## The Contraction of Gravitating Spheres (Offprint) Proceedings of the Royal Society, A, Volume 281, 1964, pp. 39-48 [1st edition: STUDY OF SPACETIME SINGULARITIES AND GRAVITATIONAL WAVES AND COLLAPSE]

London: 1964. 1st Edition. FIRST EDITION, RARE OFFPRINT OF A MAJOR PUBLICATION BY BONDI IN THE STUDY OF SPACETIME SINGULARITIES AND GRAVITATIONAL WAVES AND COLLAPSE.

In 1957 and in a paper we offer separately, Hermann Bondi demonstrated that gravitation waves indeed carry energy, and furthermore that in order to carry energy (and momentum), gravitational waves must be nonlinear. Gravitational waves, or ripples in the fabric of spacetime, were first predicted by Einstein’s 1916 general theory of relativity. In February 2016, the September 2015 detection of gravitational waves – waves first predicted by Einstein over a hundred years ago – was announced.

Bondi’s 1957 paper firmly established the physical reality of gravitational waves; his later work in the early 1960s – and this is one of those papers -- would put "their physical properties such as energy and momentum flux on a rigorous mathematical footing” (Denef, Science, Feb. 2016). I

n this 1964 paper, the contemporary discovery of quasi-stellar objects and pulsating radio sources, for example, had re-sparked “interest in the application of general-relativity theory to the structure of massive or highly condensed stars. In some of the resulting models attempts have been made to include a radiation field in the calculations” (Kaufmann, “The Exterior Solution, AJ 156, 257). Bondi’s paper presents one such model.

Of this 1964 paper, Bondi wrote: “Earlier ideas associating an invariant integral of the energy invariant with the number of nucleons in a gravitating body are shown to be fallacious, and thus do not provide a means of following through the contraction of such a body. It is shown how the full field equations of general relativity give a feasible and rigorous method of examining contracting models. Schwarzschild-type co-ordinates are introduced and are used to examine the slow adiabatic contraction of a sphere of constant density. The particle paths are found and the pressure-density relation permitting such slow adiabatic contraction is examined. It is shown that the simple 4/3 power law of Newtonian theory has to be replaced by a steeper dependence of pressure on density for high gravitational potentials. Radiation co-ordinates are introduced to examine radiating contracting systems, and equations fully specifying such a system are obtained. A simple example is given in outline to illustrate the method” (Bondi, PRS, 281, 1964, p. 39). Item #677

CONDITION & DETAILS: First edition offprint. 4to. 10 X 6.75 inches; 250 x 169mm. Fine condition in every way.

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Price:
$100.00
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