Perturbations in the Kerr-Newman Dilatonic Black Hole Background: I. Maxwell waves

In this paper we analyze the perturbations of the Kerr-Newman dilatonic black hole background. For this purpose we perform a double expansion in both the background electric charge and the wave parameters of the relevant quantities in the Newman-Penrose formalism. We then display the gravitational, dilatonic and electromagnetic equations, which reproduce the static solution (at zero order in the wave parameter) and the corresponding wave equations in the Kerr background (at first order in the wave parameter and zero order in the electric charge). At higher orders in the electric charge one encounters corrections to the propagations of waves induced by the presence of a non-vanishing dilaton. An explicit computation is carried out for the electromagnetic waves up to the asymptotic form of the Maxwell field perturbations produced by the interaction with dilatonic waves. A simple physical model is proposed which could make these perturbations relevant to the detection of radiation coming from the region of space near a black hole.Comment: RevTeX, 36 pages in preprint style, 1 figure posted as a separate PS file, submitted to Phys. Rev.

Smooth perturbations of the functional calculus and applications to Riemannian geometry on spaces of metrics

We show for a certain class of operators $A$ and holomorphic functions $f$ that the functional calculus $A\mapsto f(A)$ is holomorphic. Using this result we are able to prove that fractional Laplacians $(1+\Delta^g)^p$ depend real analytically on the metric $g$ in suitable Sobolev topologies. As an application we obtain local well-posedness of the geodesic equation for fractional Sobolev metrics on the space of all Riemannian metrics.Comment: 31 page

Statistical mechanics of Kerr-Newman dilaton black holes and the bootstrap condition

The Bekenstein-Hawking ``entropy'' of a Kerr-Newman dilaton black hole is computed in a perturbative expansion in the charge-to-mass ratio. The most probable configuration for a gas of such black holes is analyzed in the microcanonical formalism and it is argued that it does not satisfy the equipartition principle but a bootstrap condition. It is also suggested that the present results are further support for an interpretation of black holes as excitations of extended objects.Comment: RevTeX, 5 pages, 2 PS figures included (requires epsf), submitted to Phys. Rev. Let

CD163 expression in leukemia cutis

Background: Proper diagnosis of myeloid leukemia cutis (LC) is of great clinical importance but can be difficult because no single immunohistochemical marker is adequately sensitive or specific for definitive diagnosis. Thus, a broader panel of markers is often desirable. CD163 is highly specific for normal and neoplastic cells of the monocyte/histiocyte lineage. In this study, we examined the value of CD163 in the diagnosis of acute myeloid LC. Methods: A total of 34 cases, including 18 cases of myelomonocytic or monocytic LC, 10 cases of myeloid LC without monocytic component and 6 cases of acute lymphoblastic leukemia/lymphoma (ALL), were stained with CD163. Results: CD163 was expressed in 8 of 18 (44%) of myelomonocytic or monocytic LC and 1 of 10 (10%) of other myeloid LC, but in none of the ALL cases (0/6). CD163 was highly specific (90%) for myeloid LC with a monocytic component, but showed low sensitivity in the diagnosis of both myeloid LC in general (24%) and myeloid LC with a monocytic component (44%). Conclusions: Our results suggest that CD163 has utility as a specific marker for myeloid LC in conjunction with currently used immunohistochemical stains, but should not be used alone for diagnosis.Harms PW, Bandarchi B, Ma L. CD163 expression in leukemia cutis.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/78608/1/j.1600-0560.2010.01533.x.pd

Curvature weighted metrics on shape space of hypersurfaces in nn-space

Let $M$ be a compact connected oriented $n-1$ dimensional manifold without boundary. In this work, shape space is the orbifold of unparametrized immersions from $M$ to $\mathbb R^n$. The results of \cite{Michor118}, where mean curvature weighted metrics were studied, suggest incorporating Gau{\ss} curvature weights in the definition of the metric. This leads us to study metrics on shape space that are induced by metrics on the space of immersions of the form G_f(h,k) = \int_{M} \Phi . \bar g(h, k) \vol(f^*\bar{g}). Here f \in \Imm(M,\R^n) is an immersion of $M$ into $\R^n$ and $h,k\in C^\infty(M,\mathbb R^n)$ are tangent vectors at $f$. $\bar g$ is the standard metric on $\mathbb R^n$, $f^*\bar g$ is the induced metric on $M$, \vol(f^*\bar g) is the induced volume density and $\Phi$ is a suitable smooth function depending on the mean curvature and Gau{\ss} curvature. For these metrics we compute the geodesic equations both on the space of immersions and on shape space and the conserved momenta arising from the obvious symmetries. Numerical experiments illustrate the behavior of these metrics.Comment: 12 pages 3 figure