On the gravitational redshift

The study of the gravitational redshift\,---\,a relative wavelength increase of $\approx 2 \times 10^{-6}$ was predicted for solar radiation by Einstein in 1908\,---\,is still an important subject in modern physics. In a dispute whether or not atom interferometry experiments can be employed for gravitational redshift measurements, two research teams have recently disagreed on the physical cause of the shift. Regardless of any discussion on the interferometer aspect\,---\,we find that both groups of authors miss the important point that the ratio of gravitational to the electrostatic forces is generally very small. For instance, the gravitational force acting on an electron in a hydrogen atom situated in the Sun's photosphere to the electrostatic force between the proton and the electron is approximately $3 \times 10^{-21}$. A comparison of this ratio with the predicted and observed solar redshift indicates a discrepancy of many orders of magnitude. Here we show, with Einstein's early assumption of the frequency of spectral lines depending only on the generating ion itself as starting point, that a solution can be formulated based on a two-step process in analogy with Fermi's treatment of the Doppler effect. It provides a sequence of physical processes in line with the conservation of energy and momentum resulting in the observed shift and does not employ a geometric description. The gravitational field affects the release of the photon and not the atomic transition. The control parameter is the speed of light. The atomic emission is then contrasted with the gravitational redshift of matter-antimatter annihilation events.Comment: 19 Pages; 2 Table

The Boundary Layer in compact binaries

Disk accretion onto stars leads to the formation of a Boundary Layer (BL) near the stellar surface where the disk makes contact with the star. Albeit a large fraction of the total luminosity of the system originates from this tiny layer connecting the accretion disk and the accreting object, its structure has not been fully understood yet. It is the aim of this work, to obtain more insight into the Boundary Layer around the white dwarf in compact binary systems. There are still many uncertainties concerning the extent and temperature of the BL and the rotation rate of the white dwarf. We perform numerical hydrodynamical simulations, where the problem is treated in a one-dimensional, radial approximation (slim disk). The turbulence is described by the alpha parameter viscosity. We include both cooling from the disk surfaces and radial radiation transport. The radiation energy is treated in the one-temperature approximation. For a given M_dot our results show a strong dependence on the stellar mass and rotation rate. Both, the midplane and the effective temperature rise considerably with increasing stellar mass or decreasing stellar rotation rate. Our simulations further show, that the radiation energy and pressure are indeed important in the BL. However, some models show a low optical depth in the BL, making it necessary to find a better representation for optically thin regions. The combination of a high mass and a small radius, such as in white dwarfs, can lead to an enormous energy release in the BL, provided the WD rotates slowly. Since the radial extent of BLs is typically very small (about 0.02 to 0.05 R_star), this leads to surface temperatures of a few hundred thousand Kelvin. All of our models showed subsonic infall velocities with Mach numbers of < 0.4 at most.Comment: 13 pages, 10 figures, accepted for publication in Astronomy & Astrophysic

Long-term follow-up of callotasis lengthening of the capitate after resection of the lunate for the treatment of stage III lunate necrosis

The callotasis lengthening technique was used to gradually lengthen the capitate after resection of the lunate in stage IIIa necrosis in 23 patients. Results of ten patients with a follow-up of at least 5 years showed rapid and sufficient callus formation in every patient regardless of age. The callotasis lengthening modification of the Graner II operation provides all advantages and avoids the major inconvenience of the traditional Graner II operation. There was no increased rate of disturbed fracture healing. Results of the DTPA-gadolinium MRI study did not show any significant impairment of vascularization within the region of the capitate bone. With the “intrinsic bone formation,” contrary to every other intercarpal arthrodesis at the wrist, there is no need for an additional bone graft