| Wormholes could play an important role on both microscopic and macroscopic scales in the realm of classical and quantum gravity.In this paper we will introduce basic but important knowledge of mathematics,especially,differential geometry,which is now a very radical tool for investigating the Universe's structure,including manifolds,vector and tensor,metric and etc.We also introduce general relativity including mathematical model for spacetime,matter field and Einstein's Equation,wormhole and cosmology constant.We attempt to find a matter field to support wormholes,so I provide a generalized energy-momentum tensor which is confined by some mathematical conditions.Then we choose Schwarzschild metric to solve Einstein' Equation.Under certain constraints,there exists a class of exact solutions for Einstein's Equation.In the end of this paper,we study the feature of the wormhole solutions, such as wormhole radius and embedding graph. |
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