The Physics of Non-spherical Compact Objects

In this thesis, one of the well-known spacetimes named as Zipoy-Voorhees (ZV) or-metric is extended to its charged version via Ernst formalism and is called the charged ZV solution. This spacetime is then further investigated and the relevant geodesic equations, the Newtonian limit, the solution of Maxwell equations and the singularity analysis are all carried out in detail. These steps are later on followed by inspecting the physical properties of the consequent-metric, whose gravitational lensing effect is compared with the one for the stationary ZV solution. In this regard, the effect of deformation parameter on gravitational lensing and redshift is studied. With the help of Chandrasekhar-Xanthopoulos (CX) theorem and Ernst formalism, the charged and stationary version of ZV solution is also obtained. The metric functions of this new solution- which came out to be utterly complicated- are expanded up to the quadrupole terms. As a result, the closed time-like curves are examined. Another important compitation known as the singularity analysis is carried out for the uncharged and charged versions of ZV spacetime on = 2 and = planes. In the end, it has been found that both solutions are quantum regular in s-mode on the = plane for 1 < < 2. Lastly, gravitational lensing analysis is conducted on another well-known spacetime of theoretical physics, Kerr-Newman Anti de Sitter metric, and the effect of rotation on black holes is studied by using observational data from M87 and SgrA .