Role of anisotropy on the tidal deformability of compact stellar objects

In this paper, we introduced a framework to study the tidal deformation of relativistic anisotropic compact stars. Anisotropic stresses are ubiquitous in nature and widely used in modelling compact stellar object. Tidal deformability of astrophysical compact objects is a natural effect of gravity such as one produced by a companion in a binary system. In general relativity, the existence of this measurable effect of gravity level can be quantified by their tidal Love numbers (TLN) which characterize the deformability of a neutron star (NS) from sphericity. The tidal deformability or polarizability parameter of a NS depends on its complex internal structure and hence the nature of the compact object can study through measuring the love number (TLN). We choose a particular solution which is the anisotropic generalization of Tolman IV Model as the interior of the compact stellar object. The physical acceptability of the model has been shown graphically by considering the pulsar 4U1608−52 with their current estimated mass and radius. By computing quadrupole moment we calculated the tidal love number as a dependent on anisotropy of the compact object. We graphically analyze the variation of tidal love number (TLN) against anisotropy for different compact objects with compactness factor. The numerical value of TLN is given for different compact objects for physically acceptable value of anisotropic parameter.