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
