Evolution of dynamical complexity in relativistic collapse of hyperbolically symmetric stars

Abstract In this work, we study the evolution of relativistic gravitational collapse of hyperbolically symmetric stellar configurations through the lens of a gravitational complexity factor. This factor is originally a structure scalar function emerging from the $$3+1$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>3</mml:mn> <mml:mo>+</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:math> decomposition of the Riemann tensor into its constituent parts. Perfect-fluid relativistic stellar objects endowed with uniform density exhibit a zero value of the gravitational complexity factor. The degree of complexity factor can thus provide further insights into how the non-uniformity of energy density develops as the collapse evolves. The complete set of governing equations is presented and subsequently employed to evaluate the dynamics of the non-static hyperbolic stellar configuration in contrast with the standard spherically symmetric case. Furthermore, we highlight how the concept of complexity may be used to distinguish between competing models and to support their compliance with physical acceptability requirements. This study demonstrates the key role of the complexity-determining scalar function for modeling non-static dissipative stars with hyperbolically symmetric anisotropic matter distribution.