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Register a new userAnalyticity of strictly static and strictly stationary, inheriting and non-inheriting Einstein-Maxwell solutions
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Authors
Paul Tod
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Following the technique of Muller-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 inherits the symmetry.
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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 is of Petrov type I. The spacetime is geodesically complete and globally hyperbolic. The electromagnetic field is non-null and non-inheriting: it is only invariant with respect to the $SU(2)$ subgroup and is time-dependent in a stationary reference frame.
We prove that Maxwell fields of asymptotically flat solutions of the Einstein-Maxwell equations inherit the stationarity of the metric.
We obtain the Einstein-Maxwell equations for (2+1)-dimensional static space-time, which are invariant under the transformation $q_0=i,q_2,q_2=i,q_0,alpha rightleftharpoons gamma$. It is shown that the magnetic solution obtained with the help of the procedure used in Ref.~cite{Cataldo}, can be obtained from the static BTZ solution using an appropriate transformation. Superpositions of a perfect fluid and an electric or a magnetic field are separately studied and their corresponding solutions found.
We present several new exact solutions in five and higher dimensional Einstein-Maxwell theory by embedding the Nutku instanton. The metric functions for the five-dimensional solutions depend only on a radial coordinate and on two spatial coordinates for the six and higher dimensional solutions. The six and higher dimensional metric functions are convoluted-like integrals of two special functions. We find that the solutions are regular almost everywhere and some spatial sections of the solution describe wormhole handles. We also find a class of exact and nonstationary convoluted-like solutions to the Einstein-Maxwell theory with a cosmological constant.
The Einstein-Maxwell (E-M) equations in a curved spacetime that admits at least one Killing vector are derived, from a Lagrangian density adapted to symmetries. In this context, an auxiliary space of potentials is introduced, in which, the set of potentials associated to an original (seed) solution of the E-M equations are transformed to a new set, either by continuous transformations or by discrete transformations. In this article, continuous transformations are considered. Accordingly, originating from the so-called $gamma_A$-metric, other exact solutions to the E-M equations are recovered and discussed.
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