Traversable wormhole solutions in the presence of scalar field

Abstract

In the present work, exact solutions to Einstein’s field equations are obtained in the presence of a scalar field in three cases. In the first case, the equation of state constituting the matter of wormhole is considered as [Formula: see text], where [Formula: see text] is the equation of state parameter. In the second case, the pressures are assumed to follow the relation [Formula: see text], where [Formula: see text] is a nonzero constant. In the third case, the form of matter energy density is assumed as [Formula: see text], where [Formula: see text], [Formula: see text] is the scale radius and [Formula: see text] is the corresponding matter density. In every case, the shape function is derived and its necessary conditions such as throat condition, flare out condition and asymptotic conditions are examined. By using these shape functions, the wormhole solutions are obtained and energy conditions are tested.