Existence of stable wormholes on a noncommutative-geometric background in modified gravity

Abstract

In this paper, we discuss spherically symmetric wormhole solutions in $f(R,T)$ modified theory of gravity by introducing well-known non-commutative geometry in terms of Gaussian and Lorentizian distributions of string theory. For some analytic discussion, we consider an interesting model of $f(R,T)$ gravity defined by $f(R,T)=f_1(R)+\lambda T$. By taking two different choices for the function $f_1(R)$, that is, $f_1(R)=R$ and $f_1(R)=R+\alpha R^2+\gamma R^n$, we discuss the possible existence of wormhole solutions. In the presence of non-commutative Gaussian and Lorentizian distributions, we get exact and numerical solutions for both these models. By taking appropriate values of the free parameters, we discuss different properties of these wormhole models analytically and graphically. Further, using equilibrium condition, it is found that these solutions are stable. Also, we discuss the phenomenon of gravitational lensing for the exact wormhole model and it is found that the deflection angle diverges at wormhole throat.

15 pages, 18 figures

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• Traversable Wormholes in $f(R,T)$ Gravity
• Propagation of Polar Gravitational Waves in f(R,T) Scenario
• Static Traversable Wormholes in $f(R,T)=R+2\alpha \ln T$ Gravity
• Double shadows of reflection-asymmetric wormholes supported by positive energy thin-shells
• Morris-Thorne Wormholes in $f(R,T)$ modified theory of gravity
• Noncommutative inspired wormholes admitting conformal motion involving minimal coupling
• A Study of stable wormhole solution with non-commutative geometry in the framework of linear $f(R,{\mathcal{L}}_m,T)$ gravity
• Non-commutative black holes of various genera in the connection formalism
• Non-commutative Wormholes in $f(R)$ Gravity satisfying the Energy Conditions
• Phantom energy supported wormhole model in $f(R,T)$ gravity assuming conformal motion
• Conformally symmetric wormhole solutions supported by non-commutative geometry in $f(Q,T)$ gravity
• Energy Constraints for Evolving Spherical and Hyperbolic Wormholes in $f(R,T)$ Gravity