标题： 大标量场塌缩的阶段 显示英文标题

标题： Phases of massive scalar field collapse

摘要： 我们研究了球对称标量场坍缩中的临界行为。我们在黑洞形成的阈值处观察到两种不同的相变类型。当初始脉冲的径向范围$(\lambda)$小于标量场的康普顿波长 ($\mu^{-1}$) 时，发生 II 型相变。临界解是 Choptuik 在无质量标量场坍缩中发现的解。I 型相变发生在黑洞形成在有限质量下开启时，即$\lambda \mu \gg 1$成立时。临界解是具有质量$\alt 0.6 \mu^{-1}$的不稳定孤子星。我们的结果与对于杨-米尔斯场坍缩得到的结果相结合~{[ M.~W. Choptuik, T. Chmaj, 和 P. Bizon, Phys. Rev. Lett. 77, 424 (1996)]}表明，爱因斯坦-物质方程的不稳定受限解可能与其它物质模型的临界点相关。 显示英文摘要

摘要： 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.