Non-occurrence of Trapped Surfaces and Black Holes in Spherical Gravitational Collapse

Details Non-occurrence of Trapped Surfaces and Black Holes in Spherical Gravitational Collapse Non-occurrence of Trapped Surfaces and Black Holes in Spherical Gravitational Collapse

1998-10-10

arxiv.org/abs/gr-qc/9810038v4

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

Referee comments received after 4 months, minor faults removed, central derivation strengthened. Shown that Eqs.(32), (36) of

Scientific paper

We point out that although the pioneering work of Oppenheimer and Snyder (OS), technically, indicated the formation of an event horizon for a collapsing homogeneous dust ball of mass $M_b$ and radius $R_b$, the Eqs. (32) and (36) of their paper actually demand that no trapped surface is formed $ 2GM_b/ R_b c^2 \le 1$, and $M_b \equiv 0$! Anybody may verify it. Further, by analyzing the general inhomogeneous dust solutions of Tolman in a proper physical perspective, we show that, all dust solutions are characterized by $M_b=0$. Next, for a collapsing fluid endowed with radiation pressure, we discover that the collapse equations obey the same Global Constraint $2GM /R c^2 \le 1$ and which specifically shows that, contrary to the traditional intuitive Newtonian idea, which equates the gravitational mass ($M_b$) with the fixed baryonic mass ($M_0$), the trapped surfaces are not allowed in general theory of relativity (GTR). For continued collapse, the final gravitational mss $M_f \to 0$ as $R\to 0$. Thus we confirm Einstein's and Rosen's idea that Event Horizons and Schwarzschild Singularities are unphysical and can not occur in Nature. This, in turn, implies that, if there would be any continued collapse, the initial gravitational mass energy of the fluid must be radiated away $Q\to M_i c^2$. This also implies that, gravitational collapse of massive stars should give rise to Ultra Compact Objects and emission of energy much more than what is obtained in Supernova Events

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