[Paper Review] Resolving Spacetime Singularities within Quantum Gravity

Lando S Bosma, Benjamin Knorr+1 more|arXiv (Cornell University)|Apr 9, 2019

Noncommutative and Quantum Gravity Theories4 citations

TL;DR

This paper proposes a resolution to spacetime singularities in quantum gravity by computing non-perturbative quantum corrections to the graviton propagator in the asymptotic safety program. The quantum-corrected Newtonian potential approaches a constant negative value at zero separation, eliminating the classical singularity, with implications for black holes and cosmological singularities.

ABSTRACT

A key incentive of quantum gravity is the removal of spacetime singularities plaguing the classical theory. We compute the non-perturbative momentum-dependence of a specific structure function within the gravitational asymptotic safety program which encodes the quantum corrections to the graviton propagator for momenta above the Planck scale. The resulting quantum corrected Newtonian potential approaches a constant negative value as the distance between the two point masses goes to zero, thereby removing the classical singularity. The generic nature of the underlying mechanism suggests that it will remain operative in the context of black hole and cosmic singularities.

Motivation & Objective

• To address the persistent problem of spacetime singularities in classical general relativity.
• To investigate whether quantum gravity effects can remove singularities in gravitational systems.
• To compute non-perturbative quantum corrections to the graviton propagator above the Planck scale.
• To determine the behavior of the Newtonian potential at short distances under quantum gravity.
• To assess the generic applicability of the mechanism to black hole and cosmic singularities.

Proposed method

• Computes the non-perturbative momentum-dependence of a structure function in the gravitational asymptotic safety program.
• Uses the asymptotic safety approach to model quantum gravity effects on the graviton propagator.
• Derives the quantum-corrected Newtonian potential from the momentum-dependent structure function.
• Analyzes the potential's behavior as the distance between point masses approaches zero.
• Applies the framework to probe the nature of singularities in quantum gravity.
• Assesses the robustness of the mechanism across different gravitational systems.

Experimental results

Research questions

• RQ1 Can quantum gravity effects remove the classical spacetime singularity in Newtonian gravity?
• RQ2 How does the graviton propagator's momentum dependence affect the Newtonian potential at short distances?
• RQ3 Does the quantum-corrected potential remain finite at zero separation?
• RQ4 Is the mechanism for singularity resolution generic across different gravitational systems?
• RQ5 Can the asymptotic safety program provide a consistent resolution to black hole and cosmological singularities?

Key findings

• The quantum-corrected Newtonian potential approaches a constant negative value as the distance between two point masses tends to zero.
• The singularity in the classical Newtonian potential is removed due to non-perturbative quantum corrections.
• The mechanism relies on the momentum-dependent structure function derived from asymptotic safety.
• The behavior of the potential at short distances is independent of the specific details of the matter source.
• The resolution mechanism is generic and expected to apply to black hole and cosmic singularities.
• The result supports the viability of asymptotic safety as a framework for quantum gravity.