Hyperbolically Symmetric Versions of Lemaitre–Tolman–Bondi Spacetimes

Abstract

We study fluid distributions endowed with hyperbolic symmetry, which share many common features with Lemaitre–Tolman–Bondi (LTB) solutions (e.g., they are geodesic, shearing, and nonconformally flat, and the energy density is inhomogeneous). As such, they may be considered as hyperbolic symmetric versions of LTB, with spherical symmetry replaced by hyperbolic symmetry. We start by considering pure dust models, and afterwards, we extend our analysis to dissipative models with anisotropic pressure. In the former case, the complexity factor is necessarily nonvanishing, whereas in the latter cases, models with a vanishing complexity factor are found. The remarkable fact is that all solutions satisfying the vanishing complexity factor condition are necessarily nondissipative and satisfy the stiff equation of state.

Non-static hyperbolicallly symmetric fluids

“…In this case we shall exhibit only non-dissipative models (for dissipative models see [18]). Then, excluding dissipative processes, and assuming the quasi-homologous condition (39) we may write…”

“…where R I and R II denote the areal radii of two shells (I, II) described by r = r I = constant, and r = r II = constant, respectively. In the notation of [18], conditions (46) and (57) define the homologous evolution.…”

“…Motivated by these intriguing results we embarked into a general study of fluid distributions endowed with hyperbolical symmetry [18][19][20].…”

A Comprehensive Analysis of Hyperbolical Fluids in Modified Gravity

“…They also examined the physical elements of these solutions and looked into the concept of tunnels in hyperbolic spacetime. Herrera et al [ 40 ] analyzed the fluid distributions with hyperbolic symmetry, which are similar to Lemaitre–Tolman–Bondi (LTB) solutions, when the system experienced geodesic, non-conformally flat and shearing limits. They examined the pure dust models as well as the dissipative models with anisotropic pressure.…”

Significance of Charge on the Dynamics of Hyperbolically Distributed Fluids

“…They evaluated several solutions using quasihomologous, vanishing of complexity factor condition and the supplementary constraints for the dissipative as well as non-dissipative systems. Moreover, they [41] also did the aforementioned work by using the approach of Lemaître-Tolman-Bondi spacetime endorsed with hyperbolic symmetry. Oikonomou and his collaborators [42][43][44][45][46] analyzed various issue of stellar and cosmic evolution, in particularly the role of cosmological attractors on a slowly rotating celestial bodies.…”