Gravitational wave recoils in non-axisymmetric Robinson-Trautman spacetimes

We examine the gravitational wave recoil waves and the associated net kick velocities in non-axisymmetric Robinson-Trautman spacetimes. We use characteristic initial data for the dynamics corresponding to non-head-on collisions of black holes. We make a parameter study of the kick distributions, corresponding to an extended range of the incidence angle $\rho_0$ in the initial data. For the range of $\rho_0$ examined ($3^{\circ} \leq \rho_0 \leq 110^{\circ}$) the kick distributions as a function of the symmetric mass parameter $\eta$ satisfy a law obtained from an empirical modification of the Fitchett law, with a parameter $C$ that accounts for the non-zero net gravitational momentum wave fluxes for the equal mass case. The law fits accurately the kick distributions for the range of $\rho_0$ examined, with a rms normalized error of the order of $5 \%$. For the equal mass case the nonzero net gravitational wave momentum flux increases as $\rho_0$ increases, up to $\rho_0 \simeq 55^{\circ}$ beyond which it decreases. The maximum net kick velocity is about $190 {\rm km/s}$ for for the boost parameter considered. For $\rho_0 \geq 50^{\circ}$ the distribution is a monotonous function of $\eta$. The angular patterns of the gravitational waves emitted are examined. Our analysis includes the two polarization modes present in wave zone curvature.Comment: 10 pages, 5 figures. arXiv admin note: substantial text overlap with arXiv:1403.4581, arXiv:1202.1271, arXiv:1111.122

Gravitational Wave Emission and Mass Extraction from a Perturbed Schwarzschild Black Hole (continue)

A relativistic model for the emission of gravitational waves from an initially unperturbed Schwarzschild black hole, or spherical collapsing configuration, is completely integrated. The model consists basically of gravitational perturbations of the Robinson-Trautman type on the Schwarzschild spacetime. In our scheme of perturbation, gravitational waves may extract mass from the collapsing configuration. Robinson-Trautmann perturbations also include another mode of emission of mass, which we denote shell emission mode: in the equatorial plane of the configuration, a timelike $(1+2)$ shell of matter may be present, whose stress-energy tensor is modelled by neutrinos and strings emitted radially on the shell; no gravitational waves are present in this mode. The invariant characterization of gravitational wave perturbations and of the gravitational wave zone is made through the analysis of the structure of the curvature tensor and the use of the Peeling Theorem.Comment: 26 pages, LaTex, no figure

Experimental realization of the Yang-Baxter Equation via NMR interferometry

The Yang-Baxter equation is an important tool in theoretical physics, with many applications in different domains that span from condensed matter to string theory. Recently, the interest on the equation has increased due to its connection to quantum information processing. It has been shown that the Yang-Baxter equation is closely related to quantum entanglement and quantum computation. Therefore, owing to the broad relevance of this equation, besides theoretical studies, it also became significant to pursue its experimental implementation. Here, we show an experimental realization of the Yang-Baxter equation and verify its validity through a Nuclear Magnetic Resonance (NMR) interferometric setup. Our experiment was performed on a liquid state Iodotrifluoroethylene sample which contains molecules with three qubits. We use Controlled-transfer gates that allow us to build a pseudo-pure state from which we are able to apply a quantum information protocol that implements the Yang-Baxter equation.Comment: 10 pages and 6 figure