The Einstein-Proca equations, describing a spin-1 massive vector field in general relativity, are studied in the static, spherically-symmetric case. The Proca field equation is a highly nonlinear wave equation, but can be solved to good accuracy in perturbation theory, which should be very accurate for a wide range of mass scales. The resulting first order metric reduces to the Reissner-Nordstrom solution in the limit as the range parameter µ goes to zero. The additional terms in the g00 metric are positive, as in Reissner-Nordstrom, in agreement with previous numerical solutions, and hence involve naked singularities. Note: This paper was published in General Relativity and Gravitation, May 2002.
We perform numerical simulations of the critical gravitational collapse of a massive vector field. The result is that there are two critical solutions. One is equivalent to the Choptuik critical solution for a massless scalar field. The other is periodic.
The Klein-Gordon equations are solved for the case of a planesymmetric static massless scalar field in general relativity with cosmological constant, generalizing the solutions found by Taub, Novotny and Horsky, and Singh. A separate class of solutions is obtained in which the metrics reduce to flat space in the limit that → 0. The static solutions can be used to generate time-dependent cosmological solutions, one of which exhibits rapid inflation followed by continued exponential expansion at all later times.
The motion of a thin wall is treated in the case where the regions on either side of the wall have vacuum energy. This treatment generalises previous results involving domain walls in vacuum and also previous results involving the properties of false vacuum bubbles. The equation of state for a domain wall is tau = sigma where tau is the tension in the wall and sigma is the energy density. The authors consider the motion of a more general class of walls having equation of state tau = Gamma sigma with 0
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