Energy Localization Invariance of Tidal Work in General Relativity

It is well known that, when an external general relativistic (electric-type) tidal field E(t) interacts with the evolving quadrupole moment I(t) of an isolated body, the tidal field does work on the body (``tidal work'') -- i.e., it transfers energy to the body -- at a rate given by the same formula as in Newtonian theory: dW/dt = -1/2 E dI/dt. Thorne has posed the following question: In view of the fact that the gravitational interaction energy between the tidal field and the body is ambiguous by an amount of order E(t)I(t), is the tidal work also ambiguous by this amount, and therefore is the formula dW/dt = -1/2 E dI/dt only valid unambiguously when integrated over timescales long compared to that for I(t) to change substantially? This paper completes a demonstration that the answer is no; dW/dt is not ambiguous in this way. More specifically, this paper shows that dW/dt is unambiguously given by -1/2 E dI/dt independently of one's choice of how to localize gravitational energy in general relativity. This is proved by explicitly computing dW/dt using various gravitational stress-energy pseudotensors (Einstein, Landau-Lifshitz, Moller) as well as Bergmann's conserved quantities which generalize many of the pseudotensors to include an arbitrary function of position. A discussion is also given of the problem of formulating conservation laws in general relativity and the role played by the various pseudotensors.Comment: 15 pages, no figures, revtex. Submitted to Phys. Rev.

On the Kelvin Problem

The Kelvin problem of an isotropic elastic space subject to a concentrated load is solved in a manner that exploits the problem's built-in symmetries so as to determine in the first place the unique balanced and compatible stress field

A nonlinear theory for fibre-reinforced magneto-elastic rods

We derive a model for the finite motion of a magneto-elastic rod reinforced with isotropic (spherical) or anisotropic (ellipsoidal) inclusions. The particles are assumed weakly and uniformly magnetised, rigid and firmly embedded into the elastomeric matrix. We deduce closed form expressions of the quasi-static motion of the rod in terms of the external magnetic field and of the body forces. The dependences of the motion on the shape of the inclusions, their orientation, their anisotropic magnetic properties and the Young modulus of the matrix are analysed and discussed. Two case studies are presented in which the rod is used as an actuator suspended in a cantilever configuration. This work can foster new applications in the field of soft-actuators

A REBO-potential-based model for graphene bending by Γ\Gamma-convergence

An atomistic to continuum model for a graphene sheet undergoing bending is presented. Under the assumption that the atomic interactions are governed by a harmonic approximation of the 2nd-generation Brenner REBO (reactive empirical bond-order) potential, involving first, second and third nearest neighbors of any given atom, we determine the variational limit of the energy functionals. It turns out that the $\Gamma$-limit depends on the linearized mean and Gaussian curvatures. If some specific contributions in the atomic interaction are neglected, the variational limit is non-local

XMM-Newton survey of two Upper Scorpius regions

We study X-ray emission from young stars by analyzing deep XMM-Newton observations of two regions of the Upper Scorpius association, having an age of 5 Myr. Based on near infrared and optical photometry we identify 22 Upper Scorpius photometric members among the 224 detected X-ray sources. We derive coronal properties of Upper Scorpius stars by performing X-ray spectral and timing analysis. The study of four strong and isolated stellar flares allows us to derive the length of the flaring loops. Among the 22 Upper Scorpius stars, 13 are identified as Upper Scorpius photometric members for the first time. The sample includes 7 weak-line T Tauri stars and 1 classical T Tauri star, while the nature of the remaining sources is unknown. Except for the intermediate mass star HD 142578, all the detected USco sources are low mass stars of spectral type ranging from G to late M. The X-ray emission spectrum of the most intense Upper Scorpius sources indicates metal depleted plasma with temperature of ~10 MK, resembling the typical coronal emission of active main sequence stars. At least 59% of the detected members of the association have variable X-ray emission, and the flaring coronal structures appear shorter than or comparable to the stellar radii already at the Upper Scorpius age. We also find indication of increasing plasma metallicity (up to a factor 20) during strong flares. We identify a new galaxy cluster among the 224 X-ray source detected: the X-ray spectrum of its intra cluster medium indicates a redshift of 0.41+/-0.02.Comment: 27 pages, 15 postscript figures, accepted for publication in Astronomy and Astrophysics. A complete version of the paper, containing better qaulity figures and Appendices B & C, is available at http://www.astropa.unipa.it/Library/preprint.htm

The gravitational-wave memory effect

The nonlinear memory effect is a slowly-growing, non-oscillatory contribution to the gravitational-wave amplitude. It originates from gravitational waves that are sourced by the previously emitted waves. In an ideal gravitational-wave interferometer a gravitational-wave with memory causes a permanent displacement of the test masses that persists after the wave has passed. Surprisingly, the nonlinear memory affects the signal amplitude starting at leading (Newtonian-quadrupole) order. Despite this fact, the nonlinear memory is not easily extracted from current numerical relativity simulations. After reviewing the linear and nonlinear memory I summarize some recent work, including: (1) computations of the memory contribution to the inspiral waveform amplitude (thus completing the waveform to third post-Newtonian order); (2) the first calculations of the nonlinear memory that include all phases of binary black hole coalescence (inspiral, merger, ringdown); and (3) realistic estimates of the detectability of the memory with LISA.Comment: 11 pages, 2 figures; proceedings of the 8th Amaldi Conference on Gravitational Waves (New York, June 2009); accepted for publication in special issue of Classical and Quantum Gravit

Nonlinear gravitational-wave memory from binary black hole mergers

Some astrophysical sources of gravitational waves can produce a "memory effect," which causes a permanent displacement of the test masses in a freely falling gravitational-wave detector. The Christodoulou memory is a particularly interesting nonlinear form of memory that arises from the gravitational-wave stress-energy tensor's contribution to the distant gravitational-wave field. This nonlinear memory contributes a nonoscillatory component to the gravitational-wave signal at leading (Newtonian-quadrupole) order in the waveform amplitude. Previous computations of the memory and its detectability considered only the inspiral phase of binary black hole coalescence. Using an "effective-one-body" (EOB) approach calibrated to numerical relativity simulations, as well as a simple fully analytic model, the Christodoulou memory is computed for the inspiral, merger, and ringdown. The memory will be very difficult to detect with ground-based interferometers, but is likely to be observable in supermassive black hole mergers with LISA out to a redshift of two. Detection of the nonlinear memory could serve as an experimental test of the ability of gravity to "gravitate."Comment: 4 pages, 3 figures. v2: minor changes to text and references; published in ApJ Letter