Abstract
We adapt the dual-null foliation to the functional Schr\"odinger representation of quantum field theory and study the behavior of quantum probes in plane-wave space-times near the null-singularity. A comparison between the Einstein-Rosen and the Brinkmann patch, where the latter extends beyond the first, shows a seeming tension that can be resolved by comparing the configuration spaces. Our analysis concludes that Einstein-Rosen space-times support exclusively configurations with non-empty gravitational memory that are focussed to a set of measure zero in the focal plane with respect to a Brinkmann observer. To conclude, we provide a rough framework to estimate the qualitative influence of back-reactions on these results.
Highlights
Space-times featuring plane-fronted waves with parallel rays represent an important class of exact solutions to the Einstein equations, as they describe nonlinear gravitational waves in general relativity
We adapt the dual-null foliation to the functional Schrödinger representation of quantum field theory and study the behavior of quantum probes in plane-wave space-times near the null singularity
Our analysis concludes that Einstein-Rosen space-times support exclusively configurations with nonempty gravitational memory that are focused to a set of measure zero in the focal plane with respect to a Brinkmann observer
Summary
Space-times featuring plane-fronted waves with parallel rays (pp-wave space-times) represent an important class of exact solutions to the Einstein equations, as they describe nonlinear gravitational waves in general relativity. One special subclass thereof are plane-wave space-times which portray the even simpler situation where the profile of the wave front is constant along the transversal direction Penrose extensively studied these space-times from a geometric perspective in a series of seminal articles [2,3]. As the singularity is null, and of a different type from previous studies, it may shed some light on how the nature of the singular surface, as well as the bordering space-time, impacts previously seen effects These space-times have zero curvature everywhere away from the wave front. The resulting dual-null foliation allows for the construction of Lagrangian and Hamiltonian dynamics These support well-defined initial-value problems, as well as Hamiltonian flows, such that the Cauchy problem can be generalized to some nonglobally hyperbolic space-times. Note that we will work in the units c 1⁄4 ħ 1⁄4 GN 1⁄4 1 throughout the article
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