Inviolable energy conditions from entanglement inequalities

TL;DR

This work derives universal energy-condition-like constraints on bulk geometries from fundamental entanglement inequalities using holography. By applying the RT/HRT prescription to highly symmetric AdS spacetimes, the authors translate strong subadditivity and positivity/monotonicity of relative entropy into averaged null energy conditions and bounds on RT surfaces, including explicit results for 1+1D CFT vacua and excited states, as well as spherically symmetric AdS spacetimes. Key findings include an averaged null energy condition along RT curves, boundary-velocity dependent weak energy constraints emerging asymptotically, and a mass–area bound ΔA ≤ 2π G_N M ℓ_{AdS} for four-dimensional gravity, all within the classical holographic framework. The results illuminate how quantum information principles tightly constrain admissible spacetimes and stress-energy configurations, with potential extensions to less symmetric settings and quantum corrections via the quantum-corrected entanglement entropy framework.

Abstract

Via the AdS/CFT correspondence, fundamental constraints on the entanglement structure of quantum systems translate to constraints on spacetime geometries that must be satisfied in any consistent theory of quantum gravity. In this paper, we investigate such constraints arising from strong subadditivity and from the positivity and monotonicity of relative entropy in examples with highly-symmetric spacetimes. Our results may be interpreted as a set of energy conditions restricting the possible form of the stress-energy tensor in consistent theories of Einstein gravity coupled to matter.

Figures (3)

• Figure 1: Ryu-Takayanagi formula as a map from the space ${\bf \cal G}$ of geometries with boundary $B$ to the space ${\bf \cal S}$ of mappings from subsets of $B$ to real numbers. Mappings in region ${\bf \cal S}_{phys}$ (shaded) correspond to physically allowed entanglement entropies. Geometries in region ${\bf \cal G}_{phys}$ map into ${\bf \cal S}_{phys}$ while the remaining geometries are unphysical in any consistent theory for which the Ryu-Takayanagi formula holds (plausibly equal to the set of gravity theories with Einstein gravity coupled to matter in the classical limit).
• Figure 2: Spacelike intervals for strong subadditivity.
• Figure 3: Relative entropy constraints on coefficients in the Fefferman-Graham expansion of the metric (striped region). Constraints on the right apply only if $f_3 = g_3 = 0$. Dark blue shaded region are the constraints from the null-energy condition. Full shaded region corresponds to constraints from positivity of relative entropy, equivalent to constraints from the weak energy condition for timelike vectors with no component in the radial direction.