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Register a new userNon-singular spacetimes with a negative cosmological constant: II. Static solutions of the Einstein-Maxwell equations
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We construct infinite-dimensional families of non-singular static space times, solutions of the vacuum Einstein-Maxwell equations with a negative cosmological constant. The families include an infinite-dimensional family of solutions with the usual AdS conformal structure at conformal infinity.
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We prove existence of large families of solutions of Einstein-complex scalar field equations with a negative cosmological constant, with a stationary or static metric and a time-periodic complex scalar field.
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 $Lambda$-electrovacuum local solutions splits into two distinct subclasses, namely the non-expanding Kundt class and the expanding Robinson-Trautman class. While the Kundt class only admits electromagnetic fields which are aligned along the geometrically privileged null congruence, the Robinson-Trautman class admits both aligned and also more complex non-aligned Maxwell fields. We derive all the metric and Maxwell field components, together with explicit constraints imposed by the field equations. We also identify the most important special spacetimes of this type, namely the coupled gravitational-electromagnetic waves and charged black holes.
We classify super-symmetric solutions of the minimal $N=2$ gauged Euclidean supergravity in four dimensions. The solutions with anti-self-dual Maxwell field give rise to anti-self-dual Einstein metrics given in terms of solutions to the $SU(infty)$ Toda equation and more general three-dimensional Einstein--Weyl structures. Euclidean Kastor--Traschen metrics are also characterised by the existence of a certain super covariantly constant spinor.
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.
It is well known that string theories naturally compactify on anti-de Sitter spaces, and yet cosmological observations show no evidence of a negative cosmological constant in the early Universes evolution. In this letter we present two simple nonlocal modifications of the standard Friedmann cosmology that can lead to observationally viable cosmologies with an initial (negative) cosmological constant. The nonlocal operators we include are toy models for the quantum cosmological backreaction. In Model I an initial quasiperiodic oscillatory epoch is followed by inflation and a late time matter era, representing a dark matter candidate. The backreaction in Model II quickly compensates the negative cosmological term such that the Ricci curvature scalar rapidly approaches zero, and the Universe ends up in a late time radiation era.
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