Apparent universality of semiclassical gravity in the far field limit

The universality of semiclassical gravity is investigated by considering the behavior of the quantities $⟨{\varphi }^2⟩$ and $⟨T^a{}_b⟩$, along with quantum corrections to the effective Newtonian potential in the far field limits of static spherically symmetric objects ranging from stars in the weak field Newtonian limit to black holes. For scalar fields it is shown that when differences occur they all result from the behavior of a single mode with zero frequency and angular momentum and are thus due to a combination of infrared and $s$-wave effects. An intriguing combination of similarities and differences between the extreme cases of a Schwarzschild black hole and a star in the weak field Newtonian limit is explained.