Analytical Models of Hyperbolical Gravitational Sources

This paper aims to conduct an extensive examination of hyperbolically symmetrical static fluid distributions, wherein a precise analysis of their physical characteristics is carried out in the background of modified [Formula: see text] gravity, where [Formula: see text] and [Formula: see text] stands for Gauss Bonnet invariant and energy-momentum trace, respectively. The outcomes reveal that the energy density exhibits negative value, thus implying that any utilization of such fluids necessitates extremely demanding circumstances where quantum effects would be significantly influential. Furthermore, it has been determined that these fluid distributions cannot take the vicinity surrounding their central point of symmetry and leave behind an empty vacuum cavity in its place. Additionally, an appropriate definition for mass function and the complexity factor is determined. Eventually, we exhibit a broad strategy for accomplishing particular solutions and showcase several instances of exact analytical solutions in the presence of [Formula: see text] correction terms.