Abstract:
In this paper, we present new generalized wormhole (WH) solutions within the context of f (R) gravity.
Specifically, we focus on f (R) gravitational theories formulated in the metric formalism, with our investigation centered
on a power-law form represented by f (R) = Rχ . Here,
is an arbitrary constant, and χ is a real number. Notably,
this form possesses the advantageous property of reducing
to Einstein gravity when = 1 and χ = 1. To obtain these
novel WH solutions, we establish the general field equations
for any f (R)theory within the framework of Morris–Thorne
spacetime, assuming metric coefficients that are independent
of time. By utilizing an anisotropic matter source and a specific type of energy density associated with solitonic quantum wave (SQW) and cold dark matter (CDM) halos, we
calculate two distinct WH solutions. We thoroughly investigate the properties of the exotic matter (ExoM) residing
within the WH geometry and analyze the matter contents
through energy conditions (ECs). Both analytical and graphical methods are employed in this analysis to examine the
validity of different regions. Notably, the calculated shape
functions for the WH geometry satisfy the necessary conditions in both scenarios, emphasizing their reliability. Our investigations into specific parameter ranges in both scenarios revealed the presence of ExoM. This ExoM is characterized by an energy–momentum tensor that violates the null
energy condition (NEC) and, consequently, the weak energy
condition as well, in the vicinity of the WH throats. Furthermore, we investigated the repulsive effect of gravity and
discovered that its presence results in a negative deflection
angle for photons following null geodesics. Importantly, we
observed that the deflection angle consistently exhibits negative values across all r0 values in both scenarios, indicating
the manifestation of the repulsive gravity effect. Finally, we
compare the obtained WH solutions utilizing both distributions, as well as the f (R) power-law-like models, in order
to assess the feasibility of energetic configurations for WHs
within SQW and CDM systems.
