Kerr-Schild Approach to the Boosted Kerr Solution

Using a complex representation of the Debney-Kerr-Schild (DKS) solutions and the Kerr theorem we analyze the boosted Kerr geometries and give the exact and explicit expressions for the metrics, the principal null congruences, the coordinate systems and the location of the singularities for arbitrary value and orientation of the boost with respect to the angular momentum. In the limiting, ultrarelativistic case we obtain light-like solutions possessing diverging and twisting principal null congruences and having, contrary to the known pp-wave limiting solutions, a non-zero value of the total angular momentum. The implications of the above results in various related fields are discussed.Comment: 16 pages, LaTe

The crustal structure along the POLAR Profile from seismic refraction investigations

Seismic refraction investigations along a 440-km long profije on the northern Baltic Shield have resolved the crustal structure in this area of Archaean to Early Proterozoic lithosphere formation. The profile, called the POLAR Profile, extends approximately along a SW-NE-oriented line from the Karelian Province in northern Finland across the Lapland Granulite Belt and the Kola Peninsula Province to the Varanger Peninsula in northeastern Norway. At six shotpoints, large explosions (200–1680 kg), and at three shotpoints, small explosions (80 kg) were detonated and recorded at an average station spacing of 2 km, providing high-quality record sections. A two-dimensional cross section of the crust was obtained by forward modelling using ray-tracing techniques. High-velocity bodies are found in the upper crust related to the Karasjok-Kittilä Greenstone Belt and the Lapland Granulite Belt. They extend to a depth of 6–13 km. In the Karelian Province in the southwest, a low-velocity zone was found between the depths of 8 and 14 km. The middle crust shows a slight increase in the average velocities from the southwest to the northeast, and a small velocity jump is found along a mid-crustal boundary between 18 and 21 km. The thickness of the middle crust varies between 16 and 18 km. The lower crust and the crust-mantle boundary (Moho) show considerable lateral variation. The top of the lower crust lies between 26 and 33 km, while its thickness decreases from 21 km in the southwest to 10–14 km beneath the Lapland Granulite Belt and the Inari Terrain, reaching 20 km again in the extreme northeast. The velocities also change laterally. The thin lower crust is characterized by rather low velocities (6.8–6.9 km/s), whereas in the southwest and northeast the velocities (6.9–7.3 km/s) resemble more typical shield structures. The Moho is found at 47 km in the Karelian Province, rises to 40 km beneath the Lapland Granulite Belt and descends to 46 km in the northeastern part of the Kola Peninsula Province. The upper mantle velocities at the Moho range from 8.1 km/s in the region of the thin crust, to 8.5 km/s and more beneath the Karelian Province. It is tempting to suggest that the anomalous lower crust underlying the Lapland Granulite Belt and the Inari Terrain may represent the remnants of an Early Proterozoic back-arc basin that was active prior to the 2.0 to 1.9 Ga plate convergence event, during which the Lapland Granulite Belt was thrust onto the Archaean basement of the Karelian Province. Another explanation is to assume that the velocity reduction in the anomalous lower crust was caused by a rather pronounced uplift of this region following the 1.9-Ga collision event