Quantum Uncertainties of Static Spherically Symmetric Spacetimes

TL;DR

This paper develops a quantum framework for static spherically symmetric spacetimes, revealing uncertainty relations, limits on mass, and connections to black hole thermodynamics, offering new insights into quantum gravity effects.

Contribution

It introduces a canonical quantization approach for such spacetimes, deriving quantum uncertainties and mass bounds linked to the cosmological constant.

Findings

Classical Schwarzschild-(Anti)-de Sitter solutions recovered

Quantum uncertainty relations among geometric operators established

Derived upper and lower mass limits consistent with observed bounds

Abstract

We present a canonical quantization framework for static spherically symmetric spacetimes described by the Einstein-Hilbert action with a cosmological constant. In addition to recovering the classical Schwarzschild-(Anti)-de Sitter solutions via the Ehrenfest theorem, we investigate the quantum uncertainty relations that arise among the geometric operators in this setup. Our analysis uncovers an intriguing relation to black hole thermodynamics and opens a new angle towards generalized uncertainty relations. We further obtain an upper and a lower limit of the mass that is allowed in our model, for a given value of the cosmological constant. Both limits, when evaluated for the known value of the cosmological constant, have a stunning relation to observed bounds. These findings open a promising avenue for deeper insights into how quantum effects manifest in spacetime geometry and gravitational systems.