A Simple and Well-Adjusted Exterior Metric for a Collapsing or Anti-Collapsing Star

Metric Learning by Collapsing Classes

We present an algorithm for learning a quadratic Gaussian metric (Mahalanobis distance) for use in classification tasks. Our method relies on the simple geometric intuition that a good metric is one under which points in the same class are simultaneously near each other and far from points in the other classes. We construct a convex optimization problem whose solution generates such a metric by...

A Burst of Electromagnetic Radiation from a Collapsing Magnetized Star

The pattern of variations in the intensity of magnetodipole losses is studied with the relativistic effect of magnetic-field dissipation during collapse into a black hole taken into account. A burst-type solution can be obtained both for a direct collapse and for the formation of a rapidly-rotating, self-gravitating object — a spinar — using a simple model. Analytical dependences on radius desc...

The Wave Function of a Collapsing Star and Quantization Conditions

A very simple minisuperspace describing the Oppenheimer-Snyder collapsing star is found. The semiclassical wave function of that model turn out to describe a bound state. For fixed initial radius of the collapsing star, the corresponding Bohr-Sommerfeld quantization condition implies mass quantization. An extension of this model, and some consequences, are considered. This work is supported by ...

a simple procedure for detecting periodically collapsing rational bubbles ¤

Metric transformations under collapsing of Riemannian manifolds

Gromov-Hausdorff convergence is an important tool in comparison Riemannian geometry. Given a sequence of Riemannian manifolds of dimension n with Ricci curvature bounded from below, Gromov’s precompactness theorem says that a subsequence will converge in the pointed Gromov-Hausdorff topology to a length space [G-99, Section 5A]. If the sequence has bounded sectional curvature, then the limit wi...