A new family of gauges in linearized general relativity
Giampiero Esposito; Cosimo Stornaiolo; Giampiero Esposito; Istituto Nazionale di Fisica Nucleare, Sezione di Napoli, Complesso Universitario di Monte S. Angelo, Via Cintia, Edificio N', 80126 Napoli, Italy; Università di Napoli Federico II, Dipartimento di Scienze Fisiche, Complesso Universitario di Monte S. Angelo, Via Cintia, Edificio N', 80126 Napoli, Italy; Cosimo Stornaiolo; Istituto Nazionale di Fisica Nucleare, Sezione di Napoli, Complesso Universitario di Monte S. Angelo, Via Cintia, Edificio N', 80126 Napoli, Italy; Università di Napoli Federico II, Dipartimento di Scienze Fisiche, Complesso Universitario di Monte S. Angelo, Via Cintia, Edificio N', 80126 Napoli, Italy
Журнал:
Classical and Quantum Gravity
Дата:
2000-05-07
Аннотация:
For vacuum Maxwell theory in four dimensions, a supplementary condition exists (due to Eastwood and Singer) which is invariant under conformal rescalings of the metric, in agreement with the conformal symmetry of the Maxwell equations. Thus, starting from the de Donder gauge, which is not conformally invariant but is the gravitational counterpart of the Lorenz gauge, one can consider, led by formal analogy, a new family of gauges in general relativity, which involve fifth-order covariant derivatives of metric perturbations. The admissibility of such gauges in the classical theory is first proven in the cases of linearized theory about flat Euclidean space or flat Minkowski spacetime. In the former, the general solution of the equation for the fulfillment of the gauge condition after infinitesimal diffeomorphisms involves a 3-harmonic 1-form and an inverse Fourier transform. In the latter, one needs instead the kernel of powers of the wave operator, and a contour integral. The analysis is also used to put restrictions on the dimensionless parameter occurring in the DeWitt supermetric, while the proof of admissibility is generalized to a suitable class of curved Riemannian backgrounds. Eventually, a non-local construction of the tensor field is obtained which makes it possible to achieve conformal invariance of the above gauges.
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