Exact Static Solutions for Scalar Fields Coupled to Gravity in (3 + 1)-Dimensions

Istanbul Technical University, Faculty of Science and Letters, MathematicsEngineering Department, Maslak, TR-34469 Istanbul, TURKEYE-mail: bilge@itu.edu.tr, daghand@itu.edu.trAbstract. Einstein’s field equations for a spherically symmetric metric coupledto a massless scalar field are reduced to a system effectively of second order intime, in terms of the variables µ = m/r and y = (α/ra), where a, α, r and mare as in [W.M. Choptuik, “Universality and Scaling in Gravitational Collapse ofMassless Scalar Field”, Physical Review Letters 70 (1993), 9-12]. Solutions forwhich µ and y are time independent may arise either from scalar fields with φ

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