| Summary: | We review a special class of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="script">N</mi><mo>=</mo><mn>2</mn></mrow></semantics></math></inline-formula> supergravity model that interpolates all the single-dilaton truncations of the maximal <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>SO</mi><mo>(</mo><mn>8</mn><mo>)</mo></mrow></semantics></math></inline-formula> gauged supergravity. We also provide explicit non-extremal, charged black hole solutions and their supersymmetric limits, asymptotic charges, thermodynamics and boundary conditions. We also discuss a suitable Hamilton–Jacobi formulation and related BPS flow equations for the supersymmetric configurations, with an explicit form for the superpotential function. Finally, we briefly analyze certain models within the class under consideration as consistent truncations of the maximal, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="script">N</mi><mo>=</mo><mn>8</mn></mrow></semantics></math></inline-formula> gauged supergravity in four dimensions.
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