Showing papers by "Roger Penrose published in 1972"

Techniques of Differential Topology in Relativity

Abstract: Acquaints the specialist in relativity theory with some global techniques for the treatment of space-times and will provide the pure mathematician with a way into the subject of general relativity.

Ideal points in space-time

Abstract: A prescription is given for attaching to a space-time M , subject only to a causality condition, a collection of additional ‘ideal points’. Some of these represent ‘points at infinity’, others ‘singular points’. In particular, for asymptotically simple space-times, the ideal points can be interpreted as the boundary at conformal infinity. The construction is based entirely on the causal structure of M , and so leads to the introduction of ideal points also in a broad class of causal spaces. It is shown that domains of dependence can be characterized in terms of ideal points, and this makes possible an extension of the domain-of-dependence concept to causal spaces. A suggestion is made for assigning a topology to M together with its ideal points. This specifies some singular-point structure for a wide range of possible space-times.

On a quadratic first integral for the charged particle orbits in the charged Kerr solution

Abstract: Associated with the charged Kerr solution of the Einstein gravitational field equation there is a Killing tensor of valence two. The Killing tensor, which is related to the angular momentum of the field source, is shown to yield a quadratic first integral of the equation of the motion for charged test particles.

On the Nature of Quantum Geometry

Abstract: @As a way of honoring Professor Wheeler on his sixtieth birthday, I propose to take this opportunity to elaborate upon certain somewhat speculative ideas which I have tried to hint at on occasion, concerning the possible nature of a quantized space-time. The reader will not need to be too discerning to recognize some substantial dierences between the ideas I am proposing here and those which Professor Wheeler has on many occasions so eloquently and forcefully put forward. Nonetheless, there is little doubt in my own mind as to the very great inspirational inuence that Professor Wheeler’s own views have had in the development of several of the thoughts which I am expressing here. To begin with, let me make clear that I do not necessarily mean by \quantized space-time" something which could be obtained by applying standard (or even non-standard) techniques of quantization to Einstein’s general theory of relativity. What I wish to say has its roots in something which is really more primitive than either quantum theory or relativity as such. This is the question of the fundamental role played by the mathematical concept of continuum in virtually the whole of accepted present-day physical theory. Not only does the continuum occupy a basic position in our mathematical models of space and time (with the concomitant implication of a continuous nature for many related physical concepts such as velocity, energy, momentum, temperature, etc.), but so also does present-day quantum theory rest crucially on a continuum concept, namely on the two-dimensional complex continuum of probability amplitudes, this being the continuum which also occurs in the superposition law. Let me say at the outset that I am not happy with this state of aairs in physical theory. The mathematical continuum has always seemed to me to contain many features which are really very foreign to physics. This point = @ @

Black Holes and Gravitational Theory

Abstract: There have been several recent claims to have detected black holes. In this article Professor Penrose describes the theoretical basis of black holes and some of the recent thinking on the subject.