A new shape function and some specific wormhole solutions in braneworld scenario

TL;DR

This paper introduces a new shape function in braneworld gravity to find wormhole solutions, analyzing energy conditions for various redshift and shape functions in isotropic and anisotropic scenarios.

Contribution

It presents a novel shape function derived from braneworld field equations and explores wormhole solutions with different redshift and shape functions, examining energy conditions.

Findings

Some solutions satisfy all energy conditions near the throat.

Other solutions violate only the strong energy condition.

Multiple wormhole configurations are consistent with physical energy conditions.

Abstract

Considering a energy density of the form $\rho=q\left({\frac{r}{r_0}}\right)^{-n}$( where $q$ is an arbitrary positive constant with dimension of energy density and $n>0$), a shape function is obtained by using field equations of braneworld gravity theory in this paper. Under isotropic scenario wormhole solutions are obtained considering six different redshift functions along with the obtained new shape function. For anisotropic case wormhole solutions are obtained under the consideration of five different shape functions along with the redshift function $\phi=\beta ln(\frac{r}{r_0})$, where $\beta$ is an arbitrary constant. In each case all the energy conditions are examined and it is found that for some cases all energy conditions are satisfied in the vicinity of the wormhole throat and for the rest cases all energy conditions are satisfied except strong energy condition.