On the Hilbert Space in Quantum Gravity

This article deals with the fractional problem of Sturm-Liouville and the Hilbert space associated with the solutions of this differential equation. We apply a quantization procedure to Schwarzschild space-time and obtain a fractional differential equation. The Hilbert space for these solutions is established. We used equations arising from quantization for the FRW and Reissner-Nordstron metrics to build the respective Hilbert spaces.

Automated summary

This article discusses the fractional problem of Sturm-Liouville and the Hilbert space associated with the solutions of this differential equation by applying quantization procedure to Schwarzschild space-time and establishing the respective Hilbert spaces for FRW and Reissner-Nordstron metrics.