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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 eld equations for a spherically symmetric metric coupledto a massless scalar eld are reduced to a system eectively 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 elds with φ

EXACT STATIC SOLUTIONS FOR SCALAR FIELDS COUPLED TO GRAVITY IN (3+1)- DIMENSIONS