Asymptotically flat vacuum solutions in order-reduced semiclassical gravity

We investigate the effects of quantum backreaction on Schwarzschild geometry in semiclassical approximation. The renormalized stress-energy tensor (RSET) a scalar field is modelled via an order reduction analytical approximation derived by Anderson, Hiscock and Samuel (AHS). As resulting AHS Einstein equations are fourth-derivative metric, we follow prescription to shrink space solutions. Motivated this prescription, develop method that allows obtain novel analytic for RSET exhibits all desired properties well-posed RSET: conservation, regularity, correct estimation vacuum-state contributions. derive set sourced order-reduced AHS-RSET Boulware state. classify self-consistent solutions equations, discuss their main features address how well they resemble higher-order theory. Finally, establish comparison with previous results literature obtained through Polyakov minimally coupled fields.