Hydrodynamics Instability Around Compact Object In SdS background

Abstract

The success of general theory of relativity (GR) over a wide range of astrophysical observations is the manifestation of progress in astronomy and astrophysical studies. Whilst, there are encouraging past success of GR and future hopes there is an outstanding debates on GR field equations dated back to their origin, where Einstein himself was also puzzled in the solutions of the equations. As the consequence, Einstein did introduce a positive cosmological constant to his original field equations. Since then, the cosmological constant has remained with debate where it is being cast out at a time and reintroduced at other time. But a firm considers of is triggered in the 1960’s when an excess quasi-stellar objects (QSO’s) near the redshift Z ∼= 1.95 were observed. Moreover, the recent discovery of expanding universe at an accelerated rate favors a flat low density Cold Dark Matter with dark energy in the form of cosmological constant Λ − CDM model is more or less consistent with all the current cosmological observations. But the general perception, owing to its tiny value, questions its significance on a local gravitational phenomenon. But, a local effect of cosmological constant is claimed to be observable from relativistic accretion phenomena around massive BHs which involve distancescales. So the effect of on the dynamics of objects including jets around massive objects at kiloparsecs or more astrophysical distances need investigations. So far all the works on the effect of Λ on accreting systems were carried out under some restricted conditions owing to the complex and nonlinear character of the equations in GR; if not most were under Newtonian. Motivated by this short scientific rationale, we studied the effect of cosmological constant on dynamical systems including magnetohydrodynamic (MHD) instabilities around massive objects like BHs in the current standard Λ − CDM model where the Schwarzschild de Sitter (SdS) background is being considered then the interior and exterior solutions of Einsteins equations with a non-zero cosmological constant