A new class of traversable exponential wormhole metrics

In this work we have formulated a new class of traversable exponential wormhole metrics. Here initially we have considered a exponential wormhole metric in which the temporal component is an exponential function of $r$ but the spatial components of the metrics are fixed as a particular function $e^{\frac{2m}{r}+2\alpha r}$. Following that, we have constructed a generalised exponential wormhole metric in which the spatial component is an exponential function of $r$ but the temporal component is fixed as a particular function given by $e^{-\frac{2m}{r}-2\alpha r}$. Finally we have considered exponential metric in which both the temporal and spatial components are generalised exponential function of $r$. We have also studied some of their properties including throat radius, stability, energy conditions, examined singularity, the metric in curvature coordinates, effective refractive index, innermost stable circular orbit(ISCO) and photon sphere, Regge-Wheeler potential and determined the curvature tensor. The radius of the throat is found to be consistent with the properties of wormholes and donot contain any types of singularities, which are given by $r=m$, $r = \frac{-1+\sqrt{1+4\alpha m}}{2\alpha}$, $r=\frac{-1+\sqrt{1+8\alpha m}}{4\alpha}$, $r=m+\frac{1}{\alpha}$, $r=m+\frac{2}{\alpha}$...etc. Most interestingly, we find that their throat radius is same for the same spatial component and the same range of values of $m$. In addition to these they also violate Null Energy Condition(NEC) near the throat. These newly constructed metrics form a new class of traversable wormhole.