mass function we find new exact solutions to the Einstein field equations with an anisotropic matter distribution. The solutions are shown to be relevant for the description of compact stars. A distinguishing…
The novel proposal to invoke the split of the Ricci scalar into bulk and boundary terms in the gravitational action, opens up a new avenue of investigation into stellar dynamics. The Lagrangian contains functional forms of the bulk term…
Within the metric formalism of $f(R)$ theories of gravity, where $R$ is the Ricci scalar, we study the hydrostatic equilibrium structure of compact stars with the inclusion of anisotropic pressure. In particular, we focus on the $f(R)=…
This study explores the application of complexity factor within the context of Rastall gravity, exploring its implications on a static spacetime admitting spherical symmetry associated with anisotropic fluids under an electromagnetic field.…
We investigate the spacetime of anisotropic stars admitting conformal motion. The Einstein field equations are solved using different ansatz of the surface tension. In this investigation, we study two cases in details with the anisotropy…
We study the gravitational behaviour of a spherically symmetric radiating star when the fluid particles are in geodesic motion. We transform the governing equation into a simpler form which allows for a general analytic treatment. We find…
In order to study the type of collapse, mentioned in the title, we introduce a physically meaningful object, called the horizon function. It directly enters the expressions for many of the stellar characteristics. The main junction…
After briefly reviewing the results about polytropic stars in Palatini f(R)-theories, we first show how these results rely on the assumption of a regular function f(R). In particular, singular models allow to extend the parameter interval…
Linear diffusions are used to model a large number of stochastic processes in physics, including small mechanical and electrical systems perturbed by thermal noise, as well as Brownian particles controlled by electrical and optical forces.…