Homologous Collapse of Relativistic Cores
Date Issued
2008
Date
2008
Author(s)
Chen, Che-Yu
Abstract
The study focused on the collapse of non-rotating relativistic cores. We first investigated the collapse by considering a spherically symmetric metric. Moreover, weook advantage of comoving coordinates, which penetrate the event horizon without discontinuity. By making the high-density approximation, we found that the isothermal equation of state p = gammao could be applied to this system. Moreover, after a quasi-invariant transformation, we reached a successful separation of variables. As a result, we arrived at a set of ordinary differential equations describing the homologous solution of the collapsing process of a relativistic core. In general, thesequations can be solved by numerical integration. However, we discovered that the homologous solution would likely to encounter a critical point, which represents the sonic point of the system. The requirement of trans-sonic solution provides another boundary condition at the center, and makes our solution unique. We also calculated the metric coefficients and fluid velocity measured by observer in the static frame. These physical parameters can be used to derive the location of trapping surface, which is directly related to the evolution of a central black hole. To conclude, our results provide a way to describe the homologously collapsing process of a high-density core, like a white dwarf or a neutron star to form a black hole.
Subjects
relativistic core
gravitational collapse
homologous
comoving coordinate
isothermal equation of state
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