Achronal averaged null energy condition for extremal horizons and (A)dS

Abstract

We prove the achronal averaged null energy condition for general quantum field theories in the near horizon geometry of spherical extremal black holes (i.e. ${\mathrm{AdS}}_2\times S^{d-2}$), de Sitter and anti-de Sitter. The derivation follows from monotonicity of relative entropy after computing the modular hamiltonian of a null deformed region. For incomplete (but maximally extended) achronal null geodesics in ${\mathrm{AdS}}_2\times S^{d-2}$, we prove the positivity of a different light-ray operator for arbitrary CFTs. This agrees with a constraint recently derived for the Lorentzian cylinder.

arXiv comment47 pages, v2: updated to match published version, v3: references added

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• The Return of the Singularities: Applications of the Smeared Null Energy Condition
• Quantum BMS transformations in conformally flat space-times and holography
• The averaged null energy conditions in even dimensional curved spacetimes from AdS/CFT duality
• Endpoint contributions to excited-state modular Hamiltonians
• Light-ray moments as endpoint contributions to modular Hamiltonians