Violation of energy conditions and the gravitational radius of the proton

TL;DR

This paper investigates the proton's energy-momentum tensor using lattice QCD data, revealing violations of classical energy conditions at short distances and introducing a new gravitational radius as a hadronic observable.

Contribution

It demonstrates that the proton's EMT can violate energy conditions and introduces the gravitational radius as a novel scale for classical interpretation.

Findings

Proton's EMT may be of Hawking-Ellis type IV in the core.

Violates all pointwise energy conditions at short distances.

Defines a gravitational radius where EMT becomes classical.

Abstract

The energy-momentum tensor (EMT) of the proton encodes fundamental information about its mass, pressure, and shear distributions. Using recent lattice QCD data for the gravitational form factors, we show that the Breit-frame Wigner EMT may be of Hawking-Ellis type IV in the proton's core. Such EMT violates all pointwise energy conditions and lacks a causal rest frame so that the usual mechanical picture fails at short distances. We define the gravitational radius -- a new hadronic observable marking the scale where the EMT becomes ordinary (type I) and the classical interpretation is restored. We also derive from the Averaged Null Energy Condition (ANEC) non-perturbative, model-independent QFT constraints on gravitational form factors.