Astronomy and Astrophysics – Astrophysics
Scientific paper
Dec 1998
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1998tx19.confe.120m&link_type=abstract
Abstracts of the 19th Texas Symposium on Relativistic Astrophysics and Cosmology, held in Paris, France, Dec. 14-18, 1998. Eds.:
Astronomy and Astrophysics
Astrophysics
Scientific paper
The (actual) world lines of material particles or photons are, by definition, either time like or null, i.e., ds^2 >= 0. For a spherically symmetric collapsing fluid, this implies (1-v^2) >= 0, where, v is the speed of the fluid measured in a Local Inertial Frame. We find that the GTR collapse equations obey a simple constraint equation Gamma^2 (1-v^2) = 1 -2 GM(r,t)/R(r,t) where Gamma^2 >= 0. This result does not follow because of the use of (inappropriate) external Schwarzschild metric coefficients or any other hidden assumptions. These equations then lead to a startling conclusion, that 2G M/R <= 1, or in other words, no trapped surface is ever formed! Therefore, M_f --> 0 as R --> 0. We further show that the time like world lines describing the collapse of a system with a finite non-zero number of baryons are geodesically complete, i.e., l, tau --> infty as R --> 0 implying non-occurrence of singularities (Mitra, astro-ph/9803013, 9803014).
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