Recent advances in general relativity. Essays in honor of Ted Newman.

*(English)*Zbl 0840.53076
Einstein Studies. 4. Boston, MA: Birkhäuser Verlag. xi, 266 p. (1992).

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These proceedings of the 1990 Pittsburgh Conference are a tribute to Ted Newman. Some essays recall ideas and mathematical techniques due to him, and their developments, while others concentrate on recent advances in a few problems in general relativity. Gravitational radiation and quantum gravity are those stressed in the opening lecture (Bergmann). The analysis of the asymptotic symmetry group of future null infinity, the Bondi-Metzner-Sachs group, led him with an appropriate complexification, to \(H\)-space and the \(e\)th operator; the connections of the former with twistor theory are recalled (Penrose) and the Newman-Penrose formalism with a tetrad of non-commutative operators is constructed, as an application of the second (Sparling). Newman’s cut function is related to the Blaschke support function for a convex surface and leads to a version of the fuzzy point idea in Minkowski spacetime (Tod). The study of the asymptotic structure of spacetime adapted to “isolated” gravitating systems using the technique of the conformal extension of Minkowski spacetime is reviewed and contrasted with recent advances (Friederich). Holonomy variables introduced by Newman and Koznameh are recognized as basic in the loop quantization and their application to nonperturbative quantum gravity is discussed (Rovelli). The Kerr-Newman black hole furnishes the occasion for reviewing recent progress regarding the limitations of the “no hair” paradigm and the study of black hole interior; the latter seems to favour a bouncing universe starting from a baby universe (Israel). A few recent results concerning neutron stars (relation between maximum rotation and equation of state, possibility of quark core etc.) are outlined (J. L. Friedman). Prospects for the detection of gravitational waves (Thorne) are considered along with conflicting views on the cross-sections of resonant-bar gravitational wave detectors and on their agreement with calibrations (Weber, Thorne). The one-dimensional reductions of self-dual Yang-Mills equations (Ablowitz and Chakravarty) and self-dual classical gravity are discussed. One also finds summaries of workshops on classical and quantum gravity (Tod, Kuchar).

Reviewer: S.Kichenassamy (Paris)

##### MSC:

53Z05 | Applications of differential geometry to physics |

83-06 | Proceedings, conferences, collections, etc. pertaining to relativity and gravitational theory |

00B25 | Proceedings of conferences of miscellaneous specific interest |

83C30 | Asymptotic procedures (radiation, news functions, \(\mathcal{H} \)-spaces, etc.) in general relativity and gravitational theory |

83C35 | Gravitational waves |

83C45 | Quantization of the gravitational field |

83C57 | Black holes |

83C60 | Spinor and twistor methods in general relativity and gravitational theory; Newman-Penrose formalism |