Spatially Hyperbolic Gravitating Sources in Λ-Dominated Era

This study focuses on the impact of the cosmological constant on hyperbolically symmetric matter configurations in a static background. I extend the work of Herrera et al. 2021. and describe the influences of such a repulsive character on a few realistic features of hyperbolical anisotropic fluids. After describing the Einstein-Λ equations of motion, I elaborate the corresponding mass function along with its conservation laws. In our study, besides observing negative energy density, I notice the formation of a Minkowskian core as matter content is compelled not to follow inward motion near the axis of symmetry. Three families of solutions are found in the Λ-dominated epoch. The first is calculated by keeping the Weyl scalar to a zero value, while the second solution maintains zero complexity in the subsequent changes of the hyperbolical compact object. However, the last model encompasses stiff fluid within the self-gravitating system. Such a type of theoretical setup suggests its direct link to study a few particular quantum scenarios where negative behavior of energy density is noticed at the Λ-dominated regime.

A generalized class one static solution

In literature, there are three simplest methods of solving Einstein's field equations, namely, (a) assuming conformally flat spacetime, (b) using conformal killing vector and (c) using Karmarkar conditions. In all these approaches the two metric functions gtt and grr are link via a bridge. However, the first two approaches are facing a critical failure while determining central red-shift while the last method always yields well-behaved solution. Therefore, we are adopting the last method and discover a generalized class one solution. It is found that the maximum mass and radius of the compact star describe by the solution strongly depends on the parameter n. As n increases the maximum mass and radius also increases. For n=3.3, Mmax=1.459M⊙ and Rmax=9.52 km, and for n=4.8 have Mmax=1.766M⊙ with Rmax=10.31 km. For n=4.8 the equation of state is behaving linearly as the speed of sound is almost constant at 0.333. In overall the presented solution is well-behaved in all respects.