Static, Self-Gravitating Elastic Bodies

There is proved an existence theorem, in the Newtonian theory, for static, self-gravitating bodies composed of elastic material. The theorem covers the case where these bodies are small, but allows them to have arbitrary shape.Comment: 8 page

Bowen-York Tensors

There is derived, for a conformally flat three-space, a family of linear second-order partial differential operators which send vectors into tracefree, symmetric two-tensors. These maps, which are parametrized by conformal Killing vectors on the three-space, are such that the divergence of the resulting tensor field depends only on the divergence of the original vector field. In particular these maps send source-free electric fields into TT-tensors. Moreover, if the original vector field is the Coulomb field on $\mathbb{R}^3\backslash \lbrace0\rbrace$, the resulting tensor fields on $\mathbb{R}^3\backslash \lbrace0\rbrace$ are nothing but the family of TT-tensors originally written down by Bowen and York.Comment: 12 pages, Contribution to CQG Special Issue "A Spacetime Safari: Essays in Honour of Vincent Moncrief

Elastic deformations of compact stars

We prove existence of solutions for an elastic body interacting with itself through its Newtonian gravitational field. Our construction works for configurations near one given by a self-gravitating ball of perfect fluid. We use an implicit function argument. In so doing we have to revisit some classical work in the astrophysical literature concerning linear stability of perfect fluid stars. The results presented here extend previous work by the authors, which was restricted to the astrophysically insignificant situation of configurations near one of vanishing stress. In particular, "mountains on neutron stars", which are made possible by the presence of an elastic crust in neutron stars, can be treated using the techniques developed here.Comment: 29 page

Celestial mechanics of elastic bodies

We construct time independent configurations of two gravitating elastic bodies. These configurations either correspond to the two bodies moving in a circular orbit around their center of mass or strictly static configurations.Comment: 16 pages, 2 figures, several typos removed, erratum appeared in MathZ.263:233,200

Helically symmetric N-particle solutions in scalar gravity

Within a scalar model theory of gravity, where the interaction between particles is given by the half-retarded + half-advanced solution of the scalar wave equation, we consider an N-body problem: we investigate configurations of N particles which form an equilateral N-angle and are in helical motion about their common center. We prove that there exists a unique equilibrium configuration and compute the equilibrium radius explicitly in a post-Newtonian expansion.Comment: 5 pages, 1 figure; minor corrections and changes; accepted for publication in Physical Review Letter

Existence and uniqueness of Bowen-York Trumpets

We prove the existence of initial data sets which possess an asymptotically flat and an asymptotically cylindrical end. Such geometries are known as trumpets in the community of numerical relativists.Comment: This corresponds to the published version in Class. Quantum Grav. 28 (2011) 24500

Helical Solutions in Scalar Gravity

We construct solutions, for small values of $G$ and angular frequency $\Omega$, of special relativistic scalar gravity coupled to ideally elastic matter which have helical but no stationary or axial symmetry. They correspond to a body without any symmetries in steady rotation around one of its axes of inertia, or two bodies moving on a circle around their center of gravity. Our construction is rigorous, but modulo an unproved conjecture on the differentiability of a certain functional.Comment: 11 page

Variation of D-region nitric-oxide density with solar activity and season at the dip equator

To study the solar control on electron density (N sub e) in the equatorial D region, a program was initiated with Soviet collaboration in 1979. A total of 31 rockets were launched during the high solar activity period, and 47 rockets during the low solar activity period, from Thumba to measure the N sub e profiles. Analysis of the data shows that the average values of N sub e for the high solar activity period are higher by a factor of about 2 to 3 compared to the low solar activity values. It was found that a single nitric oxide density, (NO), profile cannot reproduce all the observed N sub e profiles. An attempt was made to reproduce theoretically the observed N sub e profiles by introducing variation in (NO) for the different solar activity periods and seasons

Behavior of boundary layer ozone and its precursors over a great alluvial plain of the world: Indo-Gangetic plains

We investigate the special behavior in the distribution of boundary layer ozone and its precursors over world's most extensive tract of uninterrupted alluvium and intensively farmed zones situated in the foothills of Himalayas as major river basin, known as Indo-Gangetic Plains (IGP). The study makes use of a Chemistry-Transport Model forced with dynamical fields and new emission inventories of pollutants established for 2001. It is found that the IGP region is highly vulnerable to human induced pollutant emissions due to conducive synoptic weather pattern which make it a source regions of ozone precursors within which these tracers remain confined and reinforce photochemical production of ozone. In addition, the continental tropical convergence zone and long range transport play a vital role. As a result, elevated levels of ozone concentration (maximum up to 80 ppbv) and its precursors with cellular structure of spatial variation with large seasonality are noticed