Abstract
When one presumes that the gravitational mass of a neutral massenpunkt is finite, the Schwarzschild coordinates appear to fail to describe the region within the event horizon (EH), of a Schwarzschild Black Hole (SBH). Accordingly, the Kruskal coordinates were invented to map the entire spacetime associated with the SBH. But it turns out that at the EH (Mitra, IJAA, 2012), and the radial timelike geodesic of a point particle would become null. Physically this would mean that, the EH is the true singularity, i.e., M = 0, and this zero mass BH could only be a limiting static solution which must never be exactly realized. However, since in certain cases , here we evaluate this derivative in such cases, and find that, for self-consistency, one again must have at the EH. This entire result gets clarified by noting that the integration constant appearing in the vacuum Schwarzschild solution (and not for a finite object like the Sun or a planet), is zero (Mitra, J. Math. Phys., 2009). Thus though the Schwarzschild solution for a point mass is formally correct even for a massenpunkt, such a point mass or a BH cannot be formed by physical gravitational collapse. Instead, physical gravitational collapse may result in finite hot quasistatic objects asymptotically approaching this ideal mathematical limit (Mitra & Glendenning, MNRAS Lett. 2010). Indeed “the discussion of physical behavior of black holes, classical or quantum, is only of academic interest” (Narlikar & Padmanbhan, Found. Phys. 1989).
Highlights
32M r e r or, ds2 16M 2e 1dv2 1 1 0; r 2M. This implies that the metric coefficients can be made to appear regular, the radial geodesic of a material particle would become null at the event horizon of a finite mass Black Holes (BHs) in contravention of the basic premises of General Theory of Relativity (GTR)! GTR must not allow occurrence of any EH at all [2,3]!
Even if one would prima-facie accept the BH paradigm which is based on the presumption that the integration constant appearing in the vacuum Schwarzschild solution
The requirement of an infinite boost and the property that nothing, not even light can escape the clutches of gravity at the EH are very much physical aspects, and they signify that the EH is a physical singularity
Summary
The metric coefficients are apparently regular everywhere except at the intrinsic singularity r 0. In the (normal) physical spacetime, in a spherically symmetric spatial geometry (as defined by the implications of r as an “invariant circumference radius”), the physical singularity corresponds to a mathematical point, in the Kruskal world view, this central singularity corresponds to a pair of hyperbolas in the u v plane. The white hole singularity belongs to “other universe” whose presence is suggested by the fact that the Kruskal metric remains unaffected by the following additional transformations: f1. Does the region interior to the EH correspond to two different universes (Sectors 2 and 4), but the structure of the physical spacetime outside the EH, too, effectively corresponds to two universes (Sectors 1 and 3). If there would be N separate BHs, as per the Kruskal prescription, there would be 2N disconnected physically weird universes describing different wormholes and other universes. If a massive star would collapse to form BH in the universe we live, other universes would be instantly born!
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