On the differentiability of Cauchy horizons

Chrusciel and Galloway constructed a Cauchy horizon that is nondifferentiable on a dense set. We prove that in a certain class of Cauchy horizons densely nondifferentiable Cauchy horizons are generic. We show that our class of densely nondifferentiable Cauchy horizons implies the existence of densely nondifferentiable Cauchy horizons arising from partial Cauchy surfaces and also the existence of densely nondifferentiable black hole event horizons.Comment: 9 pages, LaTe

Generalized Strong Curvature Singularities and Cosmic Censorship

A new definition of a strong curvature singularity is proposed. This definition is motivated by the definitions given by Tipler and Krolak, but is significantly different and more general. All causal geodesics terminating at these new singularities, which we call generalized strong curvature singularities, are classified into three possible types; the classification is based on certain relations between the curvature strength of the singularities and the causal structure in their neighborhood. A cosmic censorship theorem is formulated and proved which shows that only one class of generalized strong curvature singularities, corresponding to a single type of geodesics according to our classification, can be naked. Implications of this result for the cosmic censorship hypothesis are indicated.Comment: LaTeX, 11 pages, no figures, to appear in Mod. Phys. Lett.

Applications of distance between probability distributions to gravitational wave data analysis

We present a definition of the distance between probability distributions. Our definition is based on the $L_1$ norm on space of probability measures. We compare our distance with the well-known Kullback-Leibler divergence and with the proper distance defined using the Fisher matrix as a metric on the parameter space. We consider using our notion of distance in several problems in gravitational wave data analysis: to place templates in the parameter space in searches for gravitational-wave signals, to assess quality of search templates, and to study the signal resolution.Comment: 18 pages, 5 figure

On the dynamics for a mechanics with noncontinuous hamiltonians

.Mechanical systems with noncontinuous or numerical [11] hamiltonian are considered. The method of defining a dynamics for such mechanical systems is given

The density theorem for the actions of I.L.H.-Lie groups

.The density theorem for the action of I.L.H.-Lie group G on the I.L.H.-manifold M is proved i.e. it was shown that the stratum with trivial isotropy group is open and dense subset of M