Orbital evolution of a test particle around a black hole: higher-order corrections

We study the orbital evolution of a radiation-damped binary in the extreme mass ratio limit, and the resulting waveforms, to one order beyond what can be obtained using the conservation laws approach. The equations of motion are solved perturbatively in the mass ratio (or the corresponding parameter in the scalar field toy model), using the self force, for quasi-circular orbits around a Schwarzschild black hole. This approach is applied for the scalar model. Higher-order corrections yield a phase shift which, if included, may make gravitational-wave astronomy potentially highly accurate.Comment: 4 pages, 3 Encapsulated PostScript figure

Quantized Electric Multipole Insulators

In this article we extend the celebrated Berry-phase formulation of electric polarization in crystals to higher electric multipole moments. We determine the necessary conditions under which, and minimal models in which, the quadrupole and octupole moments are topologically quantized electromagnetic observables. Such systems exhibit gapped boundaries that are themselves lower-dimensional topological phases. Furthermore, they manifest topologically protected corner states carrying fractional charge, i.e., fractionalization at the boundary of the boundary. To characterize these new insulating phases of matter, we introduce a new paradigm whereby `nested' Wilson loops give rise to a large number of new topological invariants that have been previously overlooked. We propose three realistic experimental implementations of this new topological behavior that can be immediately tested.Comment: Main text: 9 pages, 6 figures. Supplementary Material: 37 pages, 15 figures. Submitted on Jul 25, 201

AGAPEROS: Searching for variable stars in the LMC Bar with the Pixel Method. I. Detection, astrometry and cross-identification

We extend the work developed in previous papers on microlensing with a selection of variable stars. We use the Pixel Method to select variable stars on a set of 2.5 x 10**6 pixel light curves in the LMC Bar presented elsewhere. The previous treatment was done in order to optimise the detection of long timescale variations (larger than a few days) and we further optimise our analysis for the selection of Long Timescale and Long Period Variables (LT&LPV). We choose to perform a selection of variable objects as comprehensive as possible, independent of periodicity and of their position on the colour magnitude diagram. We detail the different thresholds successively applied to the light curves, which allow to produce a catalogue of 632 variable objects. We present a table with the coordinate of each variable, its EROS magnitudes at one epoch and an indicator of blending in both colours, together with a finding chart. A cross-correlation with various catalogues shows that 90% of those variable objects were undetected before, thus enlarging the sample of LT&LPV previously known in this area by a factor of 10. Due to the limitations of both the Pixel Method and the data set, additional data -- namely a longer baseline and near infrared photometry -- are required to further characterise these variable stars, as will be addressed in subsequent papers.Comment: 11 pages with 10 figure

Extreme Mass Ratio Binary: Radiation reaction and gravitational waveform

For a successful detection of gravitational waves by LISA, it is essential to construct theoretical waveforms in a reliable manner. We discuss gravitational waves from an extreme mass ratio binary system which is expected to be a promising target of the LISA project. The extreme mass ratio binary is a binary system of a supermassive black hole and a stellar mass compact object. As the supermassive black hole dominates the gravitational field of the system, we suppose that the system might be well approximated by a metric perturbation of a Kerr black hole. We discuss a recent theoretical progress in calculating the waveforms from such a system.Comment: Classical and Quantum Gravity 22 (2005) S375-S379, Proceedings for 5th International LISA Symposiu

