Einstein equation with quantum corrections reduced to second order
Abstract
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.
- Publication:
-
Physical Review D
- Pub Date:
- February 1993
- DOI:
- 10.1103/PhysRevD.47.1339
- arXiv:
- arXiv:gr-qc/9211002
- Bibcode:
- 1993PhRvD..47.1339P
- Keywords:
-
- 98.80.Cq;
- 03.65.Sq;
- 04.20.Cv;
- 04.60.+n;
- Particle-theory and field-theory models of the early Universe;
- Semiclassical theories and applications;
- Fundamental problems and general formalism;
- General Relativity and Quantum Cosmology
- E-Print:
- 47 pages plus 4 figure pages