43 research outputs found
Unimodular Gravity and Averaging
The question of the averaging of inhomogeneous spacetimes in cosmology is
important for the correct interpretation of cosmological data. In this paper we
suggest a conceptually simpler approach to averaging in cosmology based on the
averaging of scalars within unimodular gravity. As an illustration, we consider
the example of an exact spherically symmetric dust model, and show that within
this approach averaging introduces correlations (corrections) to the effective
dynamical evolution equation in the form of a spatial curvature term.Comment: 10 page
The Evolution of Black Holes in the Mini-Superspace Approximation of Loop Quantum Gravity
Using the improved quantization technique to the mini-superspace
approximation of loop quantum gravity, we study the evolution of black holes
supported by a cosmological constant. The addition of a cosmological constant
allows for classical solutions with planar, cylindrical, toroidal and higher
genus black holes. Here we study the quantum analog of these space-times. In
all scenarios studied, the singularity present in the classical counter-part is
avoided in the quantized version and is replaced by a bounce, and in the late
evolution, a series of less severe bounces. Interestingly, although there are
differences during the evolution between the various symmetries and topologies,
the evolution on the other side of the bounce asymptotes to space-times of
Nariai-type, with the exception of the planar black hole analyzed here, whose
-=constant subspaces seem to continue expanding in the long term
evolution. For the other cases, Nariai-type universes are attractors in the
quantum evolution, albeit with different parameters. We study here the quantum
evolution of each symmetry in detail.Comment: 26 pages, 7 figures.V2 has typos corrected, references added, and a
more careful analysis of the planar case. Accepted for publication in
Physical Review
Lorentzian manifolds and scalar curvature invariants
We discuss (arbitrary-dimensional) Lorentzian manifolds and the scalar
polynomial curvature invariants constructed from the Riemann tensor and its
covariant derivatives. Recently, we have shown that in four dimensions a
Lorentzian spacetime metric is either -non-degenerate, and hence
locally characterized by its scalar polynomial curvature invariants, or is a
degenerate Kundt spacetime. We present a number of results that generalize
these results to higher dimensions and discuss their consequences and potential
physical applications.Comment: submitted to CQ
General Kundt spacetimes in higher dimensions
We investigate a general metric of the Kundt class of spacetimes in higher
dimensions. Geometrically, it admits a non-twisting, non-shearing and
non-expanding geodesic null congruence. We calculate all components of the
curvature and Ricci tensors, without assuming any specific matter content, and
discuss algebraic types and main geometric constraints imposed by general
Einstein's field equations. We explicitly derive Einstein-Maxwell equations,
including an arbitrary cosmological constant, in the case of vacuum or possibly
an aligned electromagnetic field. Finally, we introduce canonical subclasses of
the Kundt family and we identify the most important special cases, namely
generalised pp-waves, VSI or CSI spacetimes, and gyratons.Comment: 15 page
On the local structure of Lorentzian Einstein manifolds with parallel distribution of null lines
We study transformations of coordinates on a Lorentzian Einstein manifold
with a parallel distribution of null lines and show that the general Walker
coordinates can be simplified. In these coordinates, the full Lorentzian
Einstein equation is reduced to equations on a family of Einstein Riemannian
metrics.Comment: Dedicated to Dmitri Vladimirovich Alekseevsky on his 70th birthda
A spacetime not characterised by its invariants is of aligned type II
By using invariant theory we show that a (higher-dimensional) Lorentzian
metric that is not characterised by its invariants must be of aligned type II;
i.e., there exists a frame such that all the curvature tensors are
simultaneously of type II. This implies, using the boost-weight decomposition,
that for such a metric there exists a frame such that all positive boost-weight
components are zero. Indeed, we show a more general result, namely that any set
of tensors which is not characterised by its invariants, must be of aligned
type II. This result enables us to prove a number of related results, among
them the algebraic VSI conjecture.Comment: 14pages, CQG to appea
Holonomy of Einstein Lorentzian manifolds
The classification of all possible holonomy algebras of Einstein and vacuum
Einstein Lorentzian manifolds is obtained. It is shown that each such algebra
appears as the holonomy algebra of an Einstein (resp., vacuum Einstein)
Lorentzian manifold, the direct constructions are given. Also the holonomy
algebras of totally Ricci-isotropic Lorentzian manifolds are classified. The
classification of the holonomy algebras of Lorentzian manifolds is reviewed and
a complete description of the spaces of curvature tensors for these holonomies
is given.Comment: Dedicated to to Mark Volfovich Losik on his 75th birthday. This
version is an extended part of the previous version; another part of the
previous version is extended and submitted as arXiv:1001.444
Mapping trait versus species turnover reveals spatiotemporal variation in functional redundancy and network robustness in a plant-pollinator community
Functional overlap among species (redundancy) is considered important in shaping competitive and mutualistic interactions that determine how communities respond to environmental change. Most studies view functional redundancy as static, yet traits within species—which ultimately shape functional redundancy—can vary over seasonal or spatial gradients. We therefore have limited understanding of how trait turnover within and between species could lead to changes in functional redundancy or how loss of traits could differentially impact mutualistic interactions depending on where and when the interactions occur in space and time. Using an Arctic bumblebee community as a case study, and 1277 individual measures from 14 species over three annual seasons, we quantified how inter- and intraspecific body-size turnover compared to species turnover with elevation and over the season. Coupling every individual and their trait with a plant visitation, we investigated how grouping individuals by a morphological trait or by species identity altered our assessment of network structure and how this differed in space and time. Finally, we tested how the sensitivity of the network in space and time differed when simulating extinction of nodes representing either morphological trait similarity or traditional species groups. This allowed us to explore the degree to which trait-based groups increase or decrease interaction redundancy relative to species-based nodes. We found that (i) groups of taxonomically and morphologically similar bees turn over in space and time independently from each other, with trait turnover being larger over the season; (ii) networks composed of nodes representing species versus morphologically similar bees were structured differently; and (iii) simulated loss of bee trait groups caused faster coextinction of bumblebee species and flowering plants than when bee taxonomic groups were lost. Crucially, the magnitude of these effects varied in space and time, highlighting the importance of considering spatiotemporal context when studying the relative importance of taxonomic and trait contributions to interaction network architecture. Our finding that functional redundancy varies spatiotemporally demonstrates how considering the traits of individuals within networks is needed to understand the impacts of environmental variation and extinction on ecosystem functioning and resilience
Phase-space and Black Hole Entropy of Higher Genus Horizons in Loop Quantum Gravity
In the context of loop quantum gravity, we construct the phase-space of
isolated horizons with genus greater than 0. Within the loop quantum gravity
framework, these horizons are described by genus g surfaces with N punctures
and the dimension of the corresponding phase-space is calculated including the
genus cycles as degrees of freedom. From this, the black hole entropy can be
calculated by counting the microstates which correspond to a black hole of
fixed area. We find that the leading term agrees with the A/4 law and that the
sub-leading contribution is modified by the genus cycles.Comment: 22 pages, 9 figures. References updated. Minor changes to match
version to appear in Class. Quant. Gra