Abstract

Classical general relativity predicts the occurrence of spacetime singularities under very general conditions. Starting from the idea that the spacetime geometry must be described by suitable states in the complete quantum theory of matter and gravity, we shall argue that this scenario cannot be realised physically since no proper quantum state may contain the infinite momentum modes required to resolve the singularity.

Highlights

  • Exact solutions to the Einstein field equations containing spacetime singularities have been known since the early days of general relativity

  • Starting from the idea that the spacetime geometry must be described by suitable states in the complete quantum theory of matter and gravity, we shall argue that this scenario cannot be realised physically since no proper quantum state may contain the infinite momentum modes required to resolve the singularity

  • We will report here on the consequences stemming from the assumptions that (a) the expectation value of quantum gravity observables on states that are relevant for the description of reality must be very close to the classical solutions of the Einstein Equations, where experimental data support general relativity, and (b) those quantum states must be mathematically well-defined

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Summary

Introduction

Exact solutions to the Einstein field equations containing spacetime singularities have been known since the early days of general relativity. We will report here on the consequences stemming from the assumptions that (a) the expectation value of quantum gravity observables on states that are relevant for the description of reality must be very close to the classical solutions of the Einstein Equations, where experimental data support general relativity, and (b) those quantum states must be mathematically well-defined. The principal quantum number of the ground state is proportional to M2/m2p (we use units with c = 1, GN = p/mp and h = p mp, where p is the Planck length and mp is the Planck mass). The scaling of M2/m2p with an integer number can be interpreted as the quantisation of the horizon area [8]

Quantum Dust Ball
Quantum Schwarzschild Geometry
Conclusions

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