Existence of Wormholes in Einstein-kalb-ramond Space Time

In recent, Kar.S et.al [ Phys Rev D 67,044005 (2003) ] have obtained static spherically symmetric solutions of the Einstein-Kalb-Ramond field equations. We have shown that their solutions, indeed, represent Wormholes. In Einstein-Cartan theory, the symmetric Christoffel connection is modified with the introduction of an anti-symmetric tensorial term,known as space time torsion, which is presumed to have a direct relation with spin [1]. It has been shown that the massless anti-symmetric tensor Kalb-Ramond field, B µν equivalent to torsion is an inherent feature in the low energy effective string action. Several authors [2] have shown that the presence of Kalb-Ramond field in the background space time may lead to various interesting astrophysical and cosmological phenomena such as cosmic optical activity, neutrino lelicity flip, parity violation etc. Recently, Kar et.al [3] have carried out the most general study of the existence carried out of possible spherical symmetric solutions of the Einstein-Kalb-Ramond field equations. They have studied gravitational lensing and perihelion precession in these space-time. They have also shown that for a special case, one can get wormhole for a real Kalb-Ramond field. In this article, we have shown that their general solutions, indeed, always represent wormholes. According to the formation in [3], the action is given by S = d 4 x √ −g[ R(g) k − 1 12 H µνλ H µνλ ] (1) where R(g) is Ricci scalar curvature and H µνλ is Kalb-Ramond field strength and k = 8πG.