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In this work we discuss the correlation between luminosity <i>L</i> and velocity dispersion <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>σ</mi></semantics></math></inline-formula> observed in different astrophysical contexts, in particular that of early-type galaxies (ETGs; Faber–Jackson (FJ) law) and that of active galactic nuclei (AGN). Our data for the ETGs confirm the bending of the FJ at high masses and the existence of similar curvatures in the projections of the Fundamental Plane (FP) approximately at the mass scale of ∼<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mn>10</mn><mn>10</mn></msup><msub><mi>M</mi><mo>⊙</mo></msub></mrow></semantics></math></inline-formula>. We provide an explanation for such curvatures and for the presence of the Zone of Exclusion (ZoE) in these diagrams. The new prospected theory for the FJ law introduces a new framework to understand galaxy evolution in line with the hierarchical structure of the Universe. The classic analysis carried out for a class of type 1 AGN accreting gas at very high rates, confirms that a FJ law of the form <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>L</mi><mo>=</mo><msub><mi mathvariant="script">L</mi><mn>0</mn></msub><msup><mi>σ</mi><mn>4</mn></msup></mrow></semantics></math></inline-formula> is roughly consistent with the observations, with a slope quite similar to that of ETGs. We discuss the physics behind the FJ law for the AGN in different contexts and also examine the biases affecting both the luminosity and the velocity dispersion, paying particular attention to the effects induced by the spherical symmetry of the emitting sources on the accuracy of the luminosity estimates.