GT6 - Exact Solutions (mathematical aspects) |
Speaker_ |
Daghan, Durmus |
Co-autors |
Ayse H. Bilge |
Talk _ |
Exact Static Solutions for Scalar Fields Coupled to Gravity in (3+1)-Dimensions |
Abstract _ |
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 $\mu=m/r$ and $y=(\alpha/ra)$, where $a$, $\alpha$, $r$ and $m$ are as in [W.M. Choptuik, Physical Review Letters, 70(1993)]. Solutions for which $\mu$ and $y$ are time independent may arise either from scalar fields with $\phi_t=0$ or with $\phi_s=0$ but $\phi$ 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 $\mu=0$ is a saddle point for the linearized system, but the non-vacuum solution $\mu=1/4$ is a stable focus and a global attractor for the region $\mu_s+\mu>0$, $\mu<1/2$. (*Paper submitted to Classical and Quantum Gravity) |