Higher-order-in-spin interaction Hamiltonians for binary black holes from Poincar\'e invariance

The fulfillment of the space-asymptotic Poincar\'e algebra is used to derive new higher-order-in-spin interaction Hamiltonians for binary black holes in the Arnowitt-Deser-Misner canonical formalism almost completing the set of the formally $1/c^4$ spin-interaction Hamiltonians involving nonlinear spin terms. To linear order in $G$, the expressions for the $S^3p$- and the $S^2p^2$-Hamiltonians are completed. It is also shown that there are no quartic nonlinear $S^4$-Hamiltonians to linear order in $G$.Comment: REVTeX4, 14 pages; center-of-mass-vector corrected Eq. (2.25) and modified coefficients of the Hamiltonian Eq. (7.3) and corresponding source terms Eqs. (7.5) and (7.6) following hereof; version to appear in Phys Rev

Spin-squared Hamiltonian of next-to-leading order gravitational interaction

The static, i.e., linear momentum independent, part of the next-to-leading order (NLO) gravitational spin(1)-spin(1) interaction Hamiltonian within the post-Newtonian (PN) approximation is calculated from a 3-dim. covariant ansatz for the Hamilton constraint. All coefficients in this ansatz can be uniquely fixed for black holes. The resulting Hamiltonian fits into the canonical formalism of Arnowitt, Deser, and Misner (ADM) and is given in their transverse-traceless (ADMTT) gauge. This completes the recent result for the momentum dependent part of the NLO spin(1)-spin(1) ADM Hamiltonian for binary black holes (BBH). Thus, all PN NLO effects up to quadratic order in spin for BBH are now given in Hamiltonian form in the ADMTT gauge. The equations of motion resulting from this Hamiltonian are an important step toward more accurate calculations of templates for gravitational waves.Comment: REVTeX4, 10 pages, v2: minor improvements in the presentation, v3: added omission in Eq. (4) and corrected coefficients in the result, Eq. (9); version to appear in Phys. Rev.

Higher-order-in-spin interaction Hamiltonians for binary black holes from source terms of Kerr geometry in approximate ADM coordinates

The Kerr metric outside the ergosphere is transformed into ADM coordinates up to the orders $1/r^4$ and $a^2$, respectively in radial coordinate $r$ and reduced angular momentum variable $a$, starting from the Kerr solution in quasi-isotropic as well as harmonic coordinates. The distributional source terms for the approximate solution are calculated. To leading order in linear momenta, higher-order-in-spin interaction Hamiltonians for black-hole binaries are derived.Comment: REVTeX4, 20 pages, typos corrected in Eq. (124) and (130

An investigation of the laser-induced zircon 'matrix effect'

This study aims to improve our understanding of the current limitations to high-precision U-Pb analysis of zircon by LA-ICP-MS by investigating the underlying causes of variation in ablation behaviour between different zircon matrices. Multiple factors such as: the degree of accumulated radiation damage, trace element composition; crystal colour; and crystallographic orientation are all systematically investigated. Due to the marked decrease in elastic moduli of natural zircon crystals with increasing radiation damage, the accumulation of this damage is the dominant factor controlling the rate of ablation for partially damaged to highly metamict zircon samples. There are slight differences, however, in ablation behaviour between highly crystalline matrices that cannot be attributed solely to differences in the degree of accumulated radiation damage. These differences are associated with structural weakening (i.e., decrease in elastic moduli and overall lower mechanical resistance) caused by an increasing degree of cation substitution in some of the zircon samples. Effects of crystallographic orientation and of crystal opacity (i.e., colour) on ablation behaviour are negligible compared to the combined influences of accumulated radiation damage and trace element substitution into the zircon structure. Experiments performed on natural and annealed zircon grains reveal that the reduction in ablation rates observed for the treated samples compared to the untreated grains is proportional to the degree of structural reconstitution achieved after annealing. Thermal annealing of natural zircon at temperatures >1000 °C results in much more uniform ablation characteristics. This 'homogenisation' of ablation behaviour between zircon matrices produces a decrease in the laser-induced matrix effects and subsequent improvement in the accuracy of 206Pb/238U ratio determinations by LA-ICP-MS

