1,212 research outputs found
Distorted 5-dimensional vacuum black hole
In this paper we study how the distortion generated by a static and neutral
distribution of external matter affects a 5-dimensional
Schwarzschild-Tangherlini black hole. A solution representing a particular
class of such distorted black holes admits an RxU(1)xU(1) isometry group. We
show that there exists a certain duality transformation between the black hole
horizon and a stretched singularity surfaces. The space-time near the distorted
black hole singularity has the same topology and Kasner exponents as those of a
5-dimensional Schwarzschild-Tangherlini black hole. We calculate the maximal
proper time of free fall of a test particle from the distorted black hole
horizon to its singularity and find that, depending on the distortion, it can
be less, equal to, or greater than that of a Schwarzschild-Tangherlini black
hole of the same horizon area. This implies that due to the distortion, the
singularity of a Schwarzschild-Tangherlini black hole can come close to its
horizon. A relation between the Kretschmann scalar calculated on the horizon of
a 5-dimensional static, asymmetric, distorted black hole and the trace of the
square of the Ricci tensor of the horizon surface is derived.Comment: 20 pages, 9 figure
The rolling problem: overview and challenges
In the present paper we give a historical account -ranging from classical to
modern results- of the problem of rolling two Riemannian manifolds one on the
other, with the restrictions that they cannot instantaneously slip or spin one
with respect to the other. On the way we show how this problem has profited
from the development of intrinsic Riemannian geometry, from geometric control
theory and sub-Riemannian geometry. We also mention how other areas -such as
robotics and interpolation theory- have employed the rolling model.Comment: 20 page
A-twisted Landau-Ginzburg models
In this paper we discuss correlation functions in certain A-twisted
Landau-Ginzburg models. Although B-twisted Landau-Ginzburg models have been
discussed extensively in the literature, virtually no work has been done on
A-twisted theories. In particular, we study examples of Landau-Ginzburg models
over topologically nontrivial spaces - not just vector spaces - away from
large-radius limits, so that one expects nontrivial curve corrections. By
studying examples of Landau-Ginzburg models in the same universality class as
nonlinear sigma models on nontrivial Calabi-Yaus, we obtain nontrivial tests of
our methods as well as a physical realization of some simple examples of
virtual fundamental class computations.Comment: 64 Pages, LaTe
On Spacetimes with Constant Scalar Invariants
We study Lorentzian spacetimes for which all scalar invariants constructed
from the Riemann tensor and its covariant derivatives are constant (
spacetimes). We obtain a number of general results in arbitrary dimensions. We
study and construct warped product spacetimes and higher-dimensional
Kundt spacetimes. We show how these spacetimes can be constructed from
locally homogeneous spaces and spacetimes. The results suggest a number
of conjectures. In particular, it is plausible that for spacetimes that
are not locally homogeneous the Weyl type is , , or , with any
boost weight zero components being constant. We then consider the
four-dimensional spacetimes in more detail. We show that there are severe
constraints on these spacetimes, and we argue that it is plausible that they
are either locally homogeneous or that the spacetime necessarily belongs to the
Kundt class of spacetimes, all of which are constructed. The
four-dimensional results lend support to the conjectures in higher dimensions.Comment: 25 pages, 1 figure, v2: minor changes throughou
Generalizing Galileons
The Galileons are a set of terms within four-dimensional effective field
theories, obeying symmetries that can be derived from the dynamics of a
3+1-dimensional flat brane embedded in a 5-dimensional Minkowski Bulk. These
theories have some intriguing properties, including freedom from ghosts and a
non-renormalization theorem that hints at possible applications in both
particle physics and cosmology. In this brief review article, we will summarize
our attempts over the last year to extend the Galileon idea in two important
ways. We will discuss the effective field theory construction arising from
co-dimension greater than one flat branes embedded in a flat background - the
multiGalileons - and we will then describe symmetric covariant versions of the
Galileons, more suitable for general cosmological applications. While all these
Galileons can be thought of as interesting four-dimensional field theories in
their own rights, the work described here may also make it easier to embed them
into string theory, with its multiple extra dimensions and more general
gravitational backgrounds.Comment: 16 pages; invited brief review article for a special issue of
Classical and Quantum Gravity. Submitted to CQ
A Low-Dimensional Representation for Robust Partial Isometric Correspondences Computation
Intrinsic isometric shape matching has become the standard approach for pose
invariant correspondence estimation among deformable shapes. Most existing
approaches assume global consistency, i.e., the metric structure of the whole
manifold must not change significantly. While global isometric matching is well
understood, only a few heuristic solutions are known for partial matching.
Partial matching is particularly important for robustness to topological noise
(incomplete data and contacts), which is a common problem in real-world 3D
scanner data. In this paper, we introduce a new approach to partial, intrinsic
isometric matching. Our method is based on the observation that isometries are
fully determined by purely local information: a map of a single point and its
tangent space fixes an isometry for both global and the partial maps. From this
idea, we develop a new representation for partial isometric maps based on
equivalence classes of correspondences between pairs of points and their
tangent spaces. From this, we derive a local propagation algorithm that find
such mappings efficiently. In contrast to previous heuristics based on RANSAC
or expectation maximization, our method is based on a simple and sound
theoretical model and fully deterministic. We apply our approach to register
partial point clouds and compare it to the state-of-the-art methods, where we
obtain significant improvements over global methods for real-world data and
stronger guarantees than previous heuristic partial matching algorithms.Comment: 17 pages, 12 figure
Mathematical Tools for Calculation of the Effective Action in Quantum Gravity
We review the status of covariant methods in quantum field theory and quantum
gravity, in particular, some recent progress in the calculation of the
effective action via the heat kernel method. We study the heat kernel
associated with an elliptic second-order partial differential operator of
Laplace type acting on smooth sections of a vector bundle over a Riemannian
manifold without boundary. We develop a manifestly covariant method for
computation of the heat kernel asymptotic expansion as well as new algebraic
methods for calculation of the heat kernel for covariantly constant background,
in particular, on homogeneous bundles over symmetric spaces, which enables one
to compute the low-energy non-perturbative effective action.Comment: 71 pages, 2 figures, submitted for publication in the Springer book
(in preparation) "Quantum Gravity", edited by B. Booss-Bavnbek, G. Esposito
and M. Lesc
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