The Mass of the Oppenheimer-Snyder Black Hole

dc.creatorMitra, Abhas
dc.date1999-04-13
dc.date1999-04-15
dc.date.accessioned2026-07-25T21:06:49Z
dc.descriptionThe only instance when the General Relativistic (GTR) collapse equations have been solved (almost) exactly to explicitly find the metric coefficients is the case of a homogeneous spherical dust (Oppenheimer and Snyder in 1939 in Phy. Rev. 56, 455). The equation (37) of their paper showed the formation of an event horizon for a collapsing homogeneous dust ball of mass M in that the circumference radius the outermost surface, r_b = r_0= 2M in a proper time proportional to r_0^{-1/2} in the limit of large Schrarzschild time t= infinity. But Eq.(37) was approximated from the Eq. (36) whose essential character is t = log (y+1/y-1), where, at the boundary of the star y=r_b/ r_0 = r_b /2 M. And since the argument of a logarithmic function can not be negative, one must have y >= 1 or 2M/r_b <= 1. This shows that, atleast, in this case (i) trapped surfaces are not formed, (ii) if the collapse indeed proceeds upto r=0, we must have M=0, and (iii) proper time taken for collapse =infinity. Thus, the gravitational mass of OS black holes are unique and equal to zero. In the preceding paper (astro-ph/9904162), we assumed the existence of a finite mass BH and studied its properties in terms of Kruskal-Szekeres coordinates. And we showed that the radial geodesic of a material particle which must be timelike at r=2M, if M >0, actually becomes null. And this independently showed that BHs have unique mass, M=0.
dc.description6 pages using Revtex; graphically analyzes the Oppenheimer-Snyder paper to show that the resulting BH has zero mass
dc.identifierhttps://arxiv.org/abs/astro-ph/9904163
dc.identifierhttp://arxiv.org/abs/astro-ph/9904163
dc.identifier.urihttps://dspace.dare.co.zw/handle/123456789/76333
dc.subjectAstrophysics
dc.subjectGeneral Relativity and Quantum Cosmology
dc.subjectHigh Energy Physics - Theory
dc.titleThe Mass of the Oppenheimer-Snyder Black Hole
dc.typetext

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