Topological defects inspired static spherically symmetric solution

It is argued that in the past, our universe was denser and hotter. Therefore, the universe was in a systematic phase in the early stage and no topological defects were present at that time. When the universe had started the expansion, it becomes gradually cool from its hot initial state [7,20,21]. As a result, the early universe had experienced some phase transitions. These phase transitions in the early universe create several topological defects, namely monopoles, cosmic strings, textures, or domain walls. These defects may have One of the interesting characteristics of topological defects is the deficit solid angle in the hypersurfaces t = constant. The area of a sphere of radius R in this space is not 4 pi R2. In the work, we try to find the spacetime geometry of the outside of a spherically symmetric distribution of matter (within a galaxy that can be a galactic halo, etc) where the spacetime geometry is characterized by deficit solid angle in the hypersurfaces t = constant. We obtain a solution of Einstein's field equations for the outside of spherically symmetric matter distribution in the galactic region. The solution describes a black hole. The several features of the solution are discussed.