Speaker
Description
The usual approach to perturbation theory presents some mathematical flaws. For instance, when studying gravitational waves (GW) around a Minkwoski background, one usually imposes the weak-field limit, requiring the spacetime metric to be the Minkowski metric plus a small perturbation. However, the bundle of Lorentzian metrics is neither linear nor affine; thus, the addition operation is not globally well-defined. Starting from this consideration, we analyse another approach to linearisation and perturbation theory, which is completely variational. This framework presents numerous advantages: it can be applied to any classical field theory (generality), it does not involve any approximation in the computations (exactness), and, most importantly, it allows to study linearisation around all solutions of the theory at the same time (globality). As a first example, we apply the framework to standard General Relativity and we show that linearised Einstein equations are a generalisation of GW equations around a general background, as expected. Finally, we present a few considerations on the existence of solutions and on conservation laws.