Rotating charged black holes accelerated by an electric field

The Ernst method of removing nodal singularities from the charged C-metric representing uniformly accelerated black holes with mass $m$, charge $q$ and acceleration $A$ by "adding" an electric field $E$ is generalized. Utilizing the new form of the C-metric found recently, Ernst's simple "equilibrium" condition $mA=qE$ valid for small accelerations is generalized for arbitrary $A$. The nodal singularity is removed also in the case of accelerating and rotating charged black holes, and the corresponding equilibrium condition is determined.Comment: 6 pages, 1 figur

Splines and Wavelets on Geophysically Relevant Manifolds

Analysis on the unit sphere $\mathbb{S}^{2}$ found many applications in seismology, weather prediction, astrophysics, signal analysis, crystallography, computer vision, computerized tomography, neuroscience, and statistics. In the last two decades, the importance of these and other applications triggered the development of various tools such as splines and wavelet bases suitable for the unit spheres $\mathbb{S}^{2}$, $\>\>\mathbb{S}^{3}$ and the rotation group $SO(3)$. Present paper is a summary of some of results of the author and his collaborators on generalized (average) variational splines and localized frames (wavelets) on compact Riemannian manifolds. The results are illustrated by applications to Radon-type transforms on $\mathbb{S}^{d}$ and $SO(3)$.Comment: The final publication is available at http://www.springerlink.co

The wavelet transforms in Gelfand-Shilov spaces

We describe local and global properties of wavelet transforms of ultradifferentiable functions. The results are given in the form of continuity properties of the wavelet transform on Gelfand-Shilov type spaces and their duals. In particular, we introduce a new family of highly time-scale localized spaces on the upper half-space. We study the wavelet synthesis operator (the left-inverse of the wavelet transform) and obtain the resolution of identity (Calder\'{o}n reproducing formula) in the context of ultradistributions

Properties of the symplectic structure of General Relativity for spatially bounded spacetime regions

We continue a previous analysis of the covariant Hamiltonian symplectic structure of General Relativity for spatially bounded regions of spacetime. To allow for near complete generality, the Hamiltonian is formulated using any fixed hypersurface, with a boundary given by a closed spacelike 2-surface. A main result is that we obtain Hamiltonians associated to Dirichlet and Neumann boundary conditions on the gravitational field coupled to matter sources, in particular a Klein-Gordon field, an electromagnetic field, and a set of Yang-Mills-Higgs fields. The Hamiltonians are given by a covariant form of the Arnowitt-Deser-Misner Hamiltonian modified by a surface integral term that depends on the particular boundary conditions. The general form of this surface integral involves an underlying ``energy-momentum'' vector in the spacetime tangent space at the spatial boundary 2-surface. We give examples of the resulting Dirichlet and Neumann vectors for topologically spherical 2-surfaces in Minkowski spacetime, spherically symmetric spacetimes, and stationary axisymmetric spacetimes. Moreover, we show the relation between these vectors and the ADM energy-momentum vector for a 2-surface taken in a limit to be spatial infinity in asymptotically flat spacetimes. We also discuss the geometrical properties of the Dirichlet and Neumann vectors and obtain several striking results relating these vectors to the mean curvature and normal curvature connection of the 2-surface. Most significantly, the part of the Dirichlet vector normal to the 2-surface depends only the spacetime metric at this surface and thereby defines a geometrical normal vector field on the 2-surface. Properties and examples of this normal vector are discussed.Comment: 46 pages; minor errata corrected in Eqs. (3.15), (3.24), (4.37) and in discussion of examples in sections IV B,