Visualizing spacetimes via embedding diagrams

It is hard to imagine curved spacetimes of General Relativity. A simple but powerful way how to achieve this is visualizing them via embedding diagrams of both ordinary geometry and optical reference geometry. They facilitate to gain an intuitive insight into the gravitational field rendered into a curved spacetime, and to assess the influence of parameters like electric charge and spin of a black hole, magnetic field or cosmological constant. Optical reference geometry and related inertial forces and their relationship to embedding diagrams are particularly useful for investigation of test particles motion. Embedding diagrams of static and spherically symmetric, or stationary and axially symmetric black-hole and naked-singularity spacetimes thus present a useful concept for intuitive understanding of these spacetimes' nature. We concentrate on general way of embedding into 3-dimensional Euclidean space, and give a set of illustrative examples.Comment: 8 pages, 5 figure

Dynamical stability of fluid spheres in spacetimes with a nonzero cosmological constant

The Sturm-Liouville eigenvalue equation for eigenmodes of the radial oscillations is determined for spherically symmetric perfect fluid configurations in spacetimes with a nonzero cosmological constant and applied in the cases of configurations with uniform distribution of energy density and polytropic spheres. It is shown that a repulsive cosmological constant rises the critical adiabatic index and decreases the critical radius under which the dynamical instability occurs.Comment: 3 pages, 1 figure, to appear in "Proceedings of the 11th Marcel Grossmann Meeting on General Relativity", eds H. Kleinert, R. T. Jantzen, R. Ruffin

Apoptosis-induced ectodomain shedding of hypoxia-regulated carbonic anhydrase IX from tumor cells: a double-edged response to chemotherapy.

BACKGROUND: Carbonic anhydrase IX (CA IX) is a tumor-associated, highly active, transmembrane carbonic anhydrase isoform regulated by hypoxia and implicated in pH control and adhesion-migration-invasion. CA IX ectodomain (ECD) is shed from the tumor cell surface to serum/plasma of patients, where it can signify cancer prognosis. We previously showed that the CA IX ECD release is mediated by disintegrin and metalloproteinase ADAM17. Here we investigated the CA IX ECD shedding in tumor cells undergoing apoptosis in response to cytotoxic drugs, including cycloheximide and doxorubicin. METHODS: Presence of cell surface CA IX was correlated to the extent of apoptosis by flow cytometry in cell lines with natural or ectopic CA IX expression. CA IX ECD level was assessed by ELISA using CA IX-specific monoclonal antibodies. Effect of recombinant CA IX ECD on the activation of molecular pathways was evaluated using the cell-based dual-luciferase reporter assay. RESULTS: We found a significantly lower occurrence of apoptosis in the CA IX-positive cell subpopulation than in the CA IX-negative one. We also demonstrated that the cell-surface CA IX level dropped during the death progress due to an increased ECD shedding, which required a functional ADAM17. Inhibitors of metalloproteinases reduced CA IX ECD shedding, but not apoptosis. The CA IX ECD release induced by cytotoxic drugs was connected to elevated expression of CA IX in the surviving fraction of cells. Moreover, an externally added recombinant CA IX ECD activated a pathway driven by the Nanog transcription factor implicated in epithelial-mesenchymal transition and stemness. CONCLUSIONS: These findings imply that the increased level of the circulating CA IX ECD might be useful as an indicator of an effective antitumor chemotherapy. Conversely, elevated CA IX ECD might generate unwanted effects through autocrine/paracrine signaling potentially contributing to resistance and tumor progression