New Solutions of Gravitational Collapse in General Relativity and in the Newtonian Limit

We discuss the Oppenheimer-Snyder-Datt (OSD) solution from a new perspective, introduce a completely new formulation of the problem exclusively in external Schwarzschild space-time (ESM) and present a new treatment of the singularities in this new formulation. We also give a new Newtonian approximation of the problem. Furthermore, we present new numerical solutions of the modified OSD-model and of the ball-to-ball-collapse with 4 different numerical methods.

Critical collapse of massless scalar fields in asymptotically anti-de Sitter spacetime

We conduct numerical investigations on the critical collapse of spherically symmetric massless scalar fields in asymptotically anti-de Sitter spacetime.Our primary focus is on the behavior of the critical amplitude under various initial configurations of the scalar field.Through our numerical results,we obtain a formula that determines critical amplitude in terms of cosmological constantΛ:A^(*)∝(0.01360σ/v_(0)+0.001751)Λ,whereσdenotes the initial width of the scalar field and is the initial position of the scalar field.Notably,we highlight that the slope of this linear relationship depends on the initial configuration of the scalar field.

广义相对论对超新星星核坍缩的影响

随着物态方程的发展,超新星星核可坍缩至核密度以上。广义相对论(简记GR)显示出重要的影响。GR效应使内星核坍缩至更高的密度,陷入更深的势阱,释放更大的能量。但GR的内星核较非广义相对论(简记NR)的内星核小。冲击波形成地点离星核边界较远,冲击波传输途径中光裂解损耗增加。中心密度达最大时,GR过程和NR过程两坍缩速度曲线相交点(静止质量坐标略大于NR声速点坐标)以内,GR坍缩速度分布高于NR的相应值。而于相交点之外,GR坍缩速度、密度分布皆低于NR相应值。这对于反弹冲击波的传播是有利的。

Exact solutions for spherical gravitational collapse around a black hole:the effect of tangential pressure

Spherical gravitational collapse towards a black hole with non-zero tangential pressure is studied.Exact solutions corresponding to different equations of state are given.We find that when taking the tangential pressure into account,the exact solutions have three qualitatively different outcomes.For positive tangential pressure,the shell around a black hole may eventually collapse onto the black hole,or expand to infinity,or have a static but unstable solution,depending on the combination of black hole mass,mass of the shell and the pressure parameter.For vanishing or negative pressure,the shell will collapse onto the black hole.For all eventually collapsing solutions,the shell will cross the event horizon,instead of accumulating outside theeventhorizon,even if clocked by a distant stationary observer.

Two Physical Constraints upon the Motions of Celestial Bodies

There exist two physical constraints upon the motions of celestial systems. Constraint 1 reveals during collapse or explosion motion of celestial bodies that there would be an unattainability upper limit for their compact intensity (total mass M/scale size R), which arises from the Lorentz invariance of the time-like metric in local four-dimensional continuum in Einstein’s theory of special relativity. Constraint 2 points that the average mass density of nucleon would be an unsurpassed upper limit for bulk normal matter in nature, which arises from Heisenberg’s uncertainty principle. A very important effect is that the combination of these two physical constraints would prevent the formation of black holes.