: The final report covering the research performed under the Air Force Office of Scientific Research by the Dallas relativity group, summarizes information on personnel involved, on the scientific work done, and on the results obtained in the four years of the grant's duration. Topics investigated were in areas of General relativity, cosmology, and electrodynamics.

Exact Solutions of Einstein's Field Equations.

Gravitation and cosmology: Stephen Weinberg. 657 pages, diagrams, 6×9 in. New York, John Wiley & Sons, Inc., 1972. Price $18.95 (approx. £6·20).

The equilibrium problem for an axially symmetric, uniformly rotating, elastic solid neutron star is considered within the framework of a new formulation of relativistic elasticity. The analysis is fully relativistic and free of any assumption about the existence of a globally relaxed state of the star. Static configurations may exist only for rigid motions, and for such motions a set of six Einstein equations for six variables is proposed. Due both to the importance of elastic-solid lattices for the structure of neutron stars crusts and to the lack, up to now, of satisfactory axially symmetric perfect fluid interior solutions matching an asimpotically flat exterior, the results seem to indicate the possibility of constructing physically valid models of axially symmetric astrophysical objects in general relativity. The particular case of non-rotating axially symmetric elastic sources is also discussed.

Axially symmetric, uniformly rotating neutron stars in general relativity: a non-perturbative approach

Two spherical mass shells (radius R, distance d), relativistically corotating with angular velocity omega , are held in a stationary state by a Weyl strut. In the first order of the rest mass density rho , the global solution of Einstein's equations is given. In order rho 2, the conservation laws Tnu ; mu mu =0 produce singularities of the surface stresses at the 'poles' of the shells, where the Weyl strut impinges. Their strength is a measure for the force F between the shells. For d>or=2R, the attraction between rotating shells is even stronger than for static shells. For d<2R (overlapping shells), gravimagnetic repulsion can partly compensate for the attraction. For d to 0, and nu = omega R to 1, F( nu )/F(0) reaches the value 1/3 for constant mass density rho , and the value 1/10 for quadrupolar density distribution. In the limit of infinitely high 'multipolarity' of the mass density the shells degenerate to mass rings, which then exactly balance for d to 0 and nu to 1.

https://iopscience.iop.org/article/10.1088/0264-9381/4/1/017/pdf

Can gravitational attraction be compensated for by gravimagnetic effects

Static Axially Symmetric Models and Structure Scalars in Self-Interacting Brans–Dicke Gravity

A model system, consisting of a thin spherical shell with radiusR and massM and a point massm at a distances>R from the center of the sphere, held fixed by an appropriate strut, is solved to ordermM. The stresses in the shell are not of the canonical Weyl type, and it is argued that the same is true for more realistic situations, e.g., rotating matter. Owing to the nonlinearity of Einstein's field equations, the field of the point mass is shielded from the interior of the shell by a factor η lying between 1–3M/R and 1–2M/R, and the field outside the shell explicitly depends onR.

https://homepages.uni-tuebingen.de/wilfried.konrad/seiten/pfister_konrad_1984.pdf

W. Konrad

Papers

On Axially Symmetric Solutions of Einstein's Field Equations in Matter and an Example of Static Gravitational Shielding