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Einstein Equation with Quantum Corrections Reduced to Second Order

Leonard Parker
J. Simon
Journal / Anthology

Physical Review D
Year: 1993
Volume: 47
Issue: 4
Page range: 1339-1355

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 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 a 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-Lemaître universes with a cosmological constant, a spherical body of constant density, and more general conformally flat metrics.

*Science > Physics > Astrophysics
*Science > Physics > Quantum Physics
*Science > Physics > Relativity Theory

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