Equilibrium of large astrophysical structures in the Newton-Hooke spacetime

Using the scalar and tensor virial equations, the Lane-Emden equation expressing the hydrostatic equilibrium and small oscillations around the equilibrium, we show how the cosmological constant $\Lambda$ affects various astrophysical quantities important for large matter conglomeration in the universe. Among others we examine the effect of $\Lambda$ on the polytropic equation of state for spherically symmetric objects and find non-negligible results in certain realistic cases. We calculate the angular velocity for non-spherical oblate configurations which demonstrates a clear effect of $\Lambda$ on high eccentricity objects. We show that for oblate as well as prolate ellipsoids the cosmological constant influences the critical mass and the temperature of the astrophysical object. These and other results show that the effect of $\Lambda$ is large for flat astrophysical bodies.