# Does the Principle of Equivalence Prohibit Trapped Surfaces from Forming in the General Relativistic Collapse Process?

## Abstract

It has recently been shown that time-like spherical collapse of a physical fluid in General Relativity does not permit formation of “trapped surfaces.” This result followed from the fact that the formation of a trapped surface in a physical fluid would cause the time-like world lines of the collapsing fluid to become null at the would-be trapped surface, thus violating the Principle of Equivalence in General Theory of Relativity (GTR). For the case of the spherical collapse of a physical fluid, the *“no trapped surface condition”* 2*GM*(*r*, *t*)/*R*(*r*, *t*) *c*^{2}<1 was found to be required to be satisfied in all regions of spacetime, where *R*(*r*, *t*) is the invariant circumference variable, *r* is a co-moving radial coordinate and *M*(*r*, *t*) is the gravitational mass confined within the radius *r*. The above result was obtained by treating the problem from the viewpoint of an internal co-moving observer at radius *r*. The boundary of the fluid at *r*_{s}=*R*_{s}(*r*_{s}, *t*) must also behave in a similar manner, and an external stationary observer should be able to obtain a similar “no trapped surface” relationship. Accordingly, we generalize this analysis by studying the problem of a time-like collapsing radiating plasma from the point of view of the *exterior stationary observer*. We find the Principle of Equivalence implies that the physical surface surrounding the plasma must obey 1/(1+*z*_{s})>0, where *z*_{s} is the surface red shift seen by a zero-angular momentum observer. When this condition is applied to the first integral of the time-time component of the Einstein equation, it leads to the “no trapped surface condition” 2*GM*(*r*_{s}, *t*)/*R*(*r*_{s}, *t*) *c*^{2}<1 consistent with the condition obtained above for the interior co-moving metric. The Principle of Equivalence enforces the *“no trapped surface condition”* by constraining the physics of the general relativistic radiation transfer process in a manner that requires it to establish and maintain an Eddington limited secular equilibrium on the dynamics of the collapsing radiating surface so as to always keep the physical surface of the collapsing object outside of its Schwarzschild radius. The important physical implication of the *“no trapped surface condition”* is that galactic black hole candidates GBHC do not possess event horizons and hence do possess intrinsic magnetic fields. In this context the spectral characteristics of galactic black hole candidates offer strong evidence that their central nuclei are highly red-shifted Magnetospheric Eternally Collapsing Objects (MECO) within the framework of General Relativity.

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## REFERENCES

- 1.A. Mitra,
*Found. Phys. Lett.***13**, 543 (2000) (astro-ph/9910408);**15**, 439–471 (2002) (astro-ph/0207056).CrossRefGoogle Scholar - 2.S. Robertson and D. Leiter,
*Astrophys. J.***565**, 447 (2002) (astro-ph/0102381 and astro-ph/0208333).ADSCrossRefGoogle Scholar - 3.
- 4.L. D. Landau and E. M. Lifshitz,
*Classical Theory of Fields*, 4th edn. (Pergamon, New York, 1975), pp. 248-252.Google Scholar - 5.A. Wheeler and I. Ciufolini,
*Gravitation and Inertia*(University Press, Princeton, 1995), pp. 69-71.zbMATHGoogle Scholar - 6.
- 7.R. W. Lindquist, R. A. Schwartz, and C. W. Misner,
*Phys. Rev. B***137**, 1364 (1965).ADSMathSciNetCrossRefGoogle Scholar - 8.
- 9.
- 10.P. O. Mazur and E. Mottola, gr-qc/0109035 (2001).Google Scholar
- 11.
- 12.S. Shapiro and S. Teukolsky,
*Black Holes, White Dwarfs, and Neutron Stars*(Wiley, New York, 1983); see footnote on p. 396.CrossRefGoogle Scholar - 13.A. Mitra, astro-ph/9811402 (1998).Google Scholar
- 14.K. Thorne, R. H. Price, and D. A. Macdonald,
*Black Holes: The Membrane Paradigm*(Yale University Press, New Haven, 1986), Sec. III, p. 67.Google Scholar