Traversable Wormholes Supported by Entropy-Inspired Effective Matter Sectors

Abstract

The thermodynamic interpretation of gravity suggests that modifications of horizon entropy can be encoded in effective geometries and matter distributions. Motivated by the entropy--geometry correspondence, we investigate Morris--Thorne wormholes constructed from density profiles associated with Barrow, Tsallis, Kaniadakis, logarithmic, and exponential black-hole entropies. The wormhole construction retains each entropy-induced density as input to the shape-function equation, while the radial and tangential pressures are reconstructed independently from the wormhole field equations, a barotropic radial equation of state, anisotropic conservation, and throat regularity. Barrow and Tsallis yield algebraic negative-density distributions; Kaniadakis and exponential corrections produce localized profiles; and the logarithmic sector admits both negative-density and positive-density phantom-like regimes. For every regular configuration considered, radial null energy condition violation at the throat follows from the flare-out condition. Its areal-volume integral is finite and negative for every nonzero deformation: it becomes unbounded when the regular Barrow, Tsallis, and Kaniadakis branches approach their undeformed values, but remains finite in the logarithmic and exponential limits. Removing the density deformation also fails to commute with taking the infinite-radius limit in the Barrow, Tsallis, and Kaniadakis sectors, whereas the two operations agree for the logarithmic and exponential sectors in their pole-free domains. The selected entropy-induced densities can therefore be embedded consistently in traversable-wormhole reconstructions, with the pressure sector fixed by the wormhole geometry and the global source behavior controlling both the asymptotic mass and the integrated radial exoticity.