Semiclassical spacetimes at super-Planckian scales from delocalized sources

TL;DR

This paper develops a framework to derive semiclassical spacetimes generated by quantum superpositions of sources, revealing novel nonsingular black holes and wormholes with distinct geometric and thermodynamic properties.

Contribution

It introduces a method to construct quantum-effective metrics from superposed sources, extending classical solutions to include nonsingular black holes and wormholes.

Findings

Identifies three classes of asymptotically flat quantum-effective metrics.

Shows quantum uncertainty prevents the formation of singularities.

Finds conditions for nonsingular black holes and traversable wormholes.

Abstract

We derive the gravitational field and the spacetime metric generated by sources in quantum superposition of different locations. We start by working in a Newtonian approximation, in which the effective gravitational potential is computed as the expectation value of the gravitational potential operator in a Gaussian distribution of width $R$ for the position of the source. The effective gravitational potential is then covariantly uplifted to a fully relativistic metric in general relativity, describing the spacetime generated by averaging over the state of such sources. These results are then rederived and extended by adopting an independent construction in terms of quantum reference frames. We find three classes of quantum effective metrics which are all asymptotically flat and reproduce the Schwarzschild metric at great distances. The solutions differ, however, in the inner core. The quantum uncertainty $\Delta r\sim R$ in the position of the source prevents the radius of the transverse two-sphere to shrink to zero. Depending on the strength of the quantum superposition effects, we have either a nonsingular black hole with a ``quantum hair'' and an event horizon, a one-way wormhole with a critical null throat or a traversable wormhole. We also provide a detailed study of the geometric and thermodynamic properties of the spacetime structure for each of these three families of models, as well as their phenomenology.