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We put forward a new definition of complexity, for static and sphericallysymmetric self--gravitating systems, based on a quantity, hereafter referred toas complexity factor, that appears in the orthogonal splitting of the Riemanntensor, in the context of general relativity. We start by assuming that thehomogeneous (in the energy density) fluid, with isotropic pressure is endowedwith minimal complexity. For this kind of fluid distribution, the value ofcomplexity factor is zero. So, the rationale behind our proposal for thedefinition of complexity factor stems from the fact that it measures thedeparture, in the value of the active gravitational mass (Tolman mass), withrespect to its value for a zero complexity system. Such departure is producedby a specific combination of energy density inhomogeneity and pressureanisotropy. Thus, zero complexity factor may also be found in self--gravitatingsystems with inhomogeneous energy density and anisotropic pressure, providedthe effects of these two factors, on the complexity factor, cancel each other.Some exact interior solutions to the Einstein equations satisfying the zerocomplexity criterium are found, and prospective applications of this newlydefined concept, to the study of the structure and evolution of compactobjects, are discussed.

New definition of complexity for self-gravitating fluid distributions: The spherically symmetric, static case