Multi-Centered Metric In 4-Dimensional Lorentzian Manifold

摘要

In this paper, we construct explicitly a multi-centered metric in 4-dimensional Lorentzian manifolds. We consider an axial symmetric metric with zero scalar curvature which can be described by Laplace equation. Then, we consider a point source which can be interpreted as a remove point on the manifold. So, the Laplace equation becomes Poisson equation. Finally, we construct explicitly a multi-centered metric based on solution of the Poisson equation.