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 = +∞.     

The massive scalar field in a closed Friedmann universe model — new rigorous results

For the minimally coupled scalar field in Einstein's theory of gravitation we look for the space of solutions within the class of closed Friedmann universe models. We prove D ≥ 1, where D ≥ is the dimension of the set of solutions which can be integrated up to t → ∞ (D > 0 was conjectured by PAGE (1984)). We discuss concepts like “the probability of the appearance of a sufficiently long inflationary phase” and argue that it is primarily a probability measure μ in the space V of solutions (and not in the space of initial conditions) which has to be applied. μ is naturally defined for Bianchi-type I cosmological models because V is a compact cube. The problems with the closed Friedmann model (which led to controversial claims in the literature) will be shown to originate from the fact that V has a complicated non-compact non-Hausdorff Geroch topology: no natural definition of μ can be given. We conclude: the present state of our universe can be explained by models of the type discussed, but thereby the anthropic principle cannot be fully circumvented.     

TTG-type plutonic rocks formed in a modern arc batholith by hydrous fractionation in the lower arc crust

We present the geochemistry and intrusion pressures of granitoids from the Kohistan batholith, which represents, together with the intruded volcanic and sedimentary units, the middle and upper arc crust of the Kohistan paleo-island arc. Based on Al-in-hornblende barometry, the batholith records intrusion pressures from ~0.2 GPa in the north (where the volcano-sedimentary cover is intruded) to max. ~0.9 GPa in the southeast. The Al-in-hornblende barometry demonstrates that the Kohistan batholith represents a complete cross section across an arc batholith, reaching from the top at ~8–9 km depth (north) to its bottom at 25–35 km (south-central to southeast). Despite the complete outcropping and accessibility of the entire batholith, there is no observable compositional stratification across the batholith. The geochemical characteristics of the granitoids define three groups. Group 1 is characterized by strongly enriched incompatible elements and unfractionated middle rare earth elements (MREE)/heavy rare earth element patterns (HREE); Group 2 has enriched incompatible element concentrations similar to Group 1 but strongly fractionated MREE/HREE. Group 3 is characterized by only a limited incompatible element enrichment and unfractionated MREE/HREE. The origin of the different groups can be modeled through a relatively hydrous (Group 1 and 2) and of a less hydrous (Group 3) fractional crystallization line from a primitive basaltic parent at different pressures. Appropriate mafic/ultramafic cumulates that explain the chemical characteristics of each group are preserved at the base of the arc. The Kohistan batholith strengthens the conclusion that hydrous fractionation is the most important mechanism to form volumetrically significant amounts of granitoids in arcs. The Kohistan Group 2 granitoids have essentially identical trace element characteristics as Archean tonalite–trondhjemite–granodiorite (TTG) suites. Based on these observations, it is most likely that similar to the Group 2 rocks in the Kohistan arc, TTG gneisses were to a large part formed by hydrous high-pressure differentiation of primitive arc magmas in subduction zones.     

Rare earth element distribution in >400 °C hot hydrothermal fluids from 5°S, MAR: The role of anhydrite in controlling highly variable distribution patterns

Two submarine hydrothermal vent fields at 5°S, Mid-Atlantic Ridge (MAR) - Turtle Pits and Comfortless Cove - emanate vapor-phase fluids at conditions close to the critical point of seawater (407 °C, 298 bars). In this study, the concentration and distribution of rare earth element (REE) and yttrium (Y) has been investigated. Independent of the major element composition, the fluids display a strong temporal variability of their REE + Y concentrations and relative distributions at different time scales of minutes to years. Chondrite-normalized distributions range from common fluid patterns with light REE enrichment relative to the heavy REE, accompanied by positive Eu anomalies (type I), to strongly REE + Y enriched patterns with a concave-downward distribution with a maximum enrichment of Sm and weakly positive or even negative Eu anomalies (type II). The larger the sum of REE, the smaller Ce_CN/Yb_CN and Eu/Eu∗. We also observed a strong variability in fluid flow and changing fluid temperatures, correlating with the compositional variability.As evident by the positive correlation of total REE, Ca, and Sr concentrations in Turtle Pits and Comfortless Cove fluids, precipitation/dissolution of hydrothermal anhydrite controls the variability in REE concentrations and distributions in these fluids and the transformation of one fluid type to the other. The variable distribution of REE can be explained by the accumulation of particulate anhydrite (with concave-downward REE distribution and negative Eu anomaly) into a fluid with common REE distribution (type I), followed by the modification of the REE fluid signature due to dissolution of incorporated anhydrite. A second model, in which the type II fluids represent a primary REE reaction zone fluid pattern, which is variably modified by precipitation of anhydrite, can also explain the observed correlations of total REE, fractionation of LREE/HREE and size of Eu anomaly as well as Ca, Sr. The emanation of such a fluid may be favored in a young hydrothermal system in its high-activity phase with short migration paths and limited exchange with secondary minerals. However, this model is not as well constrained as the other and requires further investigations.The strongly variable REE fluid signature is restricted to the very hot, actively phase-separating hydrothermal systems Turtle Pits and Comfortless Cove at 5°S and has not been observed at the neighboring Red Lion vent field, which continuously emanates 350 °C hot fluid and displays a stable REE distribution (type I).     

