The need for dark matter in galaxies

Cooperstock and Tieu have proposed a model to account for galactic rotation curves without invoking dark matter. I argue that no model of this type can work

Quasi--local angular momentum of non--symmetric isolated and dynamical horizons from the conformal decomposition of the metric

A new definition of quasi--local angular momentum of non--axisymmetric marginally outer trapped surfaces is proposed. It is based on conformal decomposition of the two--dimensional metric and the action of the group of conformal symmetries. The definition is completely general and agrees with the standard one in axi--symmetric surfaces.Comment: Final version to appear in Classical and Quantum Gravity. One reference adde

Conformal Einstein equations and Cartan conformal connection

Necessary and sufficient conditions for a space-time to be conformal to an Einstein space-time are interpreted in terms of curvature restrictions for the corresponding Cartan conformal connection

Fundamental properties and applications of quasi-local black hole horizons

The traditional description of black holes in terms of event horizons is inadequate for many physical applications, especially when studying black holes in non-stationary spacetimes. In these cases, it is often more useful to use the quasi-local notions of trapped and marginally trapped surfaces, which lead naturally to the framework of trapping, isolated, and dynamical horizons. This framework allows us to analyze diverse facets of black holes in a unified manner and to significantly generalize several results in black hole physics. It also leads to a number of applications in mathematical general relativity, numerical relativity, astrophysics, and quantum gravity. In this review, I will discuss the basic ideas and recent developments in this framework, and summarize some of its applications with an emphasis on numerical relativity.Comment: 14 pages, 2 figures. Based on a talk presented at the 18th International Conference on General Relativity and Gravitation, 8-13 July 2007, Sydney, Australi

Coarse-graining of inhomogeneous dust flow in General Relativity via isometric embeddings

We present a new approach to coarse-graining of variables describing dust flow in GR. It is based on assigning quasi-local shear, twist and expansion to 2-dimensional surfaces with the help of isometric embeddings into the 3-dimensional Euclidean space and deriving the time evolution equations for them. In contrast to the popular Buchert's scheme it allows to coarse-grain tensorial quantities in a coordinate-independent way. The framework can be used to estimate backreaction in inhomogeneous cosmological models

Short term synaptic depression model—Analytical solution and analysis

In this article we present analytical solutions of the single and pair pulse time evolution of a plastic neocortical synapse described by the TM-model. We show that this model is equivalent to the receptor-desensitization model with three kinetic states. For the TM-model we derive the analytical form of a measure of paired pulse depression. We analyze the sensitivity of the synaptic depression phenomenon on model parameters and derive the relative importance of each of the parameters. The closed form of the measure of synaptic depression allows fitting the model to experimental data. The fitted parameters are used to make predictions about the asymptotic properties of the postsynaptic currents. We show that for synapses with the ratio of inactivation and recovery rates of the same order, the synaptic depression does not preclude the rate-coding of information: e.g. in the pyramid–pyramid connections of adult rat neocortex, rate-coding is possible for higher frequencies

Accelerating the Universe with Gravitational Waves

Inflation generically produces primordial gravitational waves with a red spectral tilt. In this paper we calculate the backreaction produced by these gravitational waves on the expansion of the universe. We find that in radiation domination the backreaction acts as a relativistic fluid, while in matter domination a small dark energy emerges with an equation of state w=-8/9.Comment: 18 pages, 4 figures. Replaced with version published by JCAP - some discussion and references added concerning second-order gravitational waves, typeset in JHEP styl

Light propagation in statistically homogeneous and isotropic universes with general matter content

We derive the relationship of the redshift and the angular diameter distance to the average expansion rate for universes which are statistically homogeneous and isotropic and where the distribution evolves slowly, but which have otherwise arbitrary geometry and matter content. The relevant average expansion rate is selected by the observable redshift and the assumed symmetry properties of the spacetime. We show why light deflection and shear remain small. We write down the evolution equations for the average expansion rate and discuss the validity of the dust approximation.Comment: 42 pages, no figures. v2: Corrected one detail about the angular diameter distance and two typos. No change in result

From Geometry to Numerics: interdisciplinary aspects in mathematical and numerical relativity

This article reviews some aspects in the current relationship between mathematical and numerical General Relativity. Focus is placed on the description of isolated systems, with a particular emphasis on recent developments in the study of black holes. Ideas concerning asymptotic flatness, the initial value problem, the constraint equations, evolution formalisms, geometric inequalities and quasi-local black hole horizons are discussed on the light of the interaction between numerical and mathematical relativists.Comment: Topical review commissioned by Classical and Quantum Gravity. Discussion inspired by the workshop "From Geometry to Numerics" (Paris, 20-24 November, 2006), part of the "General Relativity Trimester" at the Institut Henri Poincare (Fall 2006). Comments and references added. Typos corrected. Submitted to Classical and Quantum Gravit