Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
1998-01-20
Phys.Rev.D58:064015,1998
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
32 pp., LaTeX
Scientific paper
10.1103/PhysRevD.58.064015
A new approach to gravitational gauge-invariant perturbation theory begins from the fourth-order Einstein-Ricci system, a hyperbolic formulation of gravity for arbitrary lapse and shift whose centerpiece is a wave equation for curvature. In the Minkowski and Schwarzschild backgrounds, an intertwining operator procedure is used to separate physical gauge-invariant curvature perturbations from unphysical ones. In the Schwarzschild case, physical variables are found which satisfy the Regge-Wheeler equation in both odd and even parity. In both cases, the unphysical "gauge'' degrees of freedom are identified with violations of the linearized Hamiltonian and momentum constraints, and they are found to evolve among themselves as a closed subsystem. If the constraints are violated, say by numerical finite-differencing, this system describes the hyperbolic evolution of the constraint violation. It is argued that an underlying raison d'\^etre of causal hyperbolic formulations is to make the evolution of constraint violations well-posed.
Abrahams Andrew M.
Anderson Arlen
Lea Chris
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