QUANTUM gravitational effects are usually ignored in calculations of the formation and evolution of black holes. The justification for this is that the radius of curvature of space-time outside the event horizon is very large compared to the Planck length (Għ/c3)1/2 ≈ 10−33 cm, the length scale on which quantum fluctuations of the metric are expected to be of order unity. This means that the energy density of particles created by the gravitational field is small compared to the space-time curvature. Even though quantum effects may be small locally, they may still, however, add up to produce a significant effect over the lifetime of the Universe ≈ 1017 s which is very long compared to the Planck time ≈ 10−43 s. The purpose of this letter is to show that this indeed may be the case: it seems that any black hole will create and emit particles such as neutrinos or photons at just the rate that one would expect if the black hole was a body with a temperature of (κ/2π) (ħ/2k) ≈ 10−6 (M/M)K where κ is the surface gravity of the black hole1. As a black hole emits this thermal radiation one would expect it to lose mass. This in turn would increase the surface gravity and so increase the rate of emission. The black hole would therefore have a finite life of the order of 1071 (M/M)−3 s. For a black hole of solar mass this is much longer than the age of the Universe. There might, however, be much smaller black holes which were formed by fluctuations in the early Universe2. Any such black hole of mass less than 1015 g would have evaporated by now. Near the end of its life the rate of emission would be very high and about 1030 erg would be released in the last 0.1 s. This is a fairly small explosion by astronomical standards but it is equivalent to about 1 million 1 Mton hydrogen bombs. It is often said that nothing can escape from a black hole. But in 1974, Stephen Hawking realized that, owing to quantum effects, black holes should emit particles with a thermal distribution of energies — as if the black hole had a temperature inversely proportional to its mass. In addition to putting black-hole thermodynamics on a firmer footing, this discovery led Hawking to postulate 'black hole explosions', as primordial black holes end their lives in an accelerating release of energy.

Black Hole Explosions

Radio-metric Doppler tracking data received from the Pioneer 10 and 11 spacecraft from heliocentric distances of 20-70 AU has consistently indicated the presence of a small, anomalous, blue-shifted frequency drift uniformly changing with a rate of ∼ 6 × 10-9 Hz/s. Ultimately, the drift was interpreted as a constant sunward deceleration of each particular spacecraft at the level of aP = (8.74 ± 1.33) × 10-10 m/s2. This apparent violation of the Newton's gravitational inverse-square law has become known as the Pioneer anomaly; the nature of this anomaly remains unexplained. In this review, we summarize the current knowledge of the physical properties of the anomaly and the conditions that led to its detection and characterization. We review various mechanisms proposed to explain the anomaly and discuss the current state of efforts to determine its nature. A comprehensive new investigation of the anomalous behavior of the two Pioneers has begun recently. The new efforts rely on the much-extended set of radio-metric Doppler data for both spacecraft in conjunction with the newly available complete record of their telemetry files and a large archive of original project documentation. As the new study is yet to report its findings, this review provides the necessary background for the new results to appear in the near future. In particular, we provide a significant amount of information on the design, operations and behavior of the two Pioneers during their entire missions, including descriptions of various data formats and techniques used for their navigation and radio-science data analysis. As most of this information was recovered relatively recently, it was not used in the previous studies of the Pioneer anomaly, but it is critical for the new investigation.

The Pioneer Anomaly

The Origin of Elements and the Separation of Galaxies

Introduction 1. Questioning the Scientized Image 2. Why we Primates are not 'Game Theorists' 3. The Selecting of Homo Sapiens 4. Brain Matters 5. A Thirst for Meaning 6. How Experience Shapes the Brain 7. 'Who Am I?' - Where Biology and Culture Meet 8. History, the Story of Meanings through Time 9. Humankind Crosses the Rubicon, 1900-2000 10. Conflict: Control or Reconciliation 11. The Search for Autonomy Within Community

In Search of Human Nature

PrefaceChart of Main Topics1A First Tour12Einstein Geometrodynamics133Tests of Einstein Geometrodynamics874Cosmology, Standard Models, and Homogeneous Rotating Models1855The Initial-Value Problem in Einstein Geometrodynamics2696The Gravitomagnetic Field and Its Measurement3157Some Highlights of the Past and a Summary of Geometrodynamics and Inertia384Mathematical Appendix403Symbols and Notations437Author Index445Subject Index of Mathematical Appendix455Subject Index461Fundamental and Astronomical Constants and Units493

Gravitation and Inertia

The Pioneer Anomaly and a Rotating Godel Universe

The quantum temperature of accelerating cosmological models of an entangled Universe

The entangled universe

For three decades, physicists have been in search of an elusive phenomenon predicted by Einstein's general theory of relativity; gravitational radiation These weak vibrations of spacetime have, thus far, eluded conclusive Earth-based detection due in part to insufficient detector sensitivity and noise isolation The detection of gravitational waves is crucial for two reasons It would provide further evidence for the validity of Einstein's theory of relativity, the presently accepted theory of gravitation Furthermore, the ability to identify the location of a source of a detected gravitational wave event would yield a radical new type of astronomy based on non-electromagnetic emissions We continue our study of a lunar-based system which can provide an important complement to Earth-based analysis because it is completely independent of the geophysical sources of noise on Earth, while providing an Earth-Moon baseline for pin-pointing burst sources in the Universe We also propose for the first time that a simplified version of the LIGO beam detector optical system, which we will call LLIGO (Lunar LIGO), could be emplaced on the Moon as part of NASA's robotic lander program now under study (Artemis) The Earth-based investigation has two major programs underway Both involve large interferometer-type gravitational wave antennas

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Thomas L. Wilson

Papers

The Pioneer Anomaly and a Rotating Godel Universe

The quantum temperature of accelerating cosmological models of an entangled Universe

The entangled universe

The entangled universe

Lunar LIGO: A new concept in gravitational wave astronomy