On Generating Gravity Waves with Matter and Electromagnetic Waves

If a homogeneous plane light-like shell collides head-on with a homogeneous plane electromagnetic shock wave having a step-function profile then no backscattered gravitational waves are produced. We demonstrate, by explicit calculation, that if the matter is accompanied by a homogeneous plane electromagnetic shock wave with a step-function profile then backscattered gravitational waves appear after the collision.Comment: Latex file, 15 pages, accepted for publication in Physical Review

Refraction of dispersive shock waves

We study a dispersive counterpart of the classical gas dynamics problem of the interaction of a shock wave with a counter-propagating simple rarefaction wave often referred to as the shock wave refraction. The refraction of a one-dimensional dispersive shock wave (DSW) due to its head-on collision with the centred rarefaction wave (RW) is considered in the framework of defocusing nonlinear Schr\"odinger (NLS) equation. For the integrable cubic nonlinearity case we present a full asymptotic description of the DSW refraction by constructing appropriate exact solutions of the Whitham modulation equations in Riemann invariants. For the NLS equation with saturable nonlinearity, whose modulation system does not possess Riemann invariants, we take advantage of the recently developed method for the DSW description in non-integrable dispersive systems to obtain main physical parameters of the DSW refraction. The key features of the DSW-RW interaction predicted by our modulation theory analysis are confirmed by direct numerical solutions of the full dispersive problem.Comment: 45 pages, 23 figures, minor revisio

Collisions of Shock Waves in General Relativity

We show that the Nariai-Bertotti Petrov type D, homogeneous solution of Einstein's vacuum field equations with a cosmological constant describes the space-time in the interaction region following the head-on collision of two homogeneous, plane gravitational shock waves each initially traveling in a vacuum containing no cosmological constant. A shock wave in this context has a step function profile in contrast to an impulsive wave which has a delta function profile. Following the collision two light-like signals, each composed of a plane, homogeneous light-like shell of matter and a plane, homogeneous impulsive gravitational wave, travel away from each other and a cosmological constant is generated in the interaction region. Furthermore a plane, light-like signal consisting of an electromagnetic shock wave accompanying a gravitational shock wave is described with the help of two real parameters, one for each wave. The head-on collision of two such light-like signals is examined and we show that if a simple algebraic relation is satisfied between the two pairs of parameters associated with each incoming light-like signal then the space-time in the interaction region following the collision is a Bertotti space-time which is a homogeneous solution of the vacuum Einstein-Maxwell field equations with a cosmological constant.Comment: Latex file, 10 page

Radio Galaxy NGC 1265 unveils the Accretion Shock onto the Perseus Galaxy Cluster

We present a consistent 3D model for the head-tail radio galaxy NGC 1265 that explains the complex radio morphology and spectrum by a past passage of the galaxy and radio bubble through a shock wave. Using analytical solutions to the full Riemann problem and hydrodynamical simulations, we study how this passage transformed the plasma bubble into a toroidal vortex ring. Adiabatic compression of the aged electron population causes it to be energized and to emit low-surface brightness and steep-spectrum radio emission. The large infall velocity of NGC 1265 and the low Faraday rotation measure values and variance of the jet strongly argue that this transformation was due to the accretion shock onto Perseus situated roughly at R_200. Estimating the volume change of the radio bubble enables inferring a shock Mach number of M = 4.2_{-1.2}^{+0.8}, a density jump of 3.4_{-0.4}^{+0.2}, a temperature jump of 6.3_{-2.7}^{+2.5}, and a pressure jump of 21.5 +/- 10.5 while allowing for uncertainties in the equation of state of the radio plasma and volume of the torus. Extrapolating X-ray profiles, we obtain upper limits on the gas temperature and density in the infalling warm-hot intergalactic medium of kT < 0.4 keV and n < 5e-5 / cm^3. The orientation of the ellipsoidally shaped radio torus in combination with the direction of the galaxy's head and tail in the plane of the sky is impossible to reconcile with projection effects. Instead, this argues for post-shock shear flows that have been caused by curvature in the shock surface with a characteristic radius of 850 kpc. The energy density of the shear flow corresponds to a turbulent-to-thermal energy density of 14%. The shock-injected vorticity might be important in generating and amplifying magnetic fields in galaxy clusters. Future LOFAR observations of head-tail galaxies can be complementary probes of accretion shocks onto galaxy clusters.Comment: 14 pages, 4 figures, ApJ, in print; v3: typos corrected to match the published version; v2: improved presentation, added 2D numerical simulations and exact solution to the 1D Riemann problem of a shock overrunning a spherical bubble that gets transformed into a vortex rin

