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Schwarzschild mass uncertainty

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Abstract

Applying Dirac’s procedure to \(r\)-dependent constrained systems, we derive a reduced total Hamiltonian, resembling an upside down harmonic oscillator, which generates the Schwarzschild solution in the mini super-spacetime. Associated with the now \(r\)-dependent Schrodinger equation is a tower of localized Guth-Pi-Barton wave packets, orthonormal and non-singular, admitting equally spaced average-‘energy’ levels. Our approach is characterized by a universal quantum mechanical uncertainty structure which enters the game already at the flat spacetime level, and accompanies the massive Schwarzschild sector for any arbitrary mean mass. The average black hole horizon surface area is linearly quantized.

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Acknowledgments

We are very thankful to Ilya Gurwich for a constructive discussion, and especially for asking the right question at the right time. Special thanks to BGU president Prof. Rivka Carmi for the kind support.

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Authors and Affiliations

  1. Physics Department, Ben-Gurion University of the Negev, 84105 , Beer-Sheva, Israel

    Aharon Davidson & Ben Yellin

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  1. Aharon Davidson
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  2. Ben Yellin
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Correspondence to Aharon Davidson.

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Davidson, A., Yellin, B. Schwarzschild mass uncertainty. Gen Relativ Gravit 46, 1662 (2014). https://doi.org/10.1007/s10714-013-1662-2

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