Singularitäten in der Allgemeinen Relativitätstheorie

“Regular solutions of EINSTEIN 's equations” mean very different things. In the case of the empty-space equations, R_ik = 0, such solutions must be metrics g_ik(x^l) without additionaly singular “field sources” (EINSTEIN 's “Particle problem”). – However the “phenomenological matter” is defined by the EINSTEIN equations R_ik – 1/2g_ikR =–xT_ik itselves. Therefore if 10 regular functions g_ik(x^l) are given (which the inequalities of LORENTZ -signature fulfil) then these g_ik define 10 functions T_ik(x^l) without singularities. But, the matter-tensor T_ik must fulfil the two inequalities T ≥ 0, T ≥ 1/2 T only and therefore the EINSTEIN -equations with “phenomenological matter” mean the two inequalities R ≥ 0, R ≤ 0 which are incompatible with a permanently regular metric with LORENTZ -signature, generally.     

Die post-NEWTONschen Effekte in der Gravodynamik und die EINSTEIN-Effekte in der Allgemeinen Relativitätstheorie

We discuss the post-NEWTON ian effects in our HERTZ ian gravodynamics and compare its values with the EINSTEIN effects in GRT. Generally, our gravodynamics gives quite the same values of the post-NEWTON ian effects in celestial mechanics and in the gravo-optics like in GRT. However, these values are defined by measurement operations which have quite different meanings in gravodynamics and in GRT. P.e., the RIEMANN ian curvature of the three-dimensional space which is resulting in gravodynamics according to the MACH -EINSTEIN doctrine becomes bigger by a factor 3/2 than the curvature resulting by the EINSTEIN equations. — GRT and gravodynamics are congruent in reference to the astronomical fundamental system. This consequence defines the fundamental system according to MACH 's principle.     

Zur dynamischen Äquivalenz der post-NEWTONSCHEN Näherung für die Planetentheorie in der allgemeinen Relativitätstheorie und in der trägheitsfreien Mechanik mit RIEMANNSchem Gravitationspotential

Proof of the dynamical equivalence of the post-NEWTONian approximations for the LAGRANGAIN representations of planetary motions according to GRT and according to our “RIEMANNian dynamics with MACH EINSTEIN doctrine”. Finally, we discuss the equivalence problem for general post-NEWTONian LAGRANGians of the one-body Problem in celestical mechanics.     

Eigenschaften singularitätenfreier,statischer, zentralsymmetrischer Lösungen gewisser Gravitationsfeldgleichungen 4. Ordnung

FIEDLER and SCHIMMING (1983) proved that the fourth order gravitational field equations with a linear combination of Bach's and Einstein's tensors on the left-hand side, which were proposed by TREDER , admit static centrally symmetric solutions which are analytical and non-flat in some neighbourhood of the centre of symmetry. The existence of these solutions, known at first only in a small neighbourhood of r = o (r radius), can now be extended to intervals o ≦ r ≦ α with arbitrarily large α , using the abstract theorem on inverse functions. Further it is proved that the Schwarzschild metrics are in a certain sense the only solutions of the above equations that are analytic, asymptotically flat, static and centrally symmetric around r = +∞.     

40Ar-39Ar ages of Dellen,Jänisjärvi,and Sääksjärvi impact craters

Abstract— ⁴⁰Ar-³⁹Ar age measurements were made for three whole rock melt samples produced during impact events which formed the Dellen, Jänisjärvi, and Sääksjärvi craters on the Baltic Shield. An age of 109.6 ± 1.0 Ma was obtained for the Dellen sample based on an age spectrum plateau. The age spectrum shows a small (7%) loss of radiogenic ⁴⁰Ar from low temperature fractions. Ages of 698 ± 22 Ma and 560 ± 12 Ma were obtained from isochrons for the Jänisjärvi and Sääksjärvi samples, respectively. Data obtained by laser degassing support the Sääksjärvi result. The presence of excess ⁴⁰Ar is indicated in lower temperature fractions for both samples and is correlated with K concentrations in the Sääksjärvi sample. Models explaining these results may require a change in the local “atmospheric” Ar isotopic composition as cooling of melt rocks proceeded. However, it cannot be excluded that devitrification and/or alteration changed the Ar budget. A crater production rate on the Baltic Shield based on measured ages of 6 craters is (0.3 ± 0.2) · 10^?14 20-km-and-larger craters per km² per year, in satisfactory agreement with previous estimates.     

Agate as an indicator of impact structures: An example from Sääksjärvi,Finland

Abstract— Mineralogical, petrographical and chemical determinations were made for 743 agate (banded variety of chalcedonic quartz) nodules (diameters from 5 mm to 5 cm) formed during postimpact, low-temperature hydrothermal activity as vesicle fillings in the melt rocks of the Sääksjärvi meteorite impact structure (diameter 5 km) in southwest Finland. Other hydrothermal vesicle fillings in the impact melt rocks include chlorite, mordenite, smectite and kaolinite. The agates were classified into two types, whose mineralogical properties and chemical compositions fall within the range of volcanic agates (basaltic and rhyolitic host rocks). The relatively high age (～510 Ma) of the Sääksjärvi impact melt rocks, however, is reflected by the presence of recrystallization textures, which are rare in younger volcanic agates. The Sääksjärvi structure was initially located after following the fortuitous discovery of agate “path-finders” in the glacial overburden. It is recommended that wherever volcanic type agates are found as float in Precambrian shield areas devoid of younger volcanic rocks, the possible presence of impact (or volcanic) craters in the vicinity should be considered.     

