Metrics With Vanishing Quantum Corrections
نویسنده
چکیده
We investigate solutions of the classical Einstein or supergravity equations that solve any set of quantum corrected Einstein equations in which the Einstein tensor plus a multiple of the metric is equated to a symmetric conserved tensor Tμν(gαβ, ∂τgαβ, ∂τ∂σgαβ , . . . , ) constructed from sums of terms the involving contractions of the metric and powers of arbitrary covariant derivatives of the curvature tensor. A classical solution, such as an Einstein metric, is called universal if, when evaluated on that Einstein metric, Tμν is a multiple of the metric. A Ricci flat classical solution is called strongly universal if, when evaluated on that Ricci flat metric, Tμν vanishes. It is well known that pp-waves in four spacetime dimensions are strongly universal. We focus attention on a natural generalisation; Einstein metrics with holonomy Sim(n − 2) in which all scalar invariants are zero or constant. In four dimensions we demonstrate that the generalised Ghanam-Thompson metric is weakly universal and that the Goldberg-Kerr metric is strongly universal; indeed, we show that universality extends to all 4-dimensional Sim(2) Einstein metrics. We also discuss generalizations to higher dimensions.
منابع مشابه
Two loop and all loop finite 4-metrics
In pure Einstein theory, Ricci flat Lorentzian 4-metrics of Petrov types III or N have vanishing counter terms up to and including two loops. Moreover for pp-waves and type-N spacetimes of Kundt’s class which admit a non-twisting, non expanding, null congruence all possible invariants formed from the Weyl tensor and its covariant derivatives vanish. Thus these Lorentzian metrics suffer no quant...
متن کاملar X iv : h ep - t h / 99 05 15 4 v 1 2 1 M ay 1 99 9 Two loop and all loop finite 4 - metrics
In pure Einstein theory, Ricci flat Lorentzian 4-metrics of Petrov types III or N have vanishing counter terms up to and including two loops. Moreover for pp-waves and type-N spacetimes of Kundt's class which admit a non-twisting, non expanding, null congruence all possible invariants formed from the Weyl tensor and its covariant derivatives vanish. Thus these Lorentzian metrics suffer no quant...
متن کاملQuantum Geometry of the Universal Hypermultiplet
The universal hypermultiplet moduli space metric in the type-IIA superstring theory compactified on a Calabi-Yau threefold is related to integrable systems. The instanton corrections in four dimensions arise due to multiple wrapping of BPS membranes and fivebranes around certain (supersymmetric) cycles of Calabi-Yau. The exact (nonperturbative) metrics can be calculated in the special cases of ...
متن کاملGeneralized Douglas-Weyl Finsler Metrics
In this paper, we study generalized Douglas-Weyl Finsler metrics. We find some conditions under which the class of generalized Douglas-Weyl (&alpha, &beta)-metric with vanishing S-curvature reduce to the class of Berwald metrics.
متن کاملQuantum Corrections to the Reissner-Nordström and Kerr-Newman Metrics
We use effective field theory techniques to examine the quantum corrections to the gravitational metrics of charged particles, with and without spin. In momentum space the masslessness of the photon implies the presence of nonanalytic pieces ∼ √ −q2, q2 log−q2, etc. in the form factors of the energy-momentum tensor. We show how the former reproduces the classical non-linear terms of the Reissne...
متن کامل