Asymptotic Behaviour of the Proper Length and Volume of the Schwarzschild Singularity - General Relativity and Quantum CosmologyReport as inadecuate




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Abstract: Though popular presentations give the Schwarzschild singularity as a point itis known that it is spacelike and not timelike. Thus it has a -length- and isnot a -point-. In fact, its length must necessarily be infinite. It has beenproved that the proper length of the Qadir-Wheeler suture model goes toinfinity 1, while its proper volume shrinks to zero, and the asymptoticbehaviour of the length and volume have been calculated. That model consists oftwo Friedmann sections connected by a Schwarzschild -suture-. The questionarises whether a similar analysis could provide the asymptotic behaviour of theSchwarzschild black hole near the singularity. It is proved here that, unlikethe behaviour for the suture model, for the Schwarzschild essential singularity$\Delta s$ $\thicksim $ $K^{1-3}\ln K$ and $V\thicksim $ $K^{-1}\ln K$, where$K$ is the mean extrinsic curvature, or the York time.



Author: Asghar Qadir, Azad A. Siddiqui

Source: https://arxiv.org/



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