The Colônia structure,São Paulo,Brazil

Abstract– The near‐circular Colônia structure, located in the southern suburbs of the mega‐city of São Paulo, Brazil, has attracted the attention of geoscientists for several decades due to its anomalous character and the complete absence of any plausible endogenous geologic explanation for its formation. Origin by impact cratering has been suggested repeatedly since the 1960s, but no direct evidence for this has been presented to date. New seismic data have been recently acquired at Colônia, providing new insights into the characteristics and possible layering of infill of the structure, as well as into the depth to the underlying basement. We review the current knowledge about the Colônia structure, present the new seismic data, and discuss the existing—as yet still indirect—evidence for a possible origin by an impact. The new data suggest the existence of a sedimentary fill of approximately 275 m thickness and also the presence of two intermediate zones between sediment and basement: an upper zone that is approximately 65 m thick and can be interpreted as a possible crater‐fill breccia, whereas the other zone possibly represents fractured/brecciated basement, with a thickness of approximately 50 m. Although this depth to basement seems to be inconsistent with the expected geometry of a simple, bowl‐shape impact structure of such diameter, there are a number of still unconstrained parameters that could explain this, such as projectile nature, size and velocity, impact angle, and particularly the current erosion depth.     

Paleomagnetism and petrophysics of the Jänisjärvi impact structure,Russian Karelia

Abstract— Paleomagnetic, rock magnetic, and petrophysical results are presented for impactites and target rocks from the Lake Jänisjärvi impact structure, Russian Karelia. The impactites (tagamites, suevites, and lithic breccias) are characterized by increased porosity and magnetization, which is in agreement with observations performed at other impact structures. Thermomagnetic, hysteresis, and scanning electron microscope (SEM) analysis document the presence of primary multidomain titanomagnetite with additional secondary titanomaghemite and ilmenohematite. The characteristic impact‐related remanent magnetization (ChRM) direction (D = 101.5°, I = 73.1°, α₉₅ = 6.2°) yields a pole (Lat. = 45.0°N, Long. = 76.9°E, dp = 9.9°, dm = 11.0°). Additionally, the same component is observed as an overprint on some rocks located in the vicinity of the structure, which provides proofs of its primary origin. An attempt was made to determine the ancient geomagnetic field intensity. Seven reliable results were obtained, yielding an ancient intensity of 68.7 ± 7.6 μT (corresponding to VDM of 10.3 ± 1.1 times 10²² Am²). The intensity, however, appears to be biased toward high values mainly because of the concave shape of the Arai diagrams. The new paleomagnetic data and published isotopic ages for the structure are in disagreement. According to well‐defined paleomagnetic data, two possible ages for magnetization of Jänisjärvi rocks exist: 1) Late Sveconorwegian age (900–850 Myr) or 2) Late Cambrian age (?500 Myr). However, published isotopic ages are 718 ± 5 Myr (K‐Ar) and 698 ± 22 Myr (³⁹Ar‐⁴⁰Ar), but such isotopic dating methods are often ambiguous for the impactites.     

Zur Dynamotheorie kosmischer Magnetfelder. I. Gleichungen für sphärische Dynamomodelle

This paper deals with the mathematical treatment of special models of hydromagnetic dynamos. For the models considered here the conducting medium occupies a spherical region surrounded by vacuum. Both laminar and turbulent dynamos are included. The partial vector differential equations governing the models are transformed into an infinite set of differential equations for scalar functions by applying a method previously used by BULLARD and GELLMAN and on the basis of a representation of vector fields as a sum of a poloidal and a toroidal part. The scalar functions depend only on a radial coordinate and possibly on the time. In both the stationary and the periodic case, an infinite set of ordinary differential equations results which may be treated numerically. A series of relations for computing various dynamo models is prepared.     

Über die Möglichkeit,die Temperaturverteilung in Sonnenflecken durch einen anisotropen Wärmetransport zu erklären

Numerical solutions of a heat conduction problem in an anisotropic medium are used for a discussion of the possibility to explain the temperature distribution in sunspots and their environment. The anisotropy is assumed being due to the strong magnetic field in sunspots and the region below. This magnetic field forces the convection to take an anisotropic structure (two-dimensional turbulence) and thus the region gets anisotropic conduction properties, on the average. The discussion shows that the observed temperature profiles can be explained in case the depth of the region of anisotropy is about as large as the diameter of the spot or larger.     

The Suavjärvi impact structure,NW Russia

Abstract– We present the geology and interpreted shock features of the Suavjärvi circular structure. Suavjärvi is a circular feature (illustrated by satellite imagery, topography, and magnetic data) located in the central part of the Karelian Craton (lat. 63°07′N, long. 33°23′E). To date, little information on the geologic and impact features of the Suavjärvi structure is available in the literature. The structure is characterized by gravity and magnetic lows and disruption of the regional magnetic fabric. In the northeastern and southwestern parts of the structure, several erosional remnants of highly disturbed rocks occur referred to as monomict and polymict megabreccia. These comprise blocks of both basement granitoids and supracrustal greenstone rocks. The impact origin of polymict megabreccia and therefore of the Suavjärvi structure is confirmed by observations of closely spaced planar microstructures at angles consistent with planes that have Miller indices indicative of impact shock effects, mostly of ω{10¯13}. The Suavjärvi is considered to be a remnant of a deeply eroded and metamorphosed impact structure, which has a diameter of 16 km and was formed during the Paleoproterozoic (older than 2.2 Ga); this is inferred from the age of the overlying volcanic‐sedimentary Jatulian sequence. Suavjärvi underwent regional metamorphism that resulted in obliteration or transformation of shock metamorphic effects. Massive sulfides occur within megabreccia; originating probably from postimpact redeposition of pre‐existing mineralization.