Exact solutions in Einstein's theory and beyond

In this thesis we present exact solutions of geometrical theories of gravity, i.e. those of a general relativistic type. In chapter 1, we give a short introduction into the calculus of exterior differential forms, introduce the Cotton 2-form, and investigate its properties (irreducible decomposition, number of independent components, conformal transformation, classification in three dimensions, analytic properties). In view of covariantly conserved quantities, we investigate the relation between the Cotton 2-form, the Bach 3-form, and the Chevreton tensor (a superenergy tensor of the electromagnetic field). Chapter 2 is devoted to gravity in three dimensions. For a model of Mielke and Baekler (MB), we find an exact BTZ-like solution with constant axial torsion. We determine its autoparallels, extremals, Killing vectors, and global charges. Furthermore, we derive from the MB-model a teleparallelism model, Einstein-Cartan theory, and topologically massive gravity. We show how the BTZ-solution with torsion reduces to solutions of the aforementioned subcases. In conclusion we construct a new perfect fluid solution of Einstein's field equation in three dimensions. In the last chapter we turn to four-dimensional metric-affine gravity. We devise a model which allows for the breaking of Lorentz invariance by means of a vector-like quantity (aether). Therefore we take a vector-piece of the nonmetricity. We set up a Lagrangian and derive the field equations. Constraints on the coupling parameters simplify the field equations considerably. We arrive at a quasi-Einstein equation and a wave equation for the aether field. Finally, we discuss a simple solution of this model found by Baekler

Heat Load-Induced Changes in Lying Behavior and Lying Cubicle Occupancy of Lactating Dairy Cows in a Naturally Ventilated Barn

Dairy cows show a high sensitivity to changes in barn climate, which can result in physiological and ethological responses because of the homeostatic mechanisms to regulate the body temperature under heat load. The objective of this study was to analyze the lying behavior and occupancy of lying cubicles of lactating high-yielding Holstein-Friesian cows throughout the day during three summer months and three winter months. The study was conducted in summer 2016 and in winter 2016/17 in a naturally ventilated barn in Brandenburg, Germany. The determined temperaturehumidity index (THI) of the barn was calculated using the measured ambient temperature and relative humidity at eight locations inside the barn. The THI was used to define the heat load the cows were exposed to. The activity of the cows was measured with accelerometers, and a video recording was made to analyze the occupancy of the three rows of lying cubicles. The results indicated that increasing heat load led to a decrease in lying time; therefore, the daily lying time differed between summer and winter months. In addition, there were different patterns of lying behavior during the course of the day, depending on the season. A sharp decline in lying time could be observed especially in the afternoon hours during the summer. The occupancy of lying cubicles was also influenced by the heat load. The data could be helpful to enable evaluation with algorithms for early detection of heat load

The Einstein 3-form G_a and its equivalent 1-form L_a in Riemann-Cartan space

The definition of the Einstein 3-form G_a is motivated by means of the contracted 2nd Bianchi identity. This definition involves at first the complete curvature 2-form. The 1-form L_a is defined via G_a = L^b \wedge #(o_b \wedge o_a). Here # denotes the Hodge-star, o_a the coframe, and \wedge the exterior product. The L_a is equivalent to the Einstein 3-form and represents a certain contraction of the curvature 2-form. A variational formula of Salgado on quadratic invariants of the L_a 1-form is discussed, generalized, and put into proper perspective.Comment: LaTeX, 13 Pages. To appear in Gen. Rel. Gra

Einstein-aether theory, violation of Lorentz invariance, and metric-affine gravity

We show that the Einstein-aether theory of Jacobson and Mattingly (J&M) can be understood in the framework of the metric-affine (gauge theory of) gravity (MAG). We achieve this by relating the aether vector field of J&M to certain post-Riemannian nonmetricity pieces contained in an independent linear connection of spacetime. Then, for the aether, a corresponding geometrical curvature-square Lagrangian with a massive piece can be formulated straightforwardly. We find an exact spherically symmetric solution of our model.Comment: Revtex4, 38 pages, 1 figur

