Search

Summary

In this chapter we describe an important application of stochastic gravity: we derive the Einstein–Langevin equation for the metric perturbations in a Minkowski background. We solve this equation for the linearized Einstein tensor and compute the associated two-point correlation functions, as well as the two-point correlation functions for the metric perturbations. The results of this calculation show that gravitational fluctuations are negligible at length scales larger than the Planck length and predict that the fluctuations are strongly suppressed at small scales. These results also reveal an important connection between stochastic gravity and the 1/N expansion of quantum gravity. In addition, they are used to study the stability of the Minkowski metric as a solution of semiclassical gravity, which constitutes an application of the validity criterion introduced in the previous chapter. This calculation requires a discussion of the problems posed by the so-called runaway solutions and some of the methods of dealing with them.

In this paper we study the temporal convergence of a locally implicit discontinuous Galerkin method for the time-domain Maxwell’s equations modeling electromagnetic waves propagation. Particularly, we wonder whether the method retains its second-order ordinary differential equation (ODE) convergence under stable simultaneous space-time grid refinement towards the true partial differential equation (PDE) solution. This is not a priori clear due to the component splitting which can introduce order reduction

Search Results

Refine search

Refine search

Actions for selected content:

2 results

11 - Metric Fluctuations in Minkowski Spacetime

Summary

Temporal convergence of a locally implicit discontinuous Galerkin method for Maxwell’s equations ∗

Search Results

Refine search

Refine search

Actions for selected content:

Save Search

2 results

11 - Metric Fluctuations in Minkowski Spacetime

Summary

Temporal convergence of a locally implicit discontinuous Galerkin method for Maxwell’s equations∗

Temporal convergence of a locally implicit discontinuous Galerkin method for Maxwell’s equations ∗