Formation of trapped surfaces for the spherically symmetric Einstein-Vlasov system

We consider the spherically symmetric, asymptotically flat, non-vacuum Einstein equations, using as matter model a collisionless gas as described by the Vlasov equation. We find explicit conditions on the initial data which guarantee the formation of a trapped surface in the evolution which in particular implies that weak cosmic censorship holds for these data. We also analyze the evolution of solutions after a trapped surface has formed and we show that the event horizon is future complete. Furthermore we find that the apparent horizon and the event horizon do not coincide. This behavior is analogous to what is found in certain Vaidya spacetimes. The analysis is carried out in Eddington-Finkelstein coordinates.Comment: 2

On the Einstein-Vlasov system with hyperbolic symmetry

It is shown that a spacetime with collisionless matter evolving from data on a compact Cauchy surface with hyperbolic symmetry can be globally covered by compact hypersurfaces on which the mean curvature is constant and by compact hypersurfaces on which the area radius is constant. Results for the related cases of spherical and plane symmetry are reviewed and extended. The prospects of using the global time coordinates obtained in this way to investigate the global geometry of the spacetimes concerned are discusse

Global existence for the spherically symmetric Einstein-Vlasov system with outgoing matter

We prove a new global existence result for the asymptotically flat, spherically symmetric Einstein-Vlasov system which describes in the framework of general relativity an ensemble of particles which interact by gravity. The data are such that initially all the particles are moving radially outward and that this property can be bootstrapped. The resulting non-vacuum spacetime is future geodesically complete.Comment: 16 page

Existence of axially symmetric static solutions of the Einstein-Vlasov system

We prove the existence of static, asymptotically flat non-vacuum spacetimes with axial symmetry where the matter is modeled as a collisionless gas. The axially symmetric solutions of the resulting Einstein-Vlasov system are obtained via the implicit function theorem by perturbing off a suitable spherically symmetric steady state of the Vlasov-Poisson system.Comment: 32 page

On the steady states of the spherically symmetric Einstein-Vlasov system

Using both numerical and analytical tools we study various features of static, spherically symmetric solutions of the Einstein-Vlasov system. In particular, we investigate the possible shapes of their mass-energy density and find that they can be multi-peaked, we give numerical evidence and a partial proof for the conjecture that the Buchdahl inequality $\sup_{r > 0} 2 m(r)/r < 8/9$, $m(r)$ the quasi-local mass, holds for all such steady states--both isotropic {\em and} anisotropic--, and we give numerical evidence and a partial proof for the conjecture that for any given microscopic equation of state--both isotropic {\em and} anisotropic--the resulting one-parameter family of static solutions generates a spiral in the radius-mass diagram.Comment: 34 pages, 18 figures, LaTe

Extended Rein-Sehgal model for tau lepton production

The polarization density matrix formalism is employed to include the final lepton mass and spin into the popular model by Rein and Sehgal for single pion neutrinoproduction. We investigate the effect of the $\tau$ lepton mass on the differential cross sections. The lepton polarization evaluated within the extended RS model is compared against that follows from the single resonance production model based upon the Rarita-Schwinger formalism with phenomenological transition form factors.Comment: Contribution to the 3rd International Workshop on Neutrino-Nucleus Interactions in the Few-GeV Region, 17-21 March, Gran Sasso (Italy

A numerical investigation of the stability of steady states and critical phenomena for the spherically symmetric Einstein-Vlasov system

The stability features of steady states of the spherically symmetric Einstein-Vlasov system are investigated numerically. We find support for the conjecture by Zeldovich and Novikov that the binding energy maximum along a steady state sequence signals the onset of instability, a conjecture which we extend to and confirm for non-isotropic states. The sign of the binding energy of a solution turns out to be relevant for its time evolution in general. We relate the stability properties to the question of universality in critical collapse and find that for Vlasov matter universality does not seem to hold.Comment: 29 pages, 10 figure

Global existence and asymptotic behaviour in the future for the Einstein-Vlasov system with positive cosmological constant

The behaviour of expanding cosmological models with collisionless matter and a positive cosmological constant is analysed. It is shown that under the assumption of plane or hyperbolic symmetry the area radius goes to infinity, the spacetimes are future geodesically complete, and the expansion becomes isotropic and exponential at late times. This proves a form of the cosmic no hair theorem in this class of spacetimes

Disturbance Observer: Design and Flight Test of a Large Envelope Flight Controller

A new flight controller was evaluated through piloted simulation and flight test conducted at the USAF Test Pilot School. The controller, commonly called a disturbance observer, uses inertial sensor feedback routed through a simple control architecture that acts to force the desired response while rejecting sensor noise and atmospheric disturbances. The investigation included both handling qualities testing in the Octonian simulator at the Air Force Research Laboratories Air Vehicle Directorate, and initial flight test conducted as part of a Test Management Project at the USAF TPS. Simulation produced positive results with desired performance throughout a wide flight envelope. In addition, the desired response of the aircraft was easily modified by changing variables within the controller. Flight test was conducted on the Variable-stability In-flight Simulator and Test Aircraft (VISTA). Twelve test sorties totaling 16.4 flight hours were conducted and culminated in multiple landings at Edwards AFB, CA. Time delay inherent in the VISTA resulted in the requirement to gain down the control surface command signal. Sensor noise was amplified and caused a control surface ‘buzz.” Flying qualities exhibited lower damping and frequency than ‘desired’ yet were consistent throughout a larger flight envelope. Post flight analysis resulted in the determination of ways to reduce the noise causing the ‘buzz’ and improve the flying qualities by adjusting the controller’s ‘desired dynamics.