Definition of complexity for dynamical spherically symmetric dissipative self-gravitating fluid distributions

The recently proposed definition of complexity for static and spherically symmetric self-gravitating systems [Herrera, Phys. Rev. D 97, 044010 (2017)] is extended to the fully dynamic situation. In this latter case we have to consider not only the complexity factor of the structure of the fluid distribution but also the condition of minimal complexity of the pattern of evolution. As we shall see, these two issues are deeply intertwined. For the complexity factor of the structure we choose the same as for the static case, whereas for the simplest pattern of evolution we assume the homologous condition. The dissipative and nondissipative cases are considered separately. In the latter case the fluid distribution, satisfying the vanishing complexity factor condition and evolving homologously, corresponds to a homogeneous (in the energy density), geodesic and shear-free, isotropic (in the pressure) fluid. In the dissipative case the fluid is still geodesic, but shearing, and there exists (in principle) a large class of solutions. Finally, we discuss the stability of the vanishing complexity condition.