Phases of massive scalar field collapse

Abstract

We study critical behavior in the collapse of massive spherically symmetric scalar fields. We observe two distinct types of phase transition at the threshold of black hole formation. Type II phase transitions occur when the radial extent $(\lambda)$ of the initial pulse is less than the Compton wavelength ($\mu^{-1}$) of the scalar field. The critical solution is that found by Choptuik in the collapse of massless scalar fields. Type I phase transitions, where the black hole formation turns on at finite mass, occur when $\lambda \mu \gg 1$. The critical solutions are unstable soliton stars with masses $\alt 0.6 \mu^{-1}$. Our results in combination with those obtained for the collapse of a Yang-Mills field~{[M.~W. Choptuik, T. Chmaj, and P. Bizon, Phys. Rev. Lett. 77, 424 (1996)]} suggest that unstable, confined solutions to the Einstein-matter equations may be relevant to the critical point of other matter models.Comment: 5 pages, RevTex, 4 postscript figures included using psfi

Critical collapse of a massive vector field

“…Given the results of reference [2] for a massive scalar field, it is not surprising that a massive vector field has a type I periodic critical solution. What does seem surprising is that it has a DSS critical solution that is identical to that of a massless scalar field.…”

“…Given the results of reference [2] one might conjecture that similar behavior occurs in the case of a spherically symmetric massive vector field: i.e. that there is a critical solution for which the mass of the vector field becomes negligible.…”

“…al. [2] The results of reference [2] show that there are two critical solutions: one which is essentially the Choptuik critical solution for the massless scalar field, and another which is a periodic solution first found by Seidel and Suen [3]. At first it might seem puzzling that the Choptuik solution can be a critical solution for both the massless and massive scalar field.…”

A (gravitational) toy story

“…Type I critical behavior is observed when a massive scalar field is considered [9], [10]. A review of critical phenomena for gravitational collapse is available in Ref.…”

Mass loss and longevity of gravitationally bound oscillating scalar lumps (oscillatons) inDdimensions

“…Perturbed U-branch oscillatons collapse to black holes if the perturbation increases their mass, otherwise they migrate to an S-branch oscillaton. Actually, U-branch oscillatons turn out to be the critical solutions for type I critical collapse of massive scalar fields [57]. Corresponding apparently periodic objects also form in the critical collapse of massive vector fields [58].…”