## Gravitational Collapse and Space-Time Singularities, in Physical Review Letters, Vol. 14, 1965

New York: American Physical Society, 1965. 1st Edition. FIRST EDITION, FIRST ISSUE of Roger Penrose’s 1965 proof laying “the foundations of the modern mathematical theory of gravitational collapse” (DeWitt-Morette, Black Holes, 126).

In a discovery with profound ramifications for the Big Bang Theory and crucial in understanding of black holes and modern physics, Penrose used the equations of general relativity to show that “when a large object [such as enormous, dying stars] collapses under its own gravity it must, according to Einstein's theory, necessarily end up containing a ‘singularity’ [a place of zero volume and thus of infinite density such as a black hole]” (ibid). Building on the work of Wheeler and Chandrasekhar, and others, Penrose demonstrated “that if the universe obeys general relativity and several other constraints, when a very massive star has no nuclear fuel left to burn and collapses under the force of its own gravity, it will inevitably be crushed to a point of infinite density and infinite spacetime curvature, a singularity. [He showed that] this will happen even if the collapse isn’t perfectly smooth and symmetrical. No ‘might’ about it. It must” (Ferguson, Fire in the Equations, 101).

Using “the wealth of new techniques and concepts which were introduced in [Penrose’s] proof, particularly the notion of a trapped surface and the idea of treating boundary horizons as dynamic entities in their own right,” Penrose collaborated with a fellow member of his study group at Cambridge named Stephen Hawking. In 1970 they demonstrated that Penrose singularities can occur with any type of gravitational collapse, including that of the big bang at the beginning of time (DeWitt, 126). Item #222

CONDITION & DETAILS: New York: American Physical Society. Volume 14, complete. 4to (10.5 x 8 inches; 263 x 200mm). Bound in red buckram that is lightly rubbed and scuffed at the edges. Tightly and very solidly bound. Bright and clean throughout. Very good condition.

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Price:
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