Dynamical complexity and the gravitational collapse of compact stellar objects

Abstract

We investigate the dynamics of the gravitational collapse of a compact object via a complexity factor scalar which arises from the orthogonal splitting of the Riemann tensor. This scalar has the property of vanishing for systems which are isotropic in pressure and homogeneous in the energy density. In this way, the complexity factor can give further details of the progression of inhomogeneity as the collapse proceeds. Furthermore, we show that complexity may be used in comparing models and justifying their physical viability. Thus, it could become an integral part of the physical analysis of relativistic collapse in addition to energy conditions analysis, (in)stability, and recently investigated force dynamics.

Implications for vanishing complexity in dynamical spherically symmetric dissipative self-gravitating fluids

“…This is in contrast to the adiabatic case in which isotropic pressure and homogeneous energy density lead to the stability of the vanishing complexity condition [28]. It has been noted that the condition of zero complexity is affected by heat dissipation [29] and initial investigations into non-vanishing complexity for self-gravitating systems have recently been made [12].…”

“…The application of the vanishing complexity condition has become an integral part of modelling relativistic objects within the static regime. For dynamical systems, the complexity factor as given according to the above definition is less likely to vanish especially in the case of gravitational collapse [12]. This is expected due to the causal nature of dynamical processes whereby the establishment of an equilibrium with respect to pressure anisotropy, energy density inhomogeneity and heat flux cannot occur instantaneously.…”

“…In the case of dynamical systems the situation is less clear and the complexity factor might likely have a specific, non-vanishing behaviour at certain stages during collapse. Initial investigations have already been conducted in this respect [12]. In this work, we assume the contrary that the dynamical complexity factor vanishes, in order to establish the restriction on the models obtainable 0123456789().…”

Complexity and the departure from spheroidicity

“…We believe that our work sheds new light on the nature of matter and its link to complexity within an astrophysical setting. In a recent paper by Bogadi and Govender [34], the evolution of the complexity factor was investigated in a dynamical scenario in which an initial static stellar object described by Vaidya-Tikekar model used here undergoes dissipative gravitational collapse. It was shown that the complexity factor is affected by the spheroidal parameter, K particularly close to the time of formation of the horizon.…”

Relativistic models for vanishing complexity factor and isotropic star in embedding Class I spacetime using extended geometric deformation approach

“…Later on, it was shown that by considering the quasi-homologous condition, the last condition can be relaxed to increase the number of possible solutions [23]. In a recent study, the contributions from pressure anisotropy, density inhomogeneities and dissipation in the form of radial heat flux to the evolution of complexity in a radiating star have been investigated [24]. Alongside spherically symmetric cases, axially symmetric [25], cylindrically symmetric [26,27] fluid distributions have also been studied.…”