On a class of 2-surface observables in general relativity

The boundary conditions for canonical vacuum general relativity is investigated at the quasi-local level. It is shown that fixing the area element on the 2- surface S (rather than the induced 2-metric) is enough to have a well defined constraint algebra, and a well defined Poisson algebra of basic Hamiltonians parameterized by shifts that are tangent to and divergence-free on $. The evolution equations preserve these boundary conditions and the value of the basic Hamiltonian gives 2+2 covariant, gauge-invariant 2-surface observables. The meaning of these observables is also discussed.Comment: 11 pages, a discussion of the observables in stationary spacetimes is included, new references are added, typos correcte

On certain quasi-local spin-angular momentum expressions for small spheres

The Ludvigsen-Vickers and two recently suggested quasi-local spin-angular momentum expressions, based on holomorphic and anti-holomorphic spinor fields, are calculated for small spheres of radius $r$ about a point $o$. It is shown that, apart from the sign in the case of anti-holomorphic spinors in non-vacuum, the leading terms of all these expressions coincide. In non-vacuum spacetimes this common leading term is of order $r^4$, and it is the product of the contraction of the energy-momentum tensor and an average of the approximate boost-rotation Killing vector that vanishes at $o$ and of the 3-volume of the ball of radius $r$. In vacuum spacetimes the leading term is of order $r^6$, and the factor of proportionality is the contraction of the Bel-Robinson tensor and an other average of the same approximate boost-rotation Killing vector.Comment: 16 pages, Plain Te

Discovery of blue companions to two southern Cepheids: WW Car and FN Vel

A large number of high-dispersion spectra of classical Cepheids were obtained in the region of the CaII H+K spectral lines. The analysis of these spectra allowed us to detect the presence of a strong Balmer line, H$\epsilon$, for several Cepheids, interpreted as the signature of a blue companion: the presence of a sufficiently bright blue companion to the Cepheid results in a discernible strengthening of the CaII H + Hepsilon line relative to the CaII K line. We investigated 103 Cepheids, including those with known hot companions (B5-B6 main-sequence stars) in order to test the method. We could confirm the presence of a companion to WW Car and FN Vel (the existence of the former was only suspected before) and we found that these companions are blue hot stars. The method remains efficient when the orbital velocity changes in a binary system cannot be revealed and other methods of binarity detection are not efficient.Comment: 6 pages, 5 figures, 4 tables, published on MNRAS in March 201

Total angular momentum from Dirac eigenspinors

The eigenvalue problem for Dirac operators, constructed from two connections on the spinor bundle over closed spacelike 2-surfaces, is investigated. A class of divergence free vector fields, built from the eigenspinors, are found, which, for the lowest eigenvalue, reproduce the rotation Killing vectors of metric spheres, and provide rotation BMS vector fields at future null infinity. This makes it possible to introduce a well defined, gauge invariant spatial angular momentum at null infinity, which reduces to the standard expression in stationary spacetimes. The general formula for the angular momentum flux carried away be the gravitational radiation is also derived.Comment: 34 pages, typos corrected, four references added, appearing in Class. Quantum Gra

Quasi-local energy-momentum and two-surface characterization of the pp-wave spacetimes

In the present paper the determination of the {\it pp}-wave metric form the geometry of certain spacelike two-surfaces is considered. It has been shown that the vanishing of the Dougan--Mason quasi-local mass $m_{\$}$, associated with the smooth boundary $\$:=\partial\Sigma\approx S^2$ of a spacelike hypersurface $\Sigma$, is equivalent to the statement that the Cauchy development $D(\Sigma)$ is of a {\it pp}-wave type geometry with pure radiation, provided the ingoing null normals are not diverging on $\$$ and the dominant energy condition holds on $D(\Sigma)$. The metric on $D(\Sigma)$ itself, however, has not been determined. Here, assuming that the matter is a zero-rest-mass-field, it is shown that both the matter field and the {\it pp}-wave metric of $D(\Sigma)$ are completely determined by the value of the zero-rest-mass-field on $\$$ and the two dimensional Sen--geometry of $\$$ provided a convexity condition, slightly stronger than above, holds. Thus the {\it pp}-waves can be characterized not only by the usual Cauchy data on a {\it three} dimensional $\Sigma$ but by data on its {\it two} dimensional boundary $\$$ too. In addition, it is shown that the Ludvigsen--Vickers quasi-local angular momentum of axially symmetric {\it pp}-wave geometries has the familiar properties known for pure (matter) radiation.Comment: 15 pages, Plain Tex, no figure

On quasi-local charges and Newman--Penrose type quantities in Yang--Mills theories

We generalize the notion of quasi-local charges, introduced by P. Tod for Yang--Mills fields with unitary groups, to non-Abelian gauge theories with arbitrary gauge group, and calculate its small sphere and large sphere limits both at spatial and null infinity. We show that for semisimple gauge groups no reasonable definition yield conserved total charges and Newman--Penrose (NP) type quantities at null infinity in generic, radiative configurations. The conditions of their conservation, both in terms of the field configurations and the structure of the gauge group, are clarified. We also calculate the NP quantities for stationary, asymptotic solutions of the field equations with vanishing magnetic charges, and illustrate these by explicit solutions with various gauge groups.Comment: 22 pages, typos corrected, appearing in Classical and Quantum Gravit

Physical decomposition of the gauge and gravitational fields

Physical decomposition of the non-Abelian gauge field has recently solved the two-decade-lasting problem of a meaningful gluon spin. Here we extend this approach to gravity and attack the century-lasting problem of a meaningful gravitational energy. The metric is unambiguously separated into a pure geometric term which contributes null curvature tensor, and a physical term which represents the true gravitational effect and always vanishes in a flat space-time. By this decomposition the conventional pseudo-tensors of the gravitational stress-energy are easily rescued to produce definite physical result. Our decomposition applies to any symmetric tensor, and has interesting relation to the transverse-traceless (TT) decomposition discussed by Arnowitt, Deser and Misner, and by York.Comment: 11 pages, no figure; significant revision, with discussion on relations of various metric decomposition

A generalized Damour-Navier-Stokes equation applied to trapping horizons

An identity is derived from Einstein equation for any hypersurface H which can be foliated by spacelike two-dimensional surfaces. In the case where the hypersurface is null, this identity coincides with the two-dimensional Navier-Stokes-like equation obtained by Damour in the membrane approach to a black hole event horizon. In the case where H is spacelike or null and the 2-surfaces are marginally trapped, this identity applies to Hayward's trapping horizons and to the related dynamical horizons recently introduced by Ashtekar and Krishnan. The identity involves a normal fundamental form (normal connection 1-form) of the 2-surface, which can be viewed as a generalization to non-null hypersurfaces of the Hajicek 1-form used by Damour. This 1-form is also used to define the angular momentum of the horizon. The generalized Damour-Navier-Stokes equation leads then to a simple evolution equation for the angular momentum.Comment: Added subsection IV.D; corrected an error in Appendix A; added some references; accepted for publication in Phys. Rev. D (16 pages, 4 EPS figures

The kernel of the edth operators on higher-genus spacelike two-surfaces

The dimension of the kernels of the edth and edth-prime operators on closed, orientable spacelike 2-surfaces with arbitrary genus is calculated, and some of its mathematical and physical consequences are discussed.Comment: 12 page