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We employ the Noether procedure to derive a general formula for the radiallyconserved heat current in AdS planar black holes with certain transverse andtraceless perturbations, for a general class of gravity theories. For Einsteingravity, the general higher-order Lovelock gravities and also a class ofHorndeski gravities, we derive the boundary stress tensor and show that theresulting boundary heat current matches precisely the bulk Noether current.

Holographic Heat Current as Noether Current