Relattvisttc Cosmology and Space Platforms*
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RELATTVISTTC COSMOLOGY AND SPACE PLATFORMS* Remo Ruffini ** Institute for Advanced Study, Princeton, New Jersey John Archibald Wheeler Joseph Henry Laboratories, Princeton University, Princeton, New Jersey ABSTRACT Einstein's standard 1915 general relativity or geometrodynamics introduces a new dynamical participant on the scene of physics : geometry. Nowhere did the dynamics of geometry originally show up more impressively than in the expansion of the Universe. Today the role of curved space geometry, both static and dynamic, lends itself to investigation from space platforms or from the ground, or both, in many other contexts; among them, discussed here, are : properties of a superdense or neutron star; pulsar physics; collapse of a star with big dense core to a superdense star in a supernova event, or complete collapse to a black hole; physics of the black hole; galactic centers, jets, and quasi-stellar sources; gravitational radiation; Misner's mixmaster model of the universe; the primordial fireball radiation; the time-scale of the expansion of the Universe; the Universe as a lens, magnifying the apparent diameter of a far-away galaxy; the mystery of the missing matter; the formation of galaxies; reaching out via radiation receptors for more information on the physics of these phenomena; and finally the solar system itself as a testing ground for relativity including the traditional three tests of relativity; the retardation of light as it passes close to the Sun on its way to Venus and back; relativistic effects in planetary motion and searches via corner reflectors on the Moon for relativistic effects in the motion of the Moon, as predicted by Baierlein. * Expanded version of the lecture given at the Colloquium. ** ESRO-NASA Postdoctoral Fellow. 45 TABLE OF CONTENTS 1. INTRODUCTION 48 1.1 The Double Challenge - more Precision in Known Effects; the Search for New Eflfects .. 48 1.2 Space from Riemann to Einstein 48 1.3 The Local Character of Gravitation 49 1.4 Tide-producing Acceleration and Spacetime Curvature 49 1.5 Spacetime vs Space 50 1.6 Curvature and Density 50 1.7 Einstein's Equation Connecting Curvature with Density 51 2. THE PHYSICS OF A SUPERDENSE STAR 52 2.1 Results of Newtonian Treatment 54 2.2 Equilibrium Configurations for General Relativity 54 2.3 Scalar Tensor Theory and Equilibrium Configurations 56 2.4 Equation of State 57 3. PULSARS 62 3.1 Pulsars as Neutron Stars 64 3.2 The Crust and Interior of a Neutron Star 68 4. SUPERNOVAE 70 5. BLACK HOLES '.. 72 5.1 Collapse of a Spherically Symmetrical Cloud of Dust 73 5.2 The Kruskal Diagram 77 5.3 "NoBounce" 80 5.4 Small Departures from Spherical Symmetry 84 5.5 Rotation and the Kerr Geometry 87 5.6 Energy Sent Out when Mass Falls In 95 5.7 Final Outcome of Collapse of a Rotating Body 96 5.8 Search for Black Holes and their Effects 98 6. QUASI-STELLAR OBJECTS 99 7. GRAVITATIONAL RADIATION 101 7.1 Angular Distribution of Gravitational Radiation 108 7.2 Detector of Gravitational Radiation 116 7.3 Bar as Multiple-Mode Detector 118 7.4 Earth Vibrations as Detectors of Gravitational Waves 119 7.5 Seismic Response of Earth to Gravitational Radiation in the One-Hertz Region 120 7.6 Changes in Solar System Distances Not Adequate as Detectors of Gravitational Waves. 121 7.7 Sources of Gravitational Radiation 121 7.7.1 Spinning Rod 121 7.7.2 SpinningStar 122 7.7.3 Double Star System. 127 7.7.4 Pulsating Neutron Star 127 7.8 Splash of Gravitational Radiation 132 7.9 Low-Frequency Part of Splash Radiation 133 7.10 Radiation in Elliptical Orbits Treated as a Succession of Pulses 136 46 7.11 Fallinto Schwarzschild Black Hole 136 7.12 Radiation from Gravitational Collapse 139 7.13 Earthquakes and Meteorites 139 7.14 Microscopic Processes 141 7.15 Primordial Gravitational Radiation 141 8. MISNER'S MTXMASTER MODEL OF THE UNIVERSE 143 9. THE PRIMORDIAL COSMIC FIREBALL RADIATION 148 9.1 Observations at Microwave Wavelengths from Mountain Altitudes 149 9.2 Temperature from Population of Excited Molecular States 150 9.3 Rocket Measurement of Radiation in the Millimetre Range 151 9.4 Decoupling and Isotropy 151 10. THE TIME-SCALE OF EXPANSION OF THE UNIVERSE 153 11. THE UNIVERSE AS A LENS, MAGNIFYING THE APPARENT DIAMETER OF A FAR-AWAY GALAXY 155 12. THE MYSTERY OF THE MISSING MATTER 158 13. FORMATION OF GALAXIES 158 14. REACHING OUT VIA RADIATION RECEPTORS FOR MORE INFORMATION. 159 15. THE TRADITIONAL THREE TESTS OF RELATIVITY 159 16. THE RETARDATION OF LIGHT AS IT PASSES BY THE SUN ON ITS WAY TO AND RETURN FROM VENUS 160 17. RELATIVISTIC EFFECTS IN PLANETARY MOTIONS 161 18. SEARCH VIA CORNER REFLECTORS ON THE MOON FOR RELATIVISTIC EFFECTS IN THE MOTION OF THE MOON PREDICTED BY BAIERLEIN. 