Radiative spacetimes approaching the Vaidya metric

We analyze a class of exact type II solutions of the Robinson-Trautman family which contain pure radiation and (possibly) a cosmological constant. It is shown that these spacetimes exist for any sufficiently smooth initial data, and that they approach the spherically symmetric Vaidya-(anti-)de Sitter metric. We also investigate extensions of the metric, and we demonstrate that their order of smoothness is in general only finite. Some applications of the results are outlined.Comment: 12 pages, 3 figure

A radiating dyon solution

We give a non-static exact solution of the Einstein-Maxwell equations (with null fluid), which is a non-static magnetic charge generalization to the Bonnor-Vaidya solution and describes the gravitational and electromagnetic fields of a nonrotating massive radiating dyon. In addition, using the energy-momentum pseudotensors of Einstein and Landau and Lifshitz we obtain the energy, momentum, and power output of the radiating dyon and find that both prescriptions give the same result.Comment: 9 pages, LaTe

Rocket flames

Among the important parameters which characterize the rocket flames are the (1) velocity, (2) pressure, (3) temperature of the exhaust gases and (4) the nature of chemical reactions in the flame of such gases. For the determination of these quantities ordinary methods fail because the flow of exhaust gases is supersonic in character. An introduction of a probe or any foreign body will create such strong disturbances in the supersonic flow that the readings of observing instruments will have no value. Spectroscopic methods are therefore eminently suitable because observations can be taken on the flame under running conditions

Entropy and Correlation Functions of a Driven Quantum Spin Chain

We present an exact solution for a quantum spin chain driven through its critical points. Our approach is based on a many-body generalization of the Landau-Zener transition theory, applied to fermionized spin Hamiltonian. The resulting nonequilibrium state of the system, while being a pure quantum state, has local properties of a mixed state characterized by finite entropy density associated with Kibble-Zurek defects. The entropy, as well as the finite spin correlation length, are functions of the rate of sweep through the critical point. We analyze the anisotropic XY spin 1/2 model evolved with a full many-body evolution operator. With the help of Toeplitz determinants calculus, we obtain an exact form of correlation functions. The properties of the evolved system undergo an abrupt change at a certain critical sweep rate, signaling formation of ordered domains. We link this phenomenon to the behavior of complex singularities of the Toeplitz generating function.Comment: 16 pgs, 7 fg

Quasinormal mode characterization of evaporating mini black holes

According to recent theoretical developments, it might be possible to produce mini black holes in the high energy experiments in the LHC at CERN. We propose here a model based on the $n$-dimensional Vaidya metric in double null coordinates for these decaying black holes. The associated quasinormal modes are considered. It is shown that only in the very last instants of the evaporation process the stationary regime for the quasinormal modes is broken, implying specific power spectra for the perturbations around these mini black-holes. From scattered fields one could recover, in principle, the black hole parameters as well as the number of extra dimensions. The still mysterious final fate of such objects should not alter significantly our main conclusions.Comment: v4: 9 pages, 3 figures. Minor correction

Vortex Induced Oscillations of Cylinders

This article submitted to the APS-DFD 2008 conference, accompanies the fluid dynamics video depicting the various orientational dynamics of a hinged cylinder suspended in a flow tank. The different behaviors displayed by the cylinder range from steady orientation to periodic oscillation and even autorotation. We illustrate these features using a phase diagram which captures the observed phenomena as a function of Reynolds number and reduced inertia. A hydrogen bubble flow visualization technique is also used to show vortex shedding structure in the cylinder's wake which results in these oscillations.Comment: 3 page

Relativistic Green functions in a plane wave gravitational background

We consider a massive relativistic particle in the background of a gravitational plane wave. The corresponding Green functions for both spinless and spin 1/2 cases, previously computed by A. Barducci and R. Giachetti \cite{Barducci3}, are reobtained here by alternative methods, as for example, the Fock-Schwinger proper-time method and the algebraic method. In analogy to the electromagnetic case, we show that for a gravitational plane wave background a semiclassical approach is also sufficient to provide the exact result, though the lagrangian involved is far from being a quadratic one.Comment: Last paper by Professor Arvind Narayan Vaidya, 18 pages, no figure

A Note on trapped Surfaces in the Vaidya Solution

The Vaidya solution describes the gravitational collapse of a finite shell of incoherent radiation falling into flat spacetime and giving rise to a Schwarzschild black hole. There has been a question whether closed trapped surfaces can extend into the flat region (whereas closed outer trapped surfaces certainly can). For the special case of self-similar collapse we show that the answer is yes, if and only if the mass function rises fast enough.Comment: 14 pages, 4 figures; minor polish added to version