Norman Gürlebeck

On Appell Sets and the Fueter-Sce Mapping

It is proved, that the recently discussed Appell polynomials in Clifford algebras are the Fueter-Sce extension of the complex monomials z. Furthermore, it is shown, for which complex functions the Fueter-Sce extension and the extension method using Appell polynomials coincide.

No-Hair Theorem for Black Holes in Astrophysical Environments

According to the no-hair theorem, static black holes are described by a Schwarzschild spacetime provided there are no other sources of the gravitational field. This requirement, however, is in astrophysical realistic scenarios often violated, e.g., if the black hole is part of a binary system or if it is surrounded by an accretion disk. In these cases, the black hole is distorted due to tidal forces. Nonetheless, the subsequent formulation of the no-hair theorem holds: The contribution of the distorted black hole to the multipole moments that describe the gravitational field close to infinity and, thus, all sources is that of a Schwarzschild black hole. It still has no hair. This implies that there is no multipole moment induced in the black hole and that its second Love numbers, which measure some aspects of the distortion, vanish as was already shown in approximations to general relativity. But here we prove this property for astrophysical relevant black holes in full general relativity.

I-Q relation for rapidly rotating neutron stars

We consider a universal relation between moment of inertia and quadrupole moment of arbitrarily fast rotating neutron stars. Recent studies suggest that this relation breaks down for fast rotation. We find that it is still universal among various suggested equations of state for constant values of certain dimensionless parameters characterizing the magnitude of rotation. One of these parameters includes the neutron star radius, leading to a new universal relation expressing the radius through the mass, frequency, and spin parameter. This can become a powerful tool for radius measurements.

Giant Pulsar Glitches and the Inertia of Neutron-Star Crusts

Giant pulsar frequency glitches as detected in the emblematic Vela pulsar have long been thought to be the manifestation of a neutron superfluid permeating the inner crust of a neutron star. However, this superfluid has been recently found to be entrained by the crust, and as a consequence it does not carry enough angular momentum to explain giant glitches. The extent to which pulsar-timing observations can be reconciled with the standard vortex-mediated glitch theory is studied considering the current uncertainties on dense-matter properties. To this end, the crustal moment of inertia of glitching pulsars is calculated employing a series of different unified dense-matter equations of state.

Visualization of novel virulence activities of the Xanthomonas type III effectors AvrBs1, AvrBs3 and AvrBs4

Xanthomonas campestris pv. vesicatoria secretes at least 20 effector proteins through the type III secretion system directly into plant cells. In this study, we uncovered virulence activities of the effector proteins AvrBs1, AvrBs3 and AvrBs4 using Agrobacterium-mediated transient expression of the corresponding genes in Nicotiana benthamiana, followed by microscopic analyses. We showed that, in addition to the nuclear-localized AvrBs3, the effector AvrBs1, which localizes to the plant cell cytoplasm, also induces a morphological change in mesophyll cells. Comparative analyses revealed that avrBs3-expressing plant cells contain highly active nuclei. Furthermore, plant cells expressing avrBs3 or avrBs1 show a decrease in the starch content in chloroplasts and an increased number of vesicles, indicating an enlargement of the central vacuole and the cell wall. Both AvrBs1 and AvrBs3 cause an increased ion efflux when expressed in N. benthamiana. By contrast, expression of the avrBs3 homologue avrBs4 leads to large catalase crystals in peroxisomes, suggesting a possible virulence function of AvrBs4 in the suppression of the plant defence responses. Taken together, our data show that microscopic inspection can uncover subtle and novel virulence activities of type III effector proteins.

Atom interferometry in space: Thermal management and magnetic shielding

Atom interferometry is an exciting tool to probe fundamental physics. It is considered especially apt to test the universality of free fall by using two different sorts of atoms. The increasing sensitivity required for this kind of experiment sets severe requirements on its environments, instrument control, and systematic effects. This can partially be mitigated by going to space as was proposed, for example, in the Spacetime Explorer and Quantum Equivalence Principle Space Test (STE-QUEST) mission. However, the requirements on the instrument are still very challenging. For example, the specifications of the STE-QUEST mission imply that the Feshbach coils of the atom interferometer are allowed to change their radius only by about 260 nm or 2.6 × 10(-4) % due to thermal expansion although they consume an average power of 22 W. Also Earths magnetic field has to be suppressed by a factor of 10(5). We show in this article that with the right design such thermal and magnetic requirements can indeed be met and that these are not an impediment for the exciting physics possible with atom interferometers in space.

Monopole and dipole layers in curved spacetimes: Formalism and examples

The discontinuities of electromagnetic test fields generated by general layers of electric and magnetic monopoles and dipoles are investigated in general curved spacetimes. The equivalence of electric currents and magnetic dipoles is discussed. The results are used to describe exact ‘‘Schwarzschild disk’’ solutions endowed with such sources. The resulting distributions of charge and dipole densities on the disks are corroborated using the membrane paradigm.

THE AXISYMMETRIC CASE FOR THE POST-NEWTONIAN DEDEKIND ELLIPSOIDS

We consider the post-Newtonian approximation for the Dedekind ellipsoids in the case of axisymmetry. The approach taken by Chandrasekhar & Elbert excludes the possibility of finding a uniformly rotating (deformed) spheroid in the axially symmetric limit, though the solution exists at the point of axisymmetry. We consider an extension to their work that permits the possibility of such a limit.

Kerr-Newman black hole in the formalism of isolated horizons

The near horizon geometry of general black holes in equilibrium can be conveniently characterized in the formalism of weakly isolated horizons in the form of the Bondi-like expansions (Krishnan B, Class.\ Quantum Grav.\ 29, 205006, 2012). While the intrinsic geometry of the Kerr-Newman black hole has been extensively investigated in the weakly isolated horizon framework, the off-horizon description in the Bondi-like system employed by Krishnan has not been studied. We extend Krishnans work by explicit, non-perturbative construction of the Bondi-like tetrad in the full Kerr-Newman spacetime. Namely, we construct the Bondi-like tetrad which is parallelly propagated along a nontwisting null geodesic congruence transversal to the horizon and provide all Newman-Penrose scalars associated with this tetrad. This work completes the description of the Kerr-Newman spacetime in the formalism of weakly isolated horizons and is a starting point for the investigation of deformed black holes.

High-Performance Optical Frequency References for Space

A variety of future space missions rely on the availability of high-performance optical clocks with applications in fundamental physics, geoscience, Earth observation and navigation and ranging. Examples are the gravitational wave detector eLISA (evolved Laser Interferometer Space Antenna), the Earth gravity mission NGGM (Next Generation Gravity Mission) and missions, dedicated to tests of Special Relativity, e.g. by performing a Kennedy- Thorndike experiment testing the boost dependence of the speed of light. In this context we developed optical frequency references based on Doppler-free spectroscopy of molecular iodine; compactness and mechanical and thermal stability are main design criteria. With a setup on engineering model (EM) level we demonstrated a frequency stability of about 210-14 at an integration time of 1 s and below 610-15 at integration times between 100s and 1000s, determined from a beat-note measurement with a cavity stabilized laser where a linear drift was removed from the data. A cavity-based frequency reference with focus on improved long-term frequency stability is currently under development. A specific sixfold thermal shield design based on analytical methods and numerical calculations is presented.