Higher dimensional global monopole with cosmological term

We investigate the space-time of a global monopole in a five dimensional space-time in presence of the cosmological term. Also the gravitational properties of the monopole solution are discussed. Pacs Nos. : 98.80cq; 04.20jb; 04.70Bw Introduction: Recent attempts to Unify gravity with other fundamental forces in nature reveal that it is very interesting to study models where the space-time dimension is different from four. Also latest developments in super string and Yang-Mills Super Gravity theory demand, more than usual 4dimension of space-time. Solutions of Einstein Field equations are believed to of physical relevance possibly at the extremely early times before the Universe under went the compactification transitions [1]. It has also been suggested that the experimental detection of the time variation of fundamental constants could provide strong evidence of the extra dimension [2]. Phase transitions in the early Universe can give rise to topological defects of various kinds such as domain walls, monopoles, strings and their hybrids [3]. In recent, Pando, Valls-Gaboud and Fang [4] have proposed that the topological defects are responsible for structure formation of our Universe. Monopoles are localized defects, will arise if the manifold M contains surfaces, which can’t be continuously shrunk to a point i.e. when π2 (M) ≠ I. Global monopoles are important objects both for Particle Physicists and Cosmologists, which predicted to exist in grand unified theory. Using a suitable scalar field it can be shown that spontaneous symmetry breaking can give rise to such objects which are nothing but the topological knots in the vacuum expectation value of the scalar field and most of their energy is concentrated in a small region near the monopole core. In a pioneering work Barriola and Vilenkin (BV) [5] showed that existence of such a monopole solution resulting from the breaking of global S0(3) symmetry of a triplet scalar field in a Schwarzschild background. They found a peculiar result: The space-time produced by a global monopole has no Newtonian gravitational potential in spite of the geometry produced by this heavy object has a non-vanishing curvature.