The Cotton tensor in Riemannian spacetimes

Recently, the study of three-dimensional spaces is becoming of great interest. In these dimensions the Cotton tensor is prominent as the substitute for the Weyl tensor. It is conformally invariant and its vanishing is equivalent to conformal flatness. However, the Cotton tensor arises in the context of the Bianchi identities and is present in any dimension. We present a systematic derivation of the Cotton tensor. We perform its irreducible decomposition and determine its number of independent components for the first time. Subsequently, we exhibit its characteristic properties and perform a classification of the Cotton tensor in three dimensions. We investigate some solutions of Einstein's field equations in three dimensions and of the topologically massive gravity model of Deser, Jackiw, and Templeton. For each class examples are given. Finally we investigate the relation between the Cotton tensor and the energy-momentum in Einstein's theory and derive a conformally flat perfect fluid solution of Einstein's field equations in three dimensions.Comment: 27 pages, revtex

Come, tell me how you live: Habitat suitability analysis for Ostrea edulis restoration

Against the background of the UN decade on ecosystem restoration and the new EU Biodiversity Strategy for 2030, and in the context of marine spatial planning and complex maritime user conflicts, reliable information on habitat suitability for large-scale restoration is an important prerequisite for implementing conservation management and for supporting successful, sustainable, and ecologically efficient restoration measures. In this study, habitat suitability was assessed using multicriteria decision analysis (MCDA) for the restoration of the European oyster, Ostrea edulis, in marine protected areas (MPAs) of the German Bight in the North Sea: Borkum Reef Ground (Borkum Riffgrund, BRG) and Sylt Outer Reef – Eastern German Bight (Sylter Außenriff, SAR). Based on site selection criteria, exclusion and suitability factors for the MCDA were defined. Results were integrated with the available geodata to produce habitat suitability maps for oyster restoration in the area of interest. Suitable as well as unsuitable habitats have been successfully identified for both MPAs: several hundred square kilometres (≥97.2% of BRG) or several thousand square kilometres (≥74.5% of SAR) were classified as ecologically and logistically suitable for oyster restoration measures in the respective MPAs. As oyster restoration is significantly limited by human activities (e.g. bottom trawl fisheries), the management of fisheries is an important prerequisite for successful oyster restoration in both MPAs. Results show that designated fishery management measures will increase the possibilities for oyster restoration. In BRG, our results correspond to the known historical distribution. In SAR, our results significantly exceed the historically known distribution. The habitat suitability analysis will facilitate decision-making regarding ocean use, and will reduce restoration costs through targeted management activities in areas of high suitability and expand species recovery by improving the survival of reintroduced individuals. The habitat suitability analysis procedure is easily adaptable for application to other areas, other species, or other habitat restoration projects, or to other conservation management settings. The software applied is open source and the suitability calculation is described in detail to inform wider applications

Photography-based taxonomy is inadequate, unnecessary, and potentially harmful for biological sciences

The question whether taxonomic descriptions naming new animal species without type specimen(s) deposited in collections should be accepted for publication by scientific journals and allowed by the Code has already been discussed in Zootaxa (Dubois & Nemésio 2007; Donegan 2008, 2009; Nemésio 2009a–b; Dubois 2009; Gentile & Snell 2009; Minelli 2009; Cianferoni & Bartolozzi 2016; Amorim et al. 2016). This question was again raised in a letter supported by 35 signatories published in the journal Nature (Pape et al. 2016) on 15 September 2016. On 25 September 2016, the following rebuttal (strictly limited to 300 words as per the editorial rules of Nature) was submitted to Nature, which on 18 October 2016 refused to publish it. As we think this problem is a very important one for zoological taxonomy, this text is published here exactly as submitted to Nature, followed by the list of the 493 taxonomists and collection-based researchers who signed it in the short time span from 20 September to 6 October 2016