Holographic Heat Current as Noether Current
Hai-Shan Liu, H. Lu, C.N. Pope
TL;DR
This paper derives a general formula for holographic heat currents in various gravity theories using Noether's procedure, establishing a precise match between bulk and boundary descriptions in AdS black hole backgrounds.
Contribution
It introduces a unified method to compute holographic heat currents via Noether currents across multiple gravity theories, including Einstein, Lovelock, and Horndeski gravities.
Findings
Derived a general radially conserved heat current formula.
Established the equivalence of boundary heat current and bulk Noether current.
Applied the method to Einstein, Lovelock, and Horndeski gravities.
Abstract
We employ the Noether procedure to derive a general formula for the radially conserved heat current in AdS planar black holes with certain transverse and traceless perturbations, for a general class of gravity theories. For Einstein gravity, the general higher-order Lovelock gravities and also a class of Horndeski gravities, we derive the boundary stress tensor and show that the resulting boundary heat current matches precisely the bulk Noether current.
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