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This paper uses the definition of complexity for a static spherically symmetric spacetime and extends it to the case of charged distribution. We formulate the Einstein-Maxwell field equations corresponding to the anisotropic interior and…
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…
The Einstein-Maxwell equations with anisotropic pressures and electromagnetic field are studied with a polytropic equation of state. New exact solutions to the field equations are generated in terms of elementary functions. Special cases 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…
This paper constructs two immediate extensions of the existing anisotropic solutions in the context of Einstein-Maxwell framework by employing minimal geometric deformation. To achieve this, we assume a static spherical interior initially…
We show that under reasonably general assumptions, the first order asymptotics of the free energy of matrix models are generating functions for colored planar maps. This is based on the fact that solutions of the Schwinger-Dyson equations…
We present a class of exact solutions of Einstein's gravitational field equations describing spherically symmetric and static anisotropic stellar type configurations. The solutions are obtained by assuming a particular form of the…
The solution generating methods discovered earlier for integrable reductions of Einstein's and Einstein - Maxwell field equations (such as soliton generating techniques, B$\ddot{a}$cklund or symmetry transformations and other…
We study the Einstein-Maxwell system of equations in spherically symmetric gravitational fields for static interior spacetimes. The condition for pressure isotropy is reduced to a recurrence equation with variable, rational coefficients. We…
The aim of this paper (Part III) is formulating GR as a scalar field theory. The basic structural elements of it are a generating function, a generalized density and a generalized temperature. One of the axioms of this theory is a…
We present exact solutions to the Einstein-Maxwell system of equations in spherically symmetric gravitational fields with a specified form of the electric field intensity. The condition of pressure isotropy yields a difference equation with…
In this paper, we have introduced new viable solutions of Einstein-Maxwell field equations by incorporating the features of anisotropic matter distribution in the realm of General theory of Relativity ($GR$). For this procurement, we have…
A class of positive curvature spatially homogeneous but anisotropic cosmological models within an Einstein-aether gravitational framework are investigated. The matter source is assumed to be a scalar field which is coupled to the expansion…
Einstein field equations for anisotropic spheres are solved and exact interior solutions obtained. This paper extends earlier treatments to include anisotropic models which accommodate a wider variety of physically viable energy densities.…
We find two new classes of exact solutions for the Einstein-Maxwell equations. The solutions are obtained by considering charged anisotropic matter with a linear equation of state consistent with quark stars. The field equations are…
By a choice of new variables the pressure isotropy condition for spherically symmetric static perfect fluid spacetimes can be made a quadratic algebraic equation in one of the two functions appearing in it. Using the other variable as a…
We find two new classes of exact solutions to the Einstein-Maxwell system of equations. The matter content satisfies a linear equation of state consistent with quark matter; a particular form of one of the gravitational potentials is…
In the paper, 2 explicit formulas for the Euler numbers of the second kind are obtained. Based on those formulas a exponential generating function is deduced. Using the generating function some well-known and new identities for the Euler…
In this paper, we studied the behavior of relativistic objects with anisotropic matter distribution considering Tolman IV form for the gravitational potential Z. The equation of state presents a quadratic relation between the energy density…
The K\"ahler metric which has been constructed by present author is used in this paper to find an exact solution of Einstein equations with energy-momentum tensor of special type. The type of $T_{ij}$ admits in particular to use it as…