Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2011-10-27
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
Scientific paper
A pseudo-Riemannian manifold contains an inherent Hamiltonian structure within the symplectic manifold in the cotangent bundle corresponding to the metric. Using this structure, it is possible to define a Hamiltonian, which can be quantized, and substituted into The Schrodinger Equation. The wave function, despite having a very complicated structure, has the very interesting property where it vanishes at the Schwarzschild $(r=0)$ singularity. This demonstrates an apparent violation of Quantum Mechanics, in which information is required to be conserved, and gives further evidence of a wave function vanishing at the singularity point. In addition, we give conditions for this wave function vanishing in terms of quantum numbers.
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