Geometry of General Hypersurfaces in Spacetime: Junction Conditions

We study imbedded hypersurfaces in spacetime whose causal character is allowed to change from point to point. Inherited geometrical structures on these hypersurfaces are defined by two methods: first, the standard rigged connection induced by a rigging vector (a vector not tangent to the hypersurface anywhere); and a second, more physically adapted, where each observer in spacetime induces a new type of connection that we call the rigged metric connection. The generalisation of the Gauss and Codazzi equations are also given. With the above machinery, we attack the problem of matching two spacetimes across a general hypersurface. It is seen that the preliminary junction conditions allowing for the correct definition of Einstein's equations in the distributional sense reduce to the requirement that the first fundamental form of the hypersurface be continuous. The Bianchi identities are then proven to hold in the distributional sense. Next, we find the proper junction conditions which forbid the appearance of singular parts in the curvature. Finally, we derive the physical implications of the junction conditions: only six independent discontinuities of the Riemann tensor are allowed. These are six matter discontinuities at non-null points of the hypersurface. For null points, the existence of two arbitrary discontinuities of the Weyl tensor (together with four in the matter tensor) are also allowed.Comment: Latex, no figure

Megahertz-rate ultrafast X-ray scattering and holographic imaging at the European XFEL

The advent of X-ray free-electron lasers (XFELs) has revolutionized fundamental science, from atomic to condensed matter physics, from chemistry to biology, giving researchers access to X-rays with unprecedented brightness, coherence and pulse duration. All XFEL facilities built until recently provided X-ray pulses at a relatively low repetition rate, with limited data statistics. Here, results from the first megahertz-repetition-rate X-ray scattering experiments at the Spectroscopy and Coherent Scattering (SCS) instrument of the European XFEL are presented. The experimental capabilities that the SCS instrument offers, resulting from the operation at megahertz repetition rates and the availability of the novel DSSC 2D imaging detector, are illustrated. Time-resolved magnetic X-ray scattering and holographic imaging experiments in solid state samples were chosen as representative, providing an ideal test-bed for operation at megahertz rates. Our results are relevant and applicable to any other non-destructive XFEL experiments in the soft X-ray range

Megahertz-rate ultrafast X-ray scattering and holographic imaging at the European XFEL

The advent of X-ray free-electron lasers (XFELs) has revolutionized fundamental science, from atomic to condensed matter physics, from chemistry to biology, giving researchers access to X-rays with unprecedented brightness, coherence and pulse duration. All XFEL facilities built until recently provided X-ray pulses at a relatively low repetition rate, with limited data statistics. Here, results from the first megahertz-repetition-rate X-ray scattering experiments at the Spectroscopy and Coherent Scattering (SCS) instrument of the European XFEL are presented. The experimental capabilities that the SCS instrument offers, resulting from the operation at megahertz repetition rates and the availability of the novel DSSC 2D imaging detector, are illustrated. Time-resolved magnetic X-ray scattering and holographic imaging experiments in solid state samples were chosen as representative, providing an ideal test-bed for operation at megahertz rates. Our results are relevant and applicable to any other non-destructive XFEL experiments in the soft X-ray range

Megahertz-rate Ultrafast X-ray Scattering and Holographic Imaging at the European XFEL

13 pages, 5 figures. Supplementary Information as ancillary fileThe advent of X-ray free-electron lasers (XFELs) has revolutionized fundamental science, from atomic to condensed matter physics, from chemistry to biology, giving researchers access to X-rays with unprecedented brightness, coherence, and pulse duration. All XFEL facilities built until recently provided X-ray pulses at a relatively low repetition rate, with limited data statistics. Here, we present the results from the first megahertz repetition rate X-ray scattering experiments at the Spectroscopy and Coherent Scattering (SCS) instrument of the European XFEL. We illustrate the experimental capabilities that the SCS instrument offers, resulting from the operation at MHz repetition rates and the availability of the novel DSSC 2D imaging detector. Time-resolved magnetic X-ray scattering and holographic imaging experiments in solid state samples were chosen as representative, providing an ideal test-bed for operation at megahertz rates. Our results are relevant and applicable to any other non-destructive XFEL experiments in the soft X-ray range