Pb/Pb age determinations on the Newania and Sevattur carbonatites of India: evidence for multi-stage histories

The ages of Indian carbonatites are still controversial. Most of the earlier datings were done by K/Ar methods. We therefore analysed Pb/Pb ratios in carbonatites from carbonatite-alkalic complexes of Newania (NW India, Rajasthan State) and Sevattur (SW India, Tamil Nadu State) to constrain the age and geological history of these rocks. Newania carbonatites are intrusive into Precambrian Untala granite-gneiss and mainly dolomitic in composition (rauhaugite) followed by a later phase of ankerite carbonatite, while thin calcite carbonatite (sövite) dykelets are the youngest in the sequence. The analysed whole-rock samples are characterised by ²⁰⁶Pb/²⁰⁴Pb ratios between 60 and 176 and ²⁰⁷Pb/²⁰⁴Pb ratios between 22 and 40, which are extremely high in comparison to common igneous rocks and even for carbonatite compositions. One sample, New 37, shows the extreme ratios of ²⁰⁶Pb/²⁰⁴Pb = 574 and ²⁰⁷Pb/²⁰⁴Pb = 73. This requires a μ-value of about 2000 for the last 1550 Ma. If the samples are classified according to their petrographic/geochemical characteristics this results in an isochron age of 1551 ± 46 Ma for the ankerite carbonatites (six samples). The dolomites (6 samples) yield an isochron age of 2.27 Ga. Although these results fit quite well into the geological evolution scheme of the area, the extreme long age hiatus between dolomite carbonatite and ferrocarbonatite formation events raises severe problems for their petrologic interpretation.

The Proterozoic Sevattur carbonatite complex (SCC, Tamil Nadu) was emplaced contemporaneously with a large number of carbonatite complexes within the Precambrian gneissic terrane of the Eastern Ghats Mobile Belt. The main mass is composed of dolomite carbonatite (rauhaugite) with a few dikes of calcite carbonatite (sövite) and ankerite carbonatite within it. All eight samples together yield an isochron of 805 ± 10 Ma. This isochron is mainly determined on ankerite carbonatites with μ-values up to 1900 for the last 800 Ma. Taking only ankerite carbonatites into account, the resulting age is 801 ± 11 Ma. The ²⁰⁶Pb/²⁰⁴Pb and ²⁰⁷Pb/²⁰⁴Pb ratios of these samples are similar to the main group of Newania and far beyond the isotopic composition of common igneous rocks.

Our investigations show that in carbonatitic rock systems extremely high lead isotopic ratios can be established due to the crystallization of uranium-rich mineral phases. In both cases the observed high to extremely high initial Pb isotope ratios require the residence of the lead in intermediate high-μ reservoirs either within the upper mantle or the crust prior to the carbonatite formation. A high-temperature event, which completely reset the Rb/Sr and K/Ar isotopic systems of Nevania carbonatites, seems to have no influence on the lead isotopic systematics.     

Evaluation of drainage networks under moving storms utilizing the equivalent stationary storms

This paper investigates the effect of rainstorm movement on the peak discharge response (PDR) of drainage networks by comparing it with the corresponding equivalent stationary and uniform rainfall. A synthetic circular watershed is introduced to avoid biases from interaction between catchment geometry and storm orientation. The drainage network of the watershed is simulated by the Gibbsian model to examine the effect of network configuration on the peak response depending on the storm kinematics. This study utilizes two types of the equivalent stationary storm (ESS): the average rainfall intensity over the entire catchment (ESSAV) and the point stationary rainfall intensity (ESSQ) to evaluate the effect of moving rainstorms in terms of the PDR. The results show that there exists an interval in which the same rainfall duration produces higher peak responses for moving storms compared with ESSQ. The augmentation of the peak response by moving rainstorm is dependent on the relative rainstorm speed, size, and direction as well as drainage network configuration of the catchment; especially, the results show that a less efficient network tends to mitigate the effect of rainstorm movement on peak response. In contrast, a more efficient network is more sensitive to storm kinematics and the peak response increases compared with ESS. Therefore, the results in this study imply a potential improvement in urban drainage networks in terms of efficiency as well as safety to moving rainstorms. Also, this study suggests the range of variation in peak flows due to storm kinematics compared with the ESS, which can be a reference to the current design practices.