Localizing coalescing massive black hole binaries with gravitational waves

Massive black hole binary coalescences are prime targets for space-based gravitational wave (GW) observatories such as {\it LISA}. GW measurements can localize the position of a coalescing binary on the sky to an ellipse with a major axis of a few tens of arcminutes to a few degrees, depending on source redshift, and a minor axis which is $2 - 4$ times smaller. Neglecting weak gravitational lensing, the GWs would also determine the source's luminosity distance to better than percent accuracy for close sources, degrading to several percent for more distant sources. Weak lensing cannot, in fact, be neglected and is expected to limit the accuracy with which distances can be fixed to errors no less than a few percent. Assuming a well-measured cosmology, the source's redshift could be inferred with similar accuracy. GWs alone can thus pinpoint a binary to a three-dimensional ``pixel'' which can help guide searches for the hosts of these events. We examine the time evolution of this pixel, studying it at merger and at several intervals before merger. One day before merger, the major axis of the error ellipse is typically larger than its final value by a factor of $\sim 1.5-6$. The minor axis is larger by a factor of $\sim 2-9$, and, neglecting lensing, the error in the luminosity distance is larger by a factor of $\sim 1.5-7$. This large change over a short period of time is due to spin-induced precession, which is strongest in the final days before merger. The evolution is slower as we go back further in time. For $z = 1$, we find that GWs will localize a coalescing binary to within $\sim 10\ \mathrm{deg}^2$ as early as a month prior to merger and determine distance (and hence redshift) to several percent.Comment: 30 pages, 10 figures, 5 tables. Version published in Ap

An octonionic formulation of the M-theory algebra

We give an octonionic formulation of the N = 1 supersymmetry algebra in D = 11, including all brane charges. We write this in terms of a novel outer product, which takes a pair of elements of the division algebra A and returns a real linear operator on A. More generally, with this product comes the power to rewrite any linear operation on R^n (n = 1,2,4,8) in terms of multiplication in the n-dimensional division algebra A. Finally, we consider the reinterpretation of the D = 11 supersymmetry algebra as an octonionic algebra in D = 4 and the truncation to division subalgebras

A magic pyramid of supergravities

By formulating N = 1, 2, 4, 8, D = 3, Yang-Mills with a single Lagrangian and single set of transformation rules, but with fields valued respectively in R,C,H,O, it was recently shown that tensoring left and right multiplets yields a Freudenthal-Rosenfeld-Tits magic square of D = 3 supergravities. This was subsequently tied in with the more familiar R,C,H,O description of spacetime to give a unified division-algebraic description of extended super Yang-Mills in D = 3, 4, 6, 10. Here, these constructions are brought together resulting in a magic pyramid of supergravities. The base of the pyramid in D = 3 is the known 4x4 magic square, while the higher levels are comprised of a 3x3 square in D = 4, a 2x2 square in D = 6 and Type II supergravity at the apex in D = 10. The corresponding U-duality groups are given by a new algebraic structure, the magic pyramid formula, which may be regarded as being defined over three division algebras, one for spacetime and each of the left/right Yang-Mills multiplets. We also construct a conformal magic pyramid by tensoring conformal supermultiplets in D = 3, 4, 6. The missing entry in D = 10 is suggestive of an exotic theory with G/H duality structure F4(4)/Sp(3) x Sp(1).Comment: 30 pages, 6 figures. Updated to match published version. References and comments adde

Super Yang-Mills, division algebras and triality

We give a unified division algebraic description of (D=3, N=1,2,4,8), (D=4, N=1,2,4), (D=6, N=1,2) and (D=10, N=1) super Yang-Mills theories. A given (D=n+2, N) theory is completely specified by selecting a pair (A_n, A_{nN}) of division algebras, A_n, A_{nN} = R, C, H, O, where the subscripts denote the dimension of the algebras. We present a master Lagrangian, defined over A_{nN}-valued fields, which encapsulates all cases. Each possibility is obtained from the unique (O, O) (D=10, N=1) theory by a combination of Cayley-Dickson halving, which amounts to dimensional reduction, and removing points, lines and quadrangles of the Fano plane, which amounts to consistent truncation. The so-called triality algebras associated with the division algebras allow for a novel formula for the overall (spacetime plus internal) symmetries of the on-shell degrees of freedom of the theories. We use imaginary A_{nN}-valued auxiliary fields to close the non-maximal supersymmetry algebra off-shell. The failure to close for maximally supersymmetric theories is attributed directly to the non-associativity of the octonions.Comment: 24 pages, 2 figures. Updated to match published version. References adde