Related papers: On homogeneous plane waves
We show that a simply connected Riemannian homogeneous space M which admits a totally geodesic hypersurface F is isometric to either (a) the Riemannian product of a space of constant curvature and a homogeneous space, or (b) the warped…
We analyze the coset model $(E_2^c \ti E_2^c)/E_2^c$ and construct a class of exact string vacua which describe plane gravitational waves and their duals, generalizing the plane wave background found by Nappi and Witten. In particular, the…
The covariant understanding of dispersion relations as level sets of Hamilton functions on phase space enables us to derive the most general dispersion relation compatible with homogeneous and isotropic spacetimes. We use this concept to…
In this paper we develop new methods of study of generalized normal homogeneous Riemannian manifolds. In particular, we obtain a complete classification of generalized normal homogeneous Riemannian metrics on spheres. We prove that for any…
We describe degenerations of projective plane curves to curves containing a fixed line $l$ as a component, and show that $H^1({\overline V}_{n,d,m}, {\Cal O} (r))=0, r \in{\Bbb Z}$, where $V_{n,d,m}\subset {\Bbb P}^N (N = n(n+3)/2)$ is the…
We present a conformal field theory which desribes a homogeneous four dimensional Lorentz-signature space-time. The model is an ungauged WZW model based on a central extension of the Poincar\'e algebra. The central charge of this theory is…
We show that a Lorentzian homogeneous space admitting a homogeneous structure of type T1 + T3 is either a (locally) symmetric space or a singular homogeneous plane wave.
We derive the effects of a non-zero cosmological constant $\Lambda$ on gravitational wave propagation in the linearized approximation of general relativity. In this approximation we consider the situation where the metric can be written as…
Conformal field theories play a central role in modern theoretical physics with many applications to the understanding of phase transitions, gauge theories and even the quantum physics of gravity, through Maldacena's celebrated holographic…
The behaviour of a "test" electromagnetic field in the background of an exact gravitational plane wave is investigated in the framework of Einstein's general relativity. We have expressed the general solution to the de Rham equations as a…
Usually, the description of tangent spaces to the Teichmueller space $\mathscr{T}(\Sigma_{g})$ of a compact Riemann surface $\Sigma_{g}$ of genus $g \geq 2$ (which we can identify with the quotient space $\mathbb{H}^{2} / \Gamma_{g}$ of the…
We consider the three-dimensional Heisenberg group, equipped with any left-invariant metric, either Lorentzian or Riemannian. We completely classify their affine vector fields and investigate their relationship with Killing vector fields…
This paper studies the Bondi-Metzner-Sachs group in homogeneous projective coordinates, because it is then possible to write all transformations of such a group in a manifestly linear way. The 2-sphere metric, Bondi-Metzner-Sachs metric,…
In this paper we derive homogeneous vacuum plane-wave solutions to Einstein's field equations in 4+1 dimensions. The solutions come in five different types of which three generalise the vacuum plane-wave solutions in 3+1 dimensions to the…
Particle physics has for some time made extensive use of extended field configuations such as solitons, instantons, and sphalerons. However, no direct use has yet been made of the quite extensive literature on ``localized wave''…
We prove that if $P,\mathcal{L}$ are finite sets of $\delta$-separated points and lines in $\mathbb{R}^{2}$, the number of $\delta$-incidences between $P$ and $\mathcal{L}$ is no larger than a constant times $$|P|^{2/3}|\mathcal{L}|^{2/3}…
{\sl A Hamiltonian framework for 2+1 dimensional gravity coupled with matter (satisfying positive energy conditions) is considered in the asymptotically flat context. It is shown that the total energy of the system is non-negative,…
We identify a region of F(R)=R^{N} gravity without external sources which is isometric to the spacetime of colliding plane waves (CPW). From the derived curvature sources, N (N>1) measures the strength (i.e. the charge) of the source. The…
We explain how to apply techniques from integrable systems to construct $2k$-soliton homoclinic wave maps from the periodic Minkowski space $S^1\times R^1$ to a compact Lie group, and more generally to a compact symmetric space. We give a…
All classes of spatially homogeneous space-time models in the generalized scalar-tensor theory of gravity are found that allow the integration of the equations of motion of test particles and the eikonal equation by the method of %complete…