162 19. SOME OTHER TIES BETWEEN RELATIVISTIC ASTROPHYSICS AND EXPERI MENTS ON SPACE PLATFORMS 163 ACKNOWLEDGMENT 163 REFERENCES 164 47 1. INTRODUCTION 1.1 THE DOUBLE CHALLENGE: MORE PRECISION IN KNOWN EFFECTS: THE SEARCH FOR NEW EFFECTS " ...the opinion seems to have got abroad, that in a few years all the great physical constants will have been approximately estimated, and that the only occupation which will then be left to men of science will be to carry on these measurements to another place of decimals ". These words were pronounced by James Clerk Maxwell at the inauguration of the Devonshire (Cavendish) Physical Laboratory at Cambridge1. Decades later Albert A. Michelson made the idea of " the search for the next decimal place " even more famous to a still wider audience. This great tradition of precision physics flourishes still more actively in our own time, thanks not least to the development of the atomic clock, radar, the Môssbauer effect and the laser. Hopes are high that within a few years we shall have tests, with greatly improved accuracy, of the three famous predictions of general relativity, the precession of the orbit of Mercury, the bending of light by the Sun and the red shift of light from the Sun; at present none of these effects is reliably established with a precision better than 10 per cent. Ideas for these and other precision tests of Einstein's theory today receive more attention from more skilled experimenters than ever before. Measure known effects with improved precision; or explore for new effects. Those who prefer the one activity find relativity as challenging as those who prefer the other. The reason is clear. Einstein's standard 1915 geometrodynamics makes new predictions-not only about the numbers but also about the nature of physics. The geometry of space is dynamic. The Universe is closed 2. The Universe starts its life unbelievably small, reaches a maximum dimension and recontracts. It under goes complete gravitational collapse. In many ways a similar gravitational collapse overtakes certain stars with big dense cores. This collapse terminates in some cases (" supernova events ") with the formation of a neutron star. In other cases, where the star core is more massive, the collapse goes to completion. A black hole is formed. Given such a black hole, one has no way, even in principle, of measuring or even defining — one believes — how many baryons and leptons this object contains. In this sense one thinks of the law of conservation of baryons (and leptons) as being transcended in the phenomenon of complete collapse. Black holes formed in the gravitational collapse of stars with big dense cores are dotted here and there about this and other galaxies, if present expectations are correct. A star in the final stages of collapse to a neutron star or a black hole is a powerful source of gravitational radiation : waves in the geometry of space. Gravitational radiation also emerges with great strength from two compact masses in close gravitational interaction, whether the two objects are neutron stars or black holes, or one of each. 1.2 SPACE FROM RIEMANN TO EINSTEIN Space itself, until Bernhard Riemann's Gôttingen inaugural lecture3 of 10 June 1854, could be viewed as an ideal Euclidean perfection standing unmoved high above the battles of matter and energy. Einstein translated Riemann's vision of a dynamic geometry into clear-cut mathematical terms. Einstein geometrodynamics has withstood test and attack for over half a century. In the conception of Riemann and Einstein space tells matter how to move. But matter in turn tells space how to curve. Only so can the principle of action and reaction be upheld ! In a revolution, chained-up space broke loose and ceased to be the passive arena for physics. It became an active participant. The agent of this revolution, the Einstein who endowed geometry with a life of its own, also established rules for the governance of this new dynamic entity. Those rules tell us what we have now known for a decade, the structure of an edifice more magnificent than space : superspace. Superspace is the rigid and per fect arena, infinite in number of dimensions, in which the geometry of the Universe executes its dyna mic changes : expansion, vibration, undulation, attainment of maximum dimensions, recontraction and collapse. Important as it is to mention superspace for a fuller perspective of what Einstein's geome trodynamics is today, it is also true that one can dispense with mention of superspace so long as one looks apart, as we shall here, from quantum fluctuations in the geometry of space, and from the quan tum effects that dominate the final stages of gravitational collapse. Classical geometrodynamics is rich enough as a field of investigation! 48 1.3 THE LOCAL CHARACTER OF GRAVITATION4 Matter gets its moving orders from spacetime; and spacetime is curved by matter : these are the two central principles of classical general relativity.