Self-similar ultra-relativistic jetted blast wave

Following a suggestion that a directed relativistic explosion may have a universal intermediate asymptotic, we derive a self-similar solution for an ultra-relativistic jetted blast wave. The solution involves three distinct regions: an approximately paraboloid head where the Lorentz factor $\gamma$ exceeds $\sim1/2$ of its maximal, nose value; a geometrically self-similar, expanding envelope slightly narrower than a paraboloid; and an axial core in which the (cylindrically, henceforth) radial flow $u$ converges inward towards the axis. Most ($\sim 80\%$) of the energy lies well beyond the leading, head region. Here, a radial cross section shows a maximal $\gamma$ (separating the core and the envelope), a sign reversal in $u$, and a minimal $\gamma$, at respectively $\sim 1/6$, $\sim1/4$, and $\sim3/4$ of the shock radius. The solution is apparently unique, and approximately agrees with previous simulations, of different initial conditions, that resolved the head. This suggests that unlike a spherical relativistic blast wave, our solution is an attractor, and may thus describe directed blast waves such as in the external shock phase of a $\gamma$-ray burst.Comment: Revised version (discussion added) accepted by Ap

Effects of Spaceflight on the Modulation of Shock Wave Transmission to the Head During Locomotion

The ability to maintain gaze stability during locomotion requires the normal function and integration of the vestibulo-ocular reflex, vestibulo and cervico-colic reflexes with effective coordination between the trunk and lower limb segments. One hypothesized constraint on the coordination between segments during locomotion is the regulation of energy flow or shock wave transmissions through the body at high impact phases with the support surface. Allowing these excessive transmissions of energy to the head may result in compromised gaze stability during locomotion. The aim of this study was to determine the effects of microgravity adaptation on the transmissibility of shock wave to the head during locomotion. Before and after spaceflight (3-6 months) six subjects walked (6.4 km/h) on a motorized treadmill while fixating their gaze on a centrally located earth-fixed target. Triaxial accelerometers mounted on the shank and the head measured the shock wave transmission through the body during locomotion. During postflight locomotion the peak shock at the shank and the head were significantly reduced, however, the ratio of peak head to shank shock was significantly increased. These results indicate that exposure to spaceflight causes adaptive modifications in the short-latency vestibulospinal head stabilization responses required to compensate for the rapid shocks transmitted to the head during locomotion. This study was supported by NASA

Black Hole Production from High Energy Scattering in AdS/CFT

In this article we show how to set up initial states in ${\cal N} =4$ SYM theory that correspond to high energy graviton collisions, leading to black hole formation in $AdS_5\times S^5$. For this purpose, we study states in the gauge theory that are dual to graviton wavepackets localized at the center of $AdS_5$, and carrying large angular momentum along the $S^5$. These states are created by exciting only the s-wave mode of one of the complex adjoint scalars of SYM. For a single graviton, the state is 1/2 BPS and one can show that it is dual to a linearized 1/2 BPS geometry in the bulk. Exploiting this dictionary, we show how to localize the particle's wavefunciton so that the dual linearized metric has the form of a Aichelburg-Sexl shock wave. One can then put two such shock waves into a head-on collision, which is known to produce a trapped surface. Finally, we discuss the prospect of studying graviton scattering directly at strong coupling in the gauge theory using a reduced model of matrix quantum mechanics.Comment: 11 pages, revtex format, no figure

Radiation from a D-dimensional collision of shock waves: a remarkably simple fit formula

Recently, in arXiv:1105.2298 [hep-th], we have estimated the energy radiated in the head-on collision of two equal D-dimensional Aichelburg-Sexl shock waves, for even D, by solving perturbatively, to first order, the Einstein equations in the future of the collision. Here, we report on the solution for the odd D case. After finding the wave forms, we extract the estimated radiated energy for D=5,7,9 and 11 and unveil a remarkably simple pattern, given the complexity of the framework: (for all D) the estimated fraction of radiated energy matches the analytic expression 1/2-1/D, within the numerical error (less than 0.1%). Both this fit and the apparent horizon bound converge to 1/2 as D goes to infinity.Comment: 3 pages, 3 figures, Accepted in Physical Review Letter

Pairwise wave interactions in ideal polytropic gases

We consider the problem of resolving all pairwise interactions of shock waves, contact waves, and rarefaction waves in 1-dimensional flow of an ideal polytropic gas. Resolving an interaction means here to determine the types of the three outgoing (backward, contact, and forward) waves in the Riemann problem defined by the extreme left and right states of the two incoming waves, together with possible vacuum formation. This problem has been considered by several authors and turns out to be surprisingly involved. For each type of interaction (head-on, involving a contact, or overtaking) the outcome depends on the strengths of the incoming waves. In the case of overtaking waves the type of the reflected wave also depends on the value of the adiabatic constant. Our analysis provides a complete breakdown and gives the exact outcome of each interaction.Comment: 39 page