Spherically symmetric teleparallel geometries.

We are interested in the development of spherically symmetric geometries in F(T) teleparallel gravity which are of physical importance. We first express the general forms for the spherically symmetric frame and the zero curvature, metric compatible, spin connection. We then analyse the antisymmetric field equations (the solutions of which split into two cases, which we subsequently consider separately), and derive and analyse the resulting symmetric field equations. In order to further study the applications of spherically symmetric teleparallel models, we study 3 subcases in which there is an additional affine symmetry so that the resulting field equations reduce to a system of ordinary differential equations. First, we study static spherical symmetric geometries and solve the antisymmetric field equations and subsequently derive the full set of symmetric field equations. In particular, we investigate vacuum spacetimes and obtain a number of new solutions. Second, we consider an additional affine frame symmetry in order to expand the affine frame symmetry group to that of a spatially homogeneous Kantowski-Sachs geometry. Third, we study the special case of spherical symmetry with an additional fourth similarity affine vector.

Generalized teleparallel de Sitter geometries.

Theories of gravity based on teleparallel geometries are characterized by the torsion, which is a function of the coframe, derivatives of the coframe, and a zero curvature and metric compatible spin-connection. The appropriate notion of a symmetry in a teleparallel geometry is that of an affine symmetry. Due to the importance of the de Sitter geometry and Einstein spaces within General Relativity, we shall describe teleparallel de Sitter geometries and discuss their possible generalizations. In particular, we shall analyse a class of Einstein teleparallel geometries which have a 4-dimensional Lie algebra of affine symmetries, and display two one-parameter families of explicit exact solutions.

Immunocytochemical identification of electroneutral Na⁺-coupled HCO3⁻ transporters in freshly dissociated mouse medullary raphé neurons.

The medullary raphé (MR) of the medulla oblongata contains chemosensitive neurons that respond to increases in arterial [CO2], by altering firing rate, with increases being associated with serotonergic (5-hydroxytryptamine [5HT]) neurons and decreases, with GABAergic neurons. Both types of neurons contribute to increased alveolar ventilation. Decreases in intracellular pH are thought to link the rise in [CO2] to increased ventilation. Because electroneutral Na(+)-coupled HCO3(-) transporters (nNCBTs), which help protect cells from intracellular acidosis, are expressed robustly in the neurons of the central nervous system, a key question is whether these transporters are present in chemosensitive neurons. Therefore, we used an immunocytochemistry approach to identify neurons (using a microtubule associated protein-2 monoclonal antibody) and specifically 5HT neurons (TPH monoclonal antibody) or GABAergic neurons (GAD2 monoclonal antibody) in freshly dissociated cells from the mouse MR. We also co-labeled with polyclonal antibodies against the three nNCBTs: NBCn1, NDCBE, and NBCn2. We exploited ePet-EYFP (enhanced yellow fluorescent protein) mice (with EYFP-labeled 5HT neurons) as well as mice genetically deficient in each of the three nNCBTs. Quantitative image analysis distinguished positively stained cells from background signals. We found that >80% of GAD2(+) cells also were positive for NDCBE, and >90% of the TPH(+) and GAD2(+) cells were positive for the other nNCBTs. Assuming that the transporters are independently distributed among neurons, we can conclude that virtually all chemosensitive MR neurons contain at least one nNCBT.

Generating matter inhomogeneities in general relativity.

In this Letter we discuss a natural general relativistic mechanism that causes inhomogeneities and hence generates matter perturbations in the early Universe. We concentrate on spikes, both incomplete spikes and recurring spikes, that naturally occur in the initial oscillatory regime of general cosmological models. In particular, we explicitly show that spikes occurring in a class of G2 models lead to inhomogeneities that, due to gravitational instability, leave small residual imprints on matter in the form of matter perturbations. The residual matter overdensities from recurring spikes are not local but form on surfaces. We discuss the potential physical consequences of the residual matter imprints and their possible effect on the subsequent formation of large-scale structure.

Cosmological solutions in macroscopic gravity.

In the macroscopic gravity approach to the averaging problem in cosmology, the Einstein field equations on cosmological scales are modified by appropriate gravitational correlation terms. We present exact cosmological solutions to the equations of macroscopic gravity for a spatially homogeneous and isotropic macroscopic space-time and find that the correlation tensor is of the form of a spatial curvature term. We briefly discuss the physical consequences of these results.

A class of exact classical solutions to string theory.

We show that the recently obtained class of spacetimes for which all of the scalar curvature invariants vanish (which can be regarded as generalizations of pp-wave spacetimes) are exact solutions in string theory to all perturbative orders in the string tension scale. As a result the spectrum of the theory can be explicitly obtained, and these spacetimes are expected to provide some hints for the study of superstrings on more general backgrounds. Since these Lorentzian spacetimes suffer no quantum corrections to all loop orders they may also offer insights into quantum gravity.