First-order action and Euclidean quantum gravity

We show that the on-shell path integral for asymptotically flat Euclidean spacetimes can be given in the first-order formulation of general relativity, without assuming the boundary to be isometrically embedded in Euclidean space and without adding infinite counter-terms. For illustrative examples of our approach, we evaluate the first-order action for the four-dimensional Euclidean Schwarzschild and NUT-charged spacetimes to derive the corresponding on-shell partition functions, and show that the correct thermodynamic quantities for the solutions are reproduced.Comment: 8 pages; v2: references added; minor corrections; v3: typos corrected in eqns (20) and (21); v4: substantially revised; addition of NUT-charged spacetimes; to appear in Classical and Quantum Gravit

Torelli theorem for the parabolic Deligne-Hitchin moduli space

We prove that, given the isomorphism class of the parabolic Deligne-Hitchin moduli space over a smooth projective curve, we can recover the isomorphism class of the curve and the parabolic points.Comment: 20 page

Automorphism group of the moduli space of parabolic bundles over a curve

We find the automorphism group of the moduli space of parabolic bundles on a smooth curve (with fixed determinant and system of weights). This group is generated by: automorphisms of the marked curve, tensoring with a line bundle, taking the dual, and Hecke transforms (using the filtrations given by the parabolic structure). A Torelli theorem for parabolic bundles with arbitrary rank and generic weights is also obtained. These results are extended to the classification of birational equivalences which are defined over "big" open subsets (3-birational maps, i.e. birational maps giving an isomorphism between open subsets with complement of codimension at least 3). Finally, an analysis of the stability chambers for the parabolic weights is performed in order to determine precisely when two moduli spaces of parabolic vector bundles with different parameters (curve, rank, determinant and weights) can be isomorphic.Comment: 99 page

Charged rotating black holes in higher dimensions

We use a recent implementation of the large $D$ expansion in order to construct the higher-dimensional Kerr-Newman black hole and also new charged rotating black bar solutions of the Einstein-Maxwell theory, all with rotation along a single plane. We describe the space of solutions, obtain their quasinormal modes, and study the appearance of instabilities as the horizons spread along the plane of rotation. Generically, the presence of charge makes the solutions less stable. Instabilities can appear even when the angular momentum of the black hole is small, as long as the charge is sufficiently large. We expect that, although our study is performed in the limit $D\to\infty$, the results provide a good approximation for charged rotating black holes at finite $D\geq 6$.Comment: 21 pages, 1 figur

Augmented reality usage for prototyping speed up

The first part of the article describes our approach for solution of this problem by means of Augmented Reality. The merging of the real world model and digital objects allows streamline the work with the model and speed up the whole production phase significantly. The main advantage of augmented reality is the possibility of direct manipulation with the scene using a portable digital camera. Also adding digital objects into the scene could be done using identification markers placed on the surface of the model. Therefore it is not necessary to work with special input devices and lose the contact with the real world model. Adjustments are done directly on the model. The key problem of outlined solution is the ability of identification of an object within the camera picture and its replacement with the digital object. The second part of the article is focused especially on the identification of exact position and orientation of the marker within the picture. The identification marker is generalized into the triple of points which represents a general plane in space. There is discussed the space identification of these points and the description of representation of their position and orientation be means of transformation matrix. This matrix is used for rendering of the graphical objects (e. g. in OpenGL and Direct3D).Comment: Keywords: augmented reality, prototyping, pose estimation, transformation matri