## On the Invalidity of the Hawking-Penrose Singularity ‘Theorems’ and Acceleration of the Universe with Negative Cosmological Constant

**Authors:** Stephen J. Crothers

Hawking and Penrose proposed “A new theorem on spacetime singularities … which largely incorporates and generalizes the previously known results” which they claimed “implies that space-time singularities are to be expected if either the universe is spatially closed or there is an ‘object’ undergoing relativistic gravitational collapse (existence of a trapped surface)” and that their ‘Theorem’ applies if four certain physical conditions are satisfied. Hartle, Hawking and Hertog have proposed a quantum state with wave function for the Universe which they assert “raises the possibility that even fundamental theories with a negative cosmological constant can be consistent with our low-energy observations of a classical, accelerating universe.” They also relate this concept to string cosmology. It is however proven in this paper that the Hawking-Penrose Singularity ‘Theorem’ and accelerated expansion of the Universe with negative Λ are invalid because they are based upon demonstrably false foundations relating to Einstein’s field equations, trapped surfaces, and the cosmological constant.

**Comments:** 13 Pages. Versions 1 and 2 of this paper contain a misalignment of references. This has been corrected in version 3. This paper published June 2013, Global Journal of Science Physics and Space Research.

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### Submission history

[v1] 2013-04-08 10:54:01

[v2] 2013-04-18 01:53:58

[v3] 2013-06-02 10:34:44

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