Abstract
Though popular presentations give the Schwarzschild singularity as a point, it is known that it is spacelike and not timelike. Thus, it has a "length" and is not a "point." In fact, its length is necessarily infinite. It has been proven that the proper length of the Qadir-Wheeler suture model goes to infinity,1 while its proper volume shrinks to zero, and the asymptotic behavior of the length and volume has been calculated. That model consists of two Friedmann sections connected by a Schwarzschild "suture." The question arises whether a similar analysis could provide the asymptotic behavior of the Schwarzschild black hole near the singularity. It is proven here that, unlike the behavior for the suture model, for the Schwarzschild essential singularity Δs ∼ K1/3 ln K and V ∼ K-1 ln K, where K is the mean extrinsic curvature, or the York time.
| Original language | English |
|---|---|
| Pages (from-to) | 397-404 |
| Number of pages | 8 |
| Journal | International Journal of Modern Physics D |
| Volume | 18 |
| Issue number | 3 |
| DOIs | |
| State | Published - Mar 2009 |
Bibliographical note
Funding Information:We would like to thank an anonymous referee for valuable comments and suggestions regarding the earlier version of the manuscript, which significantly improved the quality of our manuscript. We would also like to thank the organizers of GR16, where a preliminary version of this work was presented. A. A. Siddiqui highly appreciates the role of the Higher Education Commission of Pakistan and is grateful for the financial support during his postdoctoral research in Sweden.
Keywords
- Essential singularity
- Mean extrinsic curvature
- Proper length
- Proper volume
ASJC Scopus subject areas
- Mathematical Physics
- Astronomy and Astrophysics
- Space and Planetary Science