https://doi.org/10.1140/epjc/s10052-024-13604-w
Regular Article
A study of stable wormhole solution with non-commutative geometry in the framework of linear
gravity
1
Institut für Theoretische Physik, Universität Leipzig, Brüderstraße 16, 04103, Leipzig, Germany
2
Department of Mathematics, Birla Institute of Technology and Science-Pilani, Hyderabad Campus, 500078, Hyderabad, India
a
pksahoo@hyderabad.bits-pilani.ac.in
Received:
6
September
2024
Accepted:
10
November
2024
Published online:
21
November
2024
This research delves into the potential existence of traversable wormholes (WHs) within the framework of modified, curvature based gravity. The modification includes linear perturbations of the matter Lagrangian and the trace of the energy-momentum tensor with specific coupling strengths and
and can thus be viewed as a special case of linear f(R, T)-gravity with a variable matter coupling or as the simplest additively separable
-model. A thorough examination of static WH solutions is undertaken using a constant redshift function; therefore, our work can be regarded as the first-order approximation of WH theories in
. The analysis involves deriving WH shape functions based on non-commutative geometry, with a particular focus on Gaussian and Lorentzian matter distributions
. Constraints on the coupling parameters are developed so that the shape function satisfies both the flaring-out and asymptotic flatness conditions. Moreover, for positive coupling parameters, violating the null energy condition (NEC) at the WH throat
demands the presence of exotic matter. For negative couplings, however, we find that exotic matter can be avoided by establishing the upper bound
. Additionally, the effects of gravitational lensing are explored, revealing the repulsive force of our modified gravity for large negative couplings. Lastly, the stability of the derived WH solutions is verified using the Tolman–Oppenheimer–Volkoff (TOV) formalism.
© The Author(s) 2024
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