We analyze the evolution of the mass density contrast in spherical perturbations of flat Friedman-Lemaitre-Robertson-Walker cosmologies. Both dark matter and dark energy are included. In the absence of dark energy the evolution equation coincides with that obtained by Bonnor within the ``Newtonian cosmology''.

The spherically symmetric steady accretion of polytropic perfect fluids onto a black hole is the simplest flow model that can demonstrate effects of backreaction (selfgravity). It has been discovered 16 years ago that backreaction does not influence some ("intensive") characteristics of sonic points, under suitable conditions. Herein we consider a wider class of equations of state, with polytropic indices in the range (1,2], and establish detailed boundary conditions that allow one to prove this fact. We find also numerical examples showing limits of our analytic criteria - if suitable analytic conditions are not satisfied, then selfgravity influences all characteristics of sonic points. That fact constrains the applicability of the recent proposal of Baumgarte and Shapiro to estimate the lifetime of black holes within compact stellar objects.

We study stationary and axially symmetric black hole-disk systems, assuming a combination of the DD2 and Timmes-Swesty equations of state and a three-parameter family of rotation laws. There exist two branches of solutions that are shown to bifurcate, for a suitable specific entropy and a parameter in the rotation law. Low entropy nuclear matter allows for the existence of moderately massive Keplerian disks.

We numerically investigate the validity of recent modifications of the Penrose inequality that include angular momentum. Formulations expressed in terms of asymptotic mass and asymptotic angular momentum are contradicted. We analyzed numerical solutions describing polytropic stationary toroids around spinning black holes.

We obtain rotation laws for axially symmetric, selfgravitating and stationary fluids around spinning black holes. They reduce --- in the Newtonian limit --- to monomial rotation curves. For spinless black hole, one obtains in the first post-Newtonian (1PN) approximation the hitherto known results, that can be interpreted as the geometric dragging and material antidragging. We find new 1PN effects, that are due to spins of black holes.

Objectives: During almost five decades, the technique of Fontan operation (FO) underwent many modifications, and nowadays, there are generally two operative methods which are used as a total cavopulmonary anastomosis: lateral tunnel (LT) and extracardiac conduit (EC). The aim of the study was to compare the mid-term outcomes after LT and EC FO.

We model self-gravitating disks in Keplerian motion around the primary black hole, in the binary black hole system OJ 287 with a torus, employing a consistently general-relativistic approach. They satisfy geometric and/or mass density requirements found by Sillanpaa, Valtonen, Lehto and their coworkers. It is plausible that essential observational features of OJ 287 can be obtained via the general-relativistic description of the Bondi-Hoyle-Lyttleton transits through these tori, within the framework of radiation hydrodynamics.

We analyze stationary self-gravitating disks around spinning black holes that satisfy the recently found general-relativistic Keplerian rotation law. There is a numerical evidence that the angular velocity, circumferential radius and angular momenta yield a bound onto the asymptotic mass of the system. This bound is proven analytically in the special case of massless disks of dust in the Kerr spacetime.

Objective: Negative intrathoracic pressure caused by spontaneous ventilation is an important driving force for blood flow in Fontan circulation. The avoidance of positive pressure ventilation in the postoperative management is therefore of potential benefit. The goal of this study was to assess the impact of immediate postoperative extubation in the operating room on hemodynamics and early outcome after Fontan operation (FO) in comparison to later extubation on the intensive care unit.

Black holes entered scientific literature as early as at the end of eighteenth century. They had been known at that time as dark stars, but their concept did not find its way to physics or astronomy, and had been abandoned for more than one hundred years. I shall sketch historical developments and discuss present mathematical and observational status of black holes.

We obtain from the first principles a general-relativistic Keplerian rotation law for self-gravitating disks around spinning black holes. This is an extension of a former rotation law that was designed mainly for toroids around spinless black holes. We integrate numerically axial stationary Einstein equations with self-gravitating disks around spinless or spinning black holes; that includes the first ever integration of the Keplerian selfgravitating tori. This construction can be used for the description of tight black hole-torus systems produced during coalescences of two neutron stars or modelling of compact active galactic nuclei.

We integrate numerically axially symmetric stationary Einstein equations describing self-gravitating disks around spinless black holes. The numerical scheme is based on a method developed by Shibata, but contains important new ingredients. We derive a new general-relativistic Keplerian rotation law for self-gravitating disks around spinning black holes. Former results concerning rotation around spin-less black holes emerge in the limit of a vanishing spin parameter. These rotation curves might be used for the description of rotating stars, after appropriate modification around the symmetry axis. They can be applied to the description of compact torus--black hole configurations, including active galactic nuclei or products of coalescences of two neutron stars.

