Wormhole structures in logarithmic-corrected R^2 gravity

I Fayyaz,M Farasat Shamir

doi:10.1140/epjc/s10052-020-8004-9

Abstract

This paper is devoted to find the feasible shape functions for the construction of static wormhole geometry in the frame work of logarithmic-corrected R^2 gravity model. We discuss the asymptotically flat wormhole solutions sustained by the matter sources with anisotropic pressure, isotropic pressure and barotropic pressure. For anisotropic case, we consider three shape functions and evaluate the null energy conditions and weak energy conditions graphically along with their regions. Moreover, for barotropic and isotropic pressures, we find shape function analytically and discuss its properties. For the formation of traversable wormhole geometries, we cautiously choose the values of parameters involved in f(R) gravity model. We show explicitly that our wormhole solutions violate the non-existence theorem even with logarithmic corrections. We discuss all physical properties via graphical analysis and it is concluded that the wormhole solutions with relativistic formalism can be well justified with logarithmic corrections.

Highlights

In recent era, the investigation about the existence of wormholes is an interesting and attractive topic for researchers
According to the classical general relativity (GR), presence of exotic matter in wormhole structure is the main cause of violation of weak energy condition (WEC) denoted as Tζ ηuζ uη ≥ 0 for any space-like vector ku [25]
We get the violation of nonexistence theorem at the throat and F > 0 provides the wormhole geometry which is filled with exotic matter at the throat found that as we decrease the value of α, wormhole solution has shown violation of WEC and null energy condition (NEC) in more of the region of wormhole space and increase in α provides d f /d R > 0 i.e

Summary

Introduction

The investigation about the existence of wormholes is an interesting and attractive topic for researchers. Bronnikov and Starobinsky [22] discussed that in general no wormhole can be formed if scalar function f (φ) is positive every where in scalar-tensor models of dark energy (commonly known as non-existence theorem). According to the classical GR, presence of exotic matter in wormhole structure is the main cause of violation of weak energy condition (WEC) denoted as Tζ ηuζ uη ≥ 0 for any space-like vector ku [25]. By imposing these conditions on ρ + pr > 0, one can find the key point that if F < 0 at r = r0, we get a wormhole solution that obeys the NEC at the throat in the context of logarithmic corrections It is clear from Eq (12) that the particular solution in the context of f (R) gravity that violates the non-existence theorem can obey WEC if < 0

Logarithmic-corrected R2 gravity

Numerical solutions

Anisotropic fluid

Isotropic fluid

Barotropic equation of state

Comparison and conclusion