Black holes and general Freudenthal transformations

Understand

We study General Freudenthal Transformations (GFT) on black hole solutions in Einstein-Maxwell-Scalar (super)gravity theories with global symmetry of type $E_7$.

• GFT can be considered as a 2-parameter, $a, b\in {\mathbb R}$, generalisation of Freudenthal duality: $x\mapsto x_F= a x+b\tilde{x}$, where $x$ is the vector of the electromagnetic charges, an element of a Freudenthal triple system (FTS), carried by a large black hole and $ \tilde{x}$ is its Freudenthal dual.
• These transformations leave the Bekenstein-Hawking entropy invariant up to a scalar factor given by $a^2\pm b^2$.
• For any $x$ there exists a one parameter subset of GFT that leave the entropy invariant, $a^2\pm b^2=1$, defining the subgroup of Freudenthal rotations.