Elimination of the spin supplementary condition in the effective field theory approach to the post-Newtonian approximation

The present paper addresses open questions regarding the handling of the spin supplementary condition within the effective field theory approach to the post-Newtonian approximation. In particular it is shown how the covariant spin supplementary condition can be eliminated at the level of the potential (which is subtle in various respects) and how the dynamics can be cast into a fully reduced Hamiltonian form. Two different methods are used and compared, one based on the well-known Dirac bracket and the other based on an action principle. It is discussed how the latter approach can be used to improve the Feynman rules by formulating them in terms of reduced canonical spin variables.Comment: 42 pages, document changed to match published version, in press; Ann. Phys. (N. Y.) (2012

Reduced Hamiltonian for next-to-leading order Spin-Squared Dynamics of General Compact Binaries

Within the post Newtonian framework the fully reduced Hamiltonian (i.e., with eliminated spin supplementary condition) for the next-to-leading order spin-squared dynamics of general compact binaries is presented. The Hamiltonian is applicable to the spin dynamics of all kinds of binaries with self-gravitating components like black holes and/or neutron stars taking into account spin-induced quadrupolar deformation effects in second post-Newtonian order perturbation theory of Einstein's field equations. The corresponding equations of motion for spin, position and momentum variables are given in terms of canonical Poisson brackets. Comparison with a nonreduced potential calculated within the Effective Field Theory approach is made.Comment: 11 pages, minor changes to match published version at CQ

ADM canonical formalism for gravitating spinning objects

In general relativity, systems of spinning classical particles are implemented into the canonical formalism of Arnowitt, Deser, and Misner [1]. The implementation is made with the aid of a symmetric stress-energy tensor and not a 4-dimensional covariant action functional. The formalism is valid to terms linear in the single spin variables and up to and including the next-to-leading order approximation in the gravitational spin-interaction part. The field-source terms for the spinning particles occurring in the Hamiltonian are obtained from their expressions in Minkowski space with canonical variables through 3-dimensional covariant generalizations as well as from a suitable shift of projections of the curved spacetime stress-energy tensor originally given within covariant spin supplementary conditions. The applied coordinate conditions are the generalized isotropic ones introduced by Arnowitt, Deser, and Misner. As applications, the Hamiltonian of two spinning compact bodies with next-to-leading order gravitational spin-orbit coupling, recently obtained by Damour, Jaranowski, and Schaefer [2], is rederived and the derivation of the next-to-leading order gravitational spin(1)-spin(2) Hamiltonian, shown for the first time in [3], is presented.Comment: REVTeX4, 18 pages. v1: published version. v2: corrected misprints in (8.4) and (9.3), updated reference

Pan-African intraplate deformation in the northern Prince Charles Mountains, east Antarctica

New structural and metamorphic data coupled with U-Pb SHRIMP zircon and Rb-Sr step-leach biotite ages help constrain a period of Early Palaeozoic (Pan-African) deformation recognised in the northern Prince Charles Mountains, east Antarctica. This period of deformation is accommodated along discrete northeast trending mylonites that preserve up-dip reverse kinematics with dominantly southeast over northwest vergence. Ambient P-T conditions of 524 ± 20°C and 7.6 ± 4 kbar accompanied deformation. This phase of deformation post-dated the intrusion of planar felsic dykes that yield ages of c. 550 Ma and pre-dated Rb-Sr biotite ages of c. 475 Ma that record cooling of the terrane below c. 300°C. These mylonites are identical in age to continental collisional events recognised in the southern Prince Charles Mountains and Prydz Bay, which lie to the south and east of the northern Prince Charles Mountains, and similar in age to orogenesis recognised to the west in Lützow-Holm Bay. These belts represent sutures between the component lithospheric blocks of east and west Gondwana. The northern Prince Charles Mountains lie between these sutures. Consequently, the mylonites we report here are interpreted to have formed in an intraplate setting and developed in response to stresses applied along the plated margins as a consequence of continental collision during the amalgamation of Gondwana