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Interior solutions of Einstein's equations with a non-zero cosmological constant are given for static and spherically symmetric configurations of uniform density. The metric tensor and pressure are determined for both positive and negative…
The Einstein/Maxwell equations reduce in the stationary and axially symmetric case to a harmonic map with prescribed singularities phi: R^3\Sigma -> H^2_C, where Sigma is a subset of the axis of symmetry, and H^2_C is the complex hyperbolic…
The computational study of chemical reactions in complex, wet environments is critical for applications in many fields. It is often essential to study chemical reactions in the presence of applied electrochemical potentials, taking into…
We find a new homogeneous solution to the Einstein-Maxwell equations with a cosmological term. The spacetime manifold is $R \times S^3$. The spacetime metric admits a simply transitive isometry group $G = R \times SU(2)$ of isometries and…
Uniqueness problem of static axially symmetric black hole in magnetic Universe filled with {\it dark matter} component has been considered. The {\it dark matter} model comprises the additional $U(1)$-gauge field ({\it dark photon})…
A procedure to find static axially symmetric solutions to the Einstein field equations is presented. We obtained two general solutions and five particular solutions, which depend on the existence conditions for circular and $z$ direction…
We apply a Harrison transformation to higher dimensional asymptotically flat black hole solutions, which puts them into an external magnetic field. First, we magnetize the Schwarzschild-Tangherlini metric in arbitrary spacetime dimension…
We derive a new class of exact solutions characterized by the Szekeres-Szafron metrics (of class I), admitting in general no isometries. The source is a fluid with viscosity but zero heat flux (adiabatic but irreversible evolution) whose…
We give an alternate proof of one of the results given in [16] showing that initial data sets with boundary for the Einstein equations $(M, g, k)$ satisfying the dominant energy condition can be conformally deformed to the strict dominant…
We obtain and study static, spherically symmetric solutions for the Einstein - generalized Maxwell field system in 2n dimensions, with possible inclusion of a massless scalar field. The generalization preserves the conformal invariance of…
Following the technique of M\"uller-zum-Hagen, refs [1,2], we show that strictly static and strictly stationary solutions of the Einstein-Maxwell equations are analytic in harmonic coordinates. This holds whether or not the Maxwell field…
The Poisson-Boltzmann equation offers an efficient way to study electrostatics in molecular settings. Its numerical solution with the boundary element method is widely used, as the complicated molecular surface is accurately represented by…
We consider the Einstein-Maxwell system as a Cauchy initial value problem taking the electric and magnetic fields as independent variables. Maxwell's equations in curved spacetimes are derived in detail using a 3+1 formalism and their…
We present a general solution of the coupled Einstein-Maxwell field equations (without the source charges and currents) in three spacetime dimensions. We also admit any value of the cosmological constant. The whole family of such…
New, simple models of ``black hole interiors'', namely spherically symmetric solutions of the Einstein field equations in matter matching the Schwarzschild vacuum at spacelike hypersurfaces ``R<2M'' are constructed. The models satisfy the…
Anomalies in the ambient magnetic field can be used as features in indoor positioning and navigation. By using Maxwell's equations, we derive and present a Bayesian non-parametric probabilistic modeling approach for interpolation and…
We apply the energy-momentum tensor which is coordinate independent to calculate the energy content of the axisymmetric solutions. Our results are compared with what have been obtained before within the framework of Einstein general…
In many numerical implementations of the Cauchy formulation of Einstein's field equations one encounters artificial boundaries which raises the issue of specifying boundary conditions. Such conditions have to be chosen carefully. In…
Previous work on exact solutions has been shown that sources need to be appended to the field equation of Einstein's unified field theory in order to achieve physically meaningful results,such sources can be included in a variational…
Using the solution phase space method, we investigate the thermodynamics of black holes in Einstein-aether-Maxwell theory, for which the traditional Wald method (covariant phase space method) fails. We show the first laws of thermodynamics…