Complexity factor Parametrization for Traversable Wormholes

Abstract: It is known that static traversable wormhole in Einstein gravity is supported by matter that violates null energy conditions (NEC). Essentially such wormhole will be characterised by a central throat with anisotropic matter lining the throat that violates NEC. This in turn provides viable geometry for the wormhole to sustain. In 2018, L. Herrera introduced a new classification for spherically symmetric bodies called ``complexity factor". It was proposed that a spherically symmetric non trivial geometry can be classified as complex or non-complex based on the nature of the inhomogeneity and anisotropy of the stress energy tensors with only homogeneous and isotropic matter distribution leading to null complexity. Mathematically there was also another way of obtaining zero complexity geometry. In this context since static traversable wormhole by default is characterised by anisotropic and inhomogeneous matter stress tensors, the question we answer is whether it is possible to obtain zero complexity class of wormholes supported by exotic matter.