Physics of Quadrupolar Compact Astrophysical Objects

The pursuit of understanding and testing general relativity involves both theoretical and observational efforts. To study the strong gravitational fields near astrophysical black holes and compact objects, which are not directly accessible, researchers often assume that these black holes are described by the Kerr solution. However, there are other objects that can mimic the properties of a black hole, making it challenging to connect theoretical models to observations. Therefore, it is important to explore deviations by introducing small additional parameters as extra physical degrees of freedom in order to establish a link between the models and observational data. This paper presents the development of an alternative background that incorporates these additional parameters. The subsequent analysis includes examining the expected astrophysical properties and validating them through comparison with observational data.