Wyman's solution, self-similarity and critical behaviour

Abstract

We show that the Wyman's solution may be obtained from the four-dimensional Einstein's equations for a spherically symmetric, minimally coupled, massless scalar field by using the continuous self-similarity of those equations. The Wyman's solution depends on two parameters, the mass $M$ and the scalar charge $\Sigma$. If one fixes $M$ to a positive value, say $M_0$, and let ${\Sigma }^2$ take values along the real line we show that this solution exhibits critical behaviour. For ${\Sigma }^2>0$ the space-times have eternal naked singularities, for ${\Sigma }^2=0$ one has a Schwarzschild black hole of mass $M_0$ and finally for $-M_0^2\le {\Sigma }^2<0$ one has eternal bouncing solutions.

Revtex version, 15pages, 6 figures

References in corpus (1)

• Dilatonic wormholes: construction, operation, maintenance and collapse to black holes

Cited by in corpus (4)

• From Brans-Dicke gravity to a geometrical scalar-tensor theory
• Critical Behavior in a Massless Scalar Field Collapse with Self-interaction Potential
• Wormholes in Wyman's solution
• Qualitative and quantitative features of orbits of massive particles and photons moving in Wyman geometry