Abstract
Freudenthal duality (F-duality), an anti-involution of charge vectors, keeps the entropy and attractor solutions invariant for an extremal supersymmetric black hole. We analyze the effect of F-duality on the entropy of a near-extremal STU black hole in $\mathcal{N}=2$ ungauged, four-dimensional supergravity. We consider double-extremal black holes, whose attractor solutions are fixed in terms of the black hole charges throughout the moduli space. It is well known that Jackiw-Teitelboim (JT) gravity governs the dynamics of the near-horizon regions of higher-dimensional, near-extremal black holes. Owing to this fact, we reduce the four-dimensional supergravity theory to two dimensions to construct a JT gravity--like model and compute the near-extremal entropy. We then analyze the effect of F-duality on this entropy. We show that the F-duality breaks down for the case of near-extremal solutions if one considers the duality operation generated through near-extremal entropy rather than the extremal one.
Highlights
Jackiw-Teitelboim (JT) gravity [1,2], a two-dimensional dilaton gravity model has recently become the pursuit of interest for many theoretical physicists, as it provides the simplest playground to study gravitational dynamics
We have studied the invariance of the entropy of a near-extremal, four-dimensional black hole in N 1⁄4 2 ungauged supergravity under Freudenthal duality (F-duality), which is an anti-involutional mapping of a black hole charge vector
Using JT gravity theory as our apparatus, we find that the invariance of entropy of a near-extremal black hole depends on how we define the duality itself
Summary
Jackiw-Teitelboim (JT) gravity [1,2], a two-dimensional dilaton gravity model has recently become the pursuit of interest for many theoretical physicists, as it provides the simplest playground to study gravitational dynamics. We show that for a double-extremal attractor solution (for which the values of the moduli fields remain fixed in terms of the charges throughout the moduli space) for a fourdimensional ungauged STU model the near-extremal entropy takes the following form: SNE. We will briefly summarize F-duality, which is a nonlinear, anti-involutive transformation of charge vector QM 1⁄4 ðpΛ; qΛÞ in which the entropy and the attractor values of an extremal, supersymmetric black hole remain fixed under this transformation. Extremal black holes are interesting objects in both classical gravity and supergravity by their own virtues In both cases, the near-horizon geometry of a fourdimensional extremal, charged black hole in asymptotically flat space factorizes as AdS2 × S2 with the same radius for AdS2 and S2. We are interested in the fate of F-duality once we perturb away from the extremal scenario
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