Freudenthal duality of near-extremal black holes and Jackiw-Teitelboim gravity

Freudenthal duality (F-duality), an anti-involution of charge vectors keep the entropy and attractor solutions invariant for extremal supersymmetric black hole. In this paper, we analyze effect F-duality on a near-extremal $STU$ hole in $\mathcal{N}=2$ ungauged, four-dimensional supergravity. We consider double-extremal holes, whose are fixed terms charges throughout moduli space. It is well known that JT gravity governs dynamics near-horizon regions higher dimensional, holes. Owing to fact, reduce supergravity theory two dimensions construct Jackiw-Teitelboim (JT) like model compute entropy. then show breaks down case if one considers operation generated through rather than one.