Eigenvalues of the static, spherically-symmetric Einstein-Proca equations

Chris Vuille

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arXiv · 1610.03703

Eigenvalues of the static, spherically-symmetric Einstein-Proca equations

Chris Vuille

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Abstract

The Proca potential has been used in many contexts in flat spacetime, but not so often in curved spacetime. Here, the static Proca potentials are derived on a Schwarzschild background, and are found to have very different forms from those in flat space. In addition, the coupling of the two fields leads to a quantum condition on the particle mass, which is found to be quantized and inversely proportional to the range parameter, $\mu$. This suggests that gravity may induce quantization in other physical fields.

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Chris Vuille. 2016-09-20. Eigenvalues of the static, spherically-symmetric Einstein-Proca equations. https://arxiv.org/abs/1610.03703

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