Petrov type D equation on horizons of nontrivial bundle topology

We consider $3$-dimensional isolated horizons (IHs) generated by null curves that form nontrivial $U(1)$ bundles. We find a natural interplay between the IH geometry and the $U(1)$-bundle geometry. In this context we consider the Petrov type D equation introduced and studied in previous works \cite{DLP1,DLP2,LS,DKLS1}. From the $4$-dimensional spacetime point of view, solutions to that equation define isolated horizons embeddable in vacuum spacetimes (with cosmological constant) as Killing horizons to the second order such that the spacetime Weyl tensor at the horizon is of the Petrov type D. From the point of view of the $U(1)$-bundle structure, the equation couples a $U(1)$-connection, a metric tensor defined on the base manifold and the surface gravity in a very nontrivial way. We focus on the $U(1)$-bundles over $2$-dimensional manifolds diffeomorphic to $2$-sphere. We have derived all the axisymmetric solutions to the Petrov type D equation. For a fixed value of the cosmological constant they set a $3$-dimensional family as one could expect. A surprising result is, that generically our horizons are not embeddable in the known exact solutions to Einstein's equations. It means that among the exact type D spacetimes there exists a new family of spacetimes that generalize the properties of the Kerr- (anti) de Sitter black holes on one hand and the Taub-NUT spacetimes on the other hand

Was the religious manichaean narrative a mythical narrative? : some remarks from the perspective of Andrzej Wierciński's definition of myth

Many specialists in Manichaeism wrote after World War II about the religious Manichaean narrative as a myth or a mythology. In this paper I examine whether the Manichaean narrative actually meets the criteria of definition of myth. This question is also worth asking because some scholars emphasise the monosemic character of the mentioned narrative. The definition of myth which I use is that of Andrzej Wierciński (1930-2003), a Polish anthropologist of religion. Among my reasons for choosing this is because it includes as many as nine features of myth and also refers to scientific narrative, which by its nature has one level of meaning. I refer this definition, above all, to Manichaean evidence in the Coptic language, but when the need arises I also invoke other sources, both polemical and apologetic

Das Zeitalter der Knappheit – Ressourcen, Konflikte, Lebenschancen

Michael N. Dobkowski and Isidor Wallimann establish a disturbing but realistic scenario of the disastrous future that awaits humankind as surplus populations collide with dwindling resources. Authors consider a number of cause-and-effect situations on industrialization, biophysical limits, exponential population growth, and genocide, to name a few. This volume is a critical contribution to the field and will serve as an ideal introduction to courses in the environment, population, resources, genocide, and social conflict.https://surface.syr.edu/books/1018/thumbnail.jp

The Coming Age of Scarcity : Preventing Mass Death and Genocide in the Twenty-first Century

The structure of the book is simple. The first part analyzes major forces having an impact on the survivability of civilization as we know it into the twenty-first century. It outlines the challenges we face, including overpopulation, pressure upon the land, migration, ecological damage, and social instability. In part two, we present more detailed discussion of the problem of scarcity and how it relates to conflict. The authors in this section argue that the current level of human activity is unsustain­able. They demonstrate that population growth in particular affects the natural world and can affect the social order and international political systems.The authors in part three go beyond the empirical and theoretical studies of the first two parts to examine how scarcity has already led to mass death and genocide in Rwanda, Bosnia, Somalia, and Haiti and to speculate on the likelihood that scarcities could be a more decisive factor in genocide in the future.https://surface.syr.edu/books/1022/thumbnail.jp

Towards the Holocaust: the social and economic collapse of the Weimar Republic

The social system of Weimar Germany has always been controversial. From the start 1Weimar society was characterized by a peculiar fluidity: between 1913 and 1933, the German Reich, commonly referred to as the Weimar Republic, was a virtual laboratory of sociocultural experimentation. In the streets of German towns and cities, political armies competed for followers--a process punctuated by assassinations and advertised by street battles embroiling monarchists, imperial militarists, nihilistic war veterans, Communists, Socialists, anarchists, and National Socialists. Parliamentary activity involved about twenty-five political parties whose shifting alliances produced twenty governmental cabinets with an average lifespan of less than nine months.https://surface.syr.edu/books/1016/thumbnail.jp

Isolated horizons of the Hopf bundle structure transversal to the null direction, the horizon equations and embeddability in NUT-like spacetimes

Isolated horizons that admit the Hopf bundle structure $H\rightarrow S_2$ are investigated, however the null direction is allowed not to be tangent to the bundle fibres. The geometry of such horizons is characterised by data set on a topological two-dimensional sphere, singular at its poles. The horizon equations induced by Einstein's equations are imposed. The existence of regular extremal horizons satisfying the vacuum (with cosmological constant) equation of extremality, obtained from singular solutions on the sphere is pointed out. All horizons (with assumed topology and in the generic case) satisfying the $\Lambda$ vacuum type D equation are derived. They are compared to the Killing horizons contained in the accelerated Kerr-NUT-(Anti) de Sitter spacetimes. Both families of horizons have the same dimension, but the problem of mutual correspondence needs to be better understood. If the cosmological constant takes special values determined by the other parameters the bundle fibers become tangent to the null direction. As an additional but also important result, spacetimes of the topology $H\times \mathbb{R}$ locally isometric to the accelerated Kerr-NUT-(Anti) de Sitter spacetimes are constructed for every value of the mass, Kerr, NUT parameters, the cosmological constant and the acceleration. When the acceleration parameter is not zero, the conical singularity can be removed whenever the NUT parameter does not vanish either.Comment: 29 pages, typos fixed, version accepted in PR

Scaling and Structural Properties of Juvenile Bull Kelp (Nereocystis luetkeana)

Bull kelp (Nereocystis luetkeana), the only canopy-forming kelp in the Salish Sea, provides primary production in the nearshore subtidal environment and serves as an important habitat for economically and ecologically important species. An annual species, each year juvenile bull kelp sporophytesmust grow fromthe hydrodynamically more benign benthos to the water column, where they experience substantial drag at the surface. Because of the differences in morphology and ecology across life stages, and the fact that previous work has focused mainly on adult bull kelp, we tested whether morphology and structural properties change with stipe length, investigating scaling of both juvenile (stipe length \u3c 40 cm) and mature (stipe length \u3e 40 cm) kelp, and testing how juvenile stipes fail. Juvenile bull kelp grow proportionally (isometric growth) when young, but lengthenmore quickly than would be predicted by bulb size (negative allometry) atmaturity. Based on our data, the predicted breakpoint between isometric and allometric growth occurred at about 33 cm, likely approximately one to two weeks of growth. Cross-sectional area of the stipe, force to failure, work to failure, and stiffness (Young\u27smodulus) all growmore slowly than would be predicted based on length, while maximum stress and toughness increase more quickly than predicted. There is no change in extensibility over the size range we tested, suggesting that this material property does not change with stipe length. The differences in biomechanics between juvenile and adult kelp are likely a response to the varied hydrodynamic environments experienced during the annual life cycle, which highlights the importance of studying organisms across life stages