The initial value problem as it relates to numerical relativity.

Spacetime is foliated by spatial hypersurfaces in the 3+1 split of general relativity. The initial value problem then consists of specifying initial data for all fields on one such a spatial hypersurface, such that the subsequent evolution forward in time is fully determined. On each hypersurface the 3-metric and extrinsic curvature describe the geometry. Together with matter fields such as fluid velocity, energy density and rest mass density, the 3-metric and extrinsic curvature then constitute the initial data. There is a lot of freedom in choosing such initial data. This freedom corresponds to the physical state of the system at the initial time. At the same time the initial data have to satisfy the Hamiltonian and momentum constraint equations of general relativity and can thus not be chosen completely freely. We discuss the conformal transverse traceless and conformal thin sandwich decompositions that are commonly used in the construction of constraint satisfying initial data. These decompositions allow us to specify certain free data that describe the physical nature of the system. The remaining metric fields are then determined by solving elliptic equations derived from the constraint equations. We describe initial data for single black holes and single neutron stars, and how we can use conformal decompositions to construct initial data for binaries made up of black holes or neutron stars. Orbiting binaries will emit gravitational radiation and thus lose energy. Since the emitted radiation tends to circularize the orbits over time, one can thus expect that the objects in a typical binary move on almost circular orbits with slowly shrinking radii. This leads us to the concept of quasi-equilibrium, which essentially assumes that time derivatives are negligible in corotating coordinates for binaries on almost circular orbits. We review how quasi-equilibrium assumptions can be used to make physically well motivated approximations that simplify the elliptic equations we have to solve.

Numerical simulation of orbiting black holes.

We present numerical simulations of binary black hole systems which for the first time last for about one orbital period for close but still separate black holes as indicated by the absence of a common apparent horizon. An important part of the method is the construction of comoving coordinates, in which both the angular and the radial motion are minimized through a dynamically adjusted shift condition. We use fixed mesh refinement for computational efficiency.

Acute alcohol effects on neuronal and attentional processing: striatal reward system and inhibitory sensory interactions under acute ethanol challenge.

The acute influence of ethanol on cerebral activity induces complex psycho-physiological effects that are considerably more pronounced during acute ethanol influx than during maximal blood alcohol concentration (elimination phase). Despite the psychiatric and forensic relevance of these different ethanol effects, the underlying neuronal mechanisms are still unclear. In total, 20 male healthy volunteers were investigated each with three different experimental conditions in a randomized order using an intravenous ethanol challenge (40 g bolus infusion): during influx phase, elimination phase, and under placebo condition. During and after the ethanol (or placebo) infusion, neuropsychological testing of divided attention for visual and auditory stimuli was performed with subsequent 18-FDG PET acquisition. The PET data were analysed using SPM99. Ethanol influx and elimination phase showed focal activations in the bilateral striatum and frontal cortex and deactivations in the occipital cortex. The comparison of influx phase vs elimination phase revealed activations in the anterior cingulate and right prefrontal cortex, relevant deactivations were found in the left superior temporal cortex including Wernicke's area. Neuropsychological testing showed an attentional impairment under ethanol influx compared to ethanol elimination and placebo with an inverse correlation of the attentional performance for auditory stimuli to occipital activity and for visual stimuli to the left temporal (including auditory) cortex. Acute ethanol administration in healthy volunteers stimulates those striatal regions that are considered to have a particular relevance for alcohol craving ('reward system'). Modality specific reciprocal inhibition of sensory cortex activity seems to be relevant for attentional performance during acute alcohol impact.