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. AdS2 × Sd−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 AdS2 × Sd−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.
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Rosso, F. Achronal averaged null energy condition for extremal horizons and (A)dS. J. High Energ. Phys. 2020, 23 (2020). https://doi.org/10.1007/JHEP07(2020)023
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DOI: https://doi.org/10.1007/JHEP07(2020)023