Ventriculocoronary connections (VCC) are a frequent phenomenon in hypoplastic left-heart syndrome (HLHS). They are especially common in fetuses manifesting HLHS with mitral stenosis und aortic atresia (MSAA subtype). According to Blake et al, there are three subtypes of ventriculocoronary connections (aterioluminal, arteriosinusoidal and ateriocapillary). The clinical importance of these VCC is still undetermined. While VCC have previously been considered to be prognostic for a poor outcome after surgical stage I palliation, some evidence suggests that they are not associated with a higher mortality. Here we will present the case of a child with HLHS of the MSAA subtype with several venticulocoronary connections who was diagnosed prenatally and treated postnatally in our centre. The child was delivered at 37+3 weeks' gestation due to a restriction in the foramen ovale. The child adapted well postnatally presenting a retrograde flow through the VCC into the ascending aorta. This rare condition caused high O2 saturations and contributed to the satisfying clinical performance of the newborn. We will discuss the details of this case and review the literature due to the importance of VVC subtyping.

We analytically construct an infinite number of trapped toroids in spherically symmetric Cauchy hypersurfaces of the Einstein equations. We focus on initial data which represent ``constant density stars'' momentarily at rest. There exists an infinite number of constant mean curvature tori, but we also deal with more general configurations. The marginally trapped toroids have been found analytically and numerically; they are unstable. The topologically toroidal trapped surfaces appear in a finite region surrounded by the Schwarzschild horizon.

Recent general-relativistic extensions of Newtonian rotation laws for self-gravitating stationary fluids allow one to rederive, in the first post-Newtonian approximation, the well known geometric dragging of frames, and two new weak-field effects within rotating tori. These are the recently discovered anti-dragging and a new effect that measures the deviation from the Keplerian motion and/or the contribution of the fluids selfgravity. They can be applied to the study of the existence of the (post-)Newtonian limits of solutions and in investigations of inequalities relating parameters of rotating black holes.

We analyze propagation equations for the polar modes of gravitational waves in cosmological space-times. We prove that polar gravitational waves must perturb the density and non-azimuthal components of the velocity of material medium of the Friedman-Lemaitre-Robertson-Walker spacetimes. Axial gravitational waves can influence only the azimuthal velocity, leading to local cosmological rotation. The whole gravitational dynamics reduces to the single 'master equation' that has the same form for polar and axial modes. That allows us to conclude that the status of the Huygens principle is the same for axial and polar gravitational waves. In particular, this principle is valid exactly in radiation spacetimes with the vanishing cosmological constant, and it is broken otherwise.

Objectives: There are only few histological studies concerning patches/conduits implanted in children and young adults. In congenital heart surgery, many reoperations are required due to limited longevity of the available materials. Structural alterations lead to a deterioration of hemodynamics (obstruction ± regurgitation). This study was performed to unravel the morphological changes of explanted tissue samples on a histological level.

We show initial data for gravitational axial waves that are twice differentiable but that are not ${C}^{2}$. They generate wave pulses that interact with matter in the radiation cosmological era. This forces the radiation matter to rotate. This rotation is permanent---it persists after the passage of the gravitational pulse. The observed inhomogeneities of the cosmic microwave background radiation put a bound onto discontinuities of superhorizon metric perturbations. We explicitly show that a class of smooth initial metrics that are at least ${C}^{2}$ gives rise to gravitational wave pulses that do not interact with the background during the radiation epoch.

We consider stationary, axially symmetric toroids rotating around spinless black holes, assuming the general-relativistic Keplerian rotation law, in the first post-Newtonian approximation. Numerical investigation shows that the angular momentum accumulates almost exclusively within toroids. It appears that various types of dragging (antidragging) effects are positively correlated with the ratio M-D/m (M-D is the mass of a toroid, and m is the mass of the black hole)-moreover, their maxima are proportional to M-D/m. The horizontal sizes of investigated toroids range from c. 50 to c. 450 of Schwarzschild radii R-S of the central black hole; their mass M-D is an element of(10(-4)m; 40m), and the radial size of the system is c. 500 R-S. We found that the relative strength of various dragging (antidragging) effects does not change with the mass ratio, but it depends on the size of toroids. Several isoperimetric inequalities involving angular momentum are shown to hold true.

We discuss the relation between the concentration of the Brown-York mass and the formation of trapped surfaces in nonspherical massive systems. In particular, we formulate and prove a precise version of the Thorne hoop conjecture in conformally flat three-geometries sliced by equipotential foliation leaves. An intriguing relationship between the total rest mass and the Brown-York mass is shown. This is a further investigation of the previous work on the Brown-York mass hoop conjecture in spherical symmetry.