Special Einstein's equations on K\"ahler manifolds

This work is devoted to the study of Einstein equations with a special shape of the energy-momentum tensor. Our results continue Stepanov's classification of Riemannian manifolds according to special properties of the energy-momentum tensor to K\"ahler manifolds. We show that in this case the number of classes reduces.Comment: 5 page

Paired accelerated arames: The perfect interferometer with everywhere smooth wave amplitudes

Rindler's acceleration-induced partitioning of spacetime leads to a nature-given interferometer. It accomodates quantum mechanical and wave mechanical processes in spacetime which in (Euclidean) optics correspond to wave processes in a ``Mach-Zehnder'' interferometer: amplitude splitting, reflection, and interference. These processes are described in terms of amplitudes which behave smoothly across the event horizons of all four Rindler sectors. In this context there arises quite naturally a complete set of orthonormal wave packet histories, one of whose key properties is their "explosivity index". In the limit of low index values the wave packets trace out fuzzy world lines. By contrast, in the asymptotic limit of high index values, there are no world lines, not even fuzzy ones. Instead, the wave packet histories are those of entities with non-trivial internal collapse and explosion dynamics. Their details are described by the wave processes in the above-mentioned Mach-Zehnder interferometer. Each one of them is a double slit interference process. These wave processes are applied to elucidate the amplification of waves in an accelerated inhomogeneous dielectric. Also discussed are the properties and relationships among the transition amplitudes of an accelerated finite-time detector.Comment: 38 pages, RevTex, 10 figures, 4 mathematical tutorials. Html version of the figures and of related papers available at http://www.math.ohio-state.edu/~gerlac

Interaction of Hawking radiation with static sources outside a Schwarzschild black hole

We show that the response rate of (i) a static source interacting with Hawking radiation of massless scalar field in Schwarzschild spacetime (with the Unruh vacuum) and that of (ii) a uniformly accelerated source with the same proper acceleration in Minkowski spacetime (with the Minkowski vacuum) are equal. We show that this equality will not hold if the Unruh vacuum is replaced by the Hartle-Hawking vacuum. It is verified that the source responds to the Hawking radiation near the horizon as if it were at rest in a thermal bath in Minkowski spacetime with the same temperature. It is also verified that the response rate in the Hartle-Hawking vacuum approaches that in Minkowski spacetime with the same temperature far away from the black hole. Finally, we compare our results with others in the literature.Comment: 18 pages (REVTEX

A massive, Late Neolithic pit structure associated with Durrington Walls Henge

YesA series of massive geophysical anomalies, located south of the Durrington Walls henge monument, were identified during fluxgate gradiometer survey undertaken by the Stonehenge Hidden Landscapes Project (SHLP). Initially interpreted as dewponds, these data have been re-evaluated, along with information on similar features revealed by archaeological contractors undertaking survey and excavation to the north of the Durrington Walls henge. Analysis of the available data identified a total of 20 comparable features, which align within a series of arcs adjacent to Durrington Walls. Further geophysical survey, supported by mechanical coring, was undertaken on several geophysical anomalies to assess their nature, and to provide dating and environmental evidence. The results of fieldwork demonstrate that some of these features, at least, were massive, circular pits with a surface diameter of 20m or more and a depth of at least 5m. Struck flint and bone were recovered from primary silts and radiocarbon dating indicates a Late Neolithic date for the lower silts of one pit. The degree of similarity across the 20 features identified suggests that they could have formed part of a circuit of large pits around Durrington Walls, and this may also have incorporated the recently discovered Larkhill causewayed enclosure. The diameter of the circuit of pits exceeds 2km and there is some evidence that an intermittent, inner post alignment may have existed within the circuit of pits. One pit may provide evidence for a recut; suggesting that some of these features could have been maintained through to the Middle Bronze Age. Together, these features represent a unique group of features related to the henge at Durrington Walls, executed at a scale not previously recorded.The University of Bradford Research Development Fund and the University of St Andrews funded this open access publication.Supplementary data can be found at https://intarch.ac.uk/journal/issue55/4/supp-text.htm

Loop Quantum Cosmology

Quantum gravity is expected to be necessary in order to understand situations where classical general relativity breaks down. In particular in cosmology one has to deal with initial singularities, i.e. the fact that the backward evolution of a classical space-time inevitably comes to an end after a finite amount of proper time. This presents a breakdown of the classical picture and requires an extended theory for a meaningful description. Since small length scales and high curvatures are involved, quantum effects must play a role. Not only the singularity itself but also the surrounding space-time is then modified. One particular realization is loop quantum cosmology, an application of loop quantum gravity to homogeneous systems, which removes classical singularities. Its implications can be studied at different levels. Main effects are introduced into effective classical equations which allow to avoid interpretational problems of quantum theory. They give rise to new kinds of early universe phenomenology with applications to inflation and cyclic models. To resolve classical singularities and to understand the structure of geometry around them, the quantum description is necessary. Classical evolution is then replaced by a difference equation for a wave function which allows to extend space-time beyond classical singularities. One main question is how these homogeneous scenarios are related to full loop quantum gravity, which can be dealt with at the level of distributional symmetric states. Finally, the new structure of space-time arising in loop quantum gravity and its application to cosmology sheds new light on more general issues such as time.Comment: 104 pages, 10 figures; online version, containing 6 movies, available at http://relativity.livingreviews.org/Articles/lrr-2005-11