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

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

Sep 2008

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2008mgm..conf.2225b&link_type=abstract

"THE ELEVENTH MARCEL GROSSMANN MEETING On Recent Developments in Theoretical and Experimental General Relativity, Gravitation an

Physics

Scientific paper

Einstein's field equations for a spherically symmetric metric coupled to a massless scalar field are reduced to a system of second order in terms of the variables μ = m/r and y = (α/ra), where a, α, r and m are as in [W.M. Choptuik, Physical Review Letters, 70(1993)]. Solutions for which μ and y are time independent may arise either from scalar fields with ∫t = 0 or with ∫s = 0 but ∫ linear in t, called respectively the positive and negative branches. For the positive branch we obtained an exact solution. For the negative branch, we prove that μ = 0 is a saddle point for the linearized system, but the non-vacuum solution μ = 1/4 is a stable focus and a global attractor for the region μs + μ > 0, μ < 1/2.

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