Ultrarelativistic black hole in an external electromagnetic field and gravitational waves in the Melvin universe

We investigate the ultrarelativistic boost of a Schwarzschild black hole immersed in an external electromagnetic field, described by an exact solution of the Einstein-Maxwell equations found by Ernst (the ``Schwarzschild-Melvin'' metric). Following the classical method of Aichelburg and Sexl, the gravitational field generated by a black hole moving ``with the speed of light'' and the transformed electromagnetic field are determined. The corresponding exact solution describes an impulsive gravitational wave propagating in the static, cylindrically symmetric, electrovac universe of Melvin, and for a vanishing electromagnetic field it reduces to the well known Aichelburg-Sexl pp-wave. In the boosting process, the original Petrov type I of the Schwarzschild-Melvin solution simplifies to the type II on the impulse, and to the type D elsewhere. The geometry of the wave front is studied, in particular its non-constant Gauss curvature. In addition, a more general class of impulsive waves in the Melvin universe is constructed by means of a six-dimensional embedding formalism adapted to the background. A coordinate system is also presented in which all the impulsive metrics take a continuous form. Finally, it is shown that these solutions are a limiting case of a family of exact gravitational waves with an arbitrary profile. This family is identified with a solution previously found by Garfinkle and Melvin. We thus complement their analysis, in particular demonstrating that such spacetimes are of type II and belong to the Kundt class.Comment: 11 pages, REVTeX

True substrates: The exceptional resolution and unexceptional preservation of deep time snapshots on bedding surfaces

Abstract: Rock outcrops of the sedimentary–stratigraphic record often reveal bedding planes that can be considered to be true substrates: preserved surfaces that demonstrably existed at the sediment–water or sediment–air interface at the time of deposition. These surfaces have high value as repositories of palaeoenvironmental information, revealing fossilized snapshots of microscale topography from deep time. Some true substrates are notable for their sedimentary, palaeontological and ichnological signatures that provide windows into key intervals of Earth history, but countless others occur routinely throughout the sedimentary–stratigraphic record. They frequently reveal patterns that are strikingly familiar from modern sedimentary environments, such as ripple marks, animal trackways, raindrop impressions or mudcracks: all phenomena that are apparently ephemeral in modern settings, and which form on recognizably human timescales. This paper sets out to explain why these short‐term, transient, small‐scale features are counter‐intuitively abundant within a 3.8 billion year‐long sedimentary–stratigraphic record that is known to be inherently time‐incomplete. True substrates are fundamentally related to a state of stasis in ancient sedimentation systems, and distinguishable from other types of bedding surfaces that formed from a dominance of states of deposition or erosion. Stasis is shown to play a key role in both their formation and preservation, rendering them faithful and valuable archives of palaeoenvironmental and temporal information. Further, the intersection between the time–length scale of their formative processes and outcrop expressions can be used to explain why they are so frequently encountered in outcrop investigations. Explaining true substrates as inevitable and unexceptional by‐products of the accrual of the sedimentary–stratigraphic record should shift perspectives on what can be understood about Earth history from field studies of the sedimentary–stratigraphic record. They should be recognized as providing high‐definition information about the mundane day to day operation of ancient environments, and critically assuage the argument that the incomplete sedimentary–stratigraphic record is unrepresentative of the geological past