Einstein Equation with Quantum Corrections Reduced to Second Order

Details Einstein Equation with Quantum Corrections Reduced to Second Order Einstein Equation with Quantum Corrections Reduced to Second Order

1992-11-03

arxiv.org/abs/gr-qc/9211002v1

Phys.Rev.D47:1339-1355,1993

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

47 pages plus 4 figure pages

Scientific paper

10.1103/PhysRevD.47.1339

We consider the Einstein equation with first order (semiclassical) quantum corrections. Although the quantum corrections contain up to fourth order derivatives of the metric, the solutions which are physically relevant satisfy a reduced equations which contain derivatives no higher than second order. We obtain the reduced equations for a range of stress-energy tensors. These reduced equations are suitable for numerical solution, are expected to contain fewer numerical instabilities than the original fourth order equations, and yield only physically relevant solutions. We give analytic and numerical solutions or reduced equations for particular examples, including Friedmann-Lema\^\i tre universes with cosmological constant, a spherical body of constant density, and more general conformally flat metrics.

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