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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

Motivated by ideas about quantum gravity, a tremendous amount of effort over the past decade has gone into testing Lorentz invariance in various regimes. This review summarizes both the theoretical frameworks for tests of Lorentz invariance and experimental advances that have made new high precision tests possible. The current constraints on Lorentz violating effects from both terrestrial experiments and astrophysical observations are presented.

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Modern Tests of Lorentz Invariance

Associate DIETRICH BELITZ, University of Oregon Editors: Condensed Matter Physics (Theoretical) J. IGNACIO CIRAC, Max-Planck-Institut für Quantenoptik Quantum Information RAYMOND E. GOLDSTEIN, University of Cambridge Biological Physics ARTHUR F. HEBARD, University of Florida Condensed Matter Physics (Experimental) RANDALL D. KAMIEN, University of Pennsylvania Soft Condensed Matter DANIEL KLEPPNER, Massachusetts Institute of Technology Atomic, Molecular, and Optical Physics (Experimental) PAUL G. LANGACKER, Institute for Advanced Study, Princeton University Particle Physics (Theoretical) VERA LÜTH, Stanford University Particle Physics (Experimental) DAVID D. MEYERHOFER, University of Rochester Physics of Plasmas and Matter at High-Energy Density WITOLD NAZAREWICZ, University of Tennessee, Oak Ridge National Laboratory Nuclear Physics JOHN H. SCHWARZ, California Institute of Technology Mathematical Physics FRIEDRICH-KARL THIELEMANN, Universität Basel Astrophysics Senior Assistant Editor: DEBBIE BRODBAR, APS Editorial Office American Physical Society

Reviews of Modern Physics

We established superfluidity in a two-state mixture of ultracold fermionic atoms with imbalanced state populations. This study relates to the long-standing debate about the nature of the superfluid state in Fermi systems. Indicators for superfluidity were condensates of fermion pairs and vortices in rotating clouds. For strong interactions, near a Feshbach resonance, superfluidity was observed for a broad range of population imbalances. We mapped out the superfluid regime as a function of interaction strength and population imbalance and characterized the quantum phase transition to the normal state, known as the Pauli limit of superfluidity.

Fermionic Superfluidity with Imbalanced Spin Populations

We study noncommutative geometry at the quantum mechanics level by means of a model where noncommutativity of both configuration and momentum spaces is considered. We analyze how this model affects the problem of the two-dimensional gravitational quantum well and use the latest experimental results for the two lowest energy states of neutrons in the Earth's gravitational field to establish an upper bound on the fundamental momentum scale introduced by noncommutativity, namely, $\sqrt{\ensuremath{\eta}}\ensuremath{\lesssim}1\text{ }\mathrm{meV}/c$, a value that can be improved in the future by up to $3$ orders of magnitude. We show that the configuration space noncommutativity has, in leading order, no effect on the problem. We also analyze some features introduced by the model, especially a correction to the presently accepted value of Planck's constant to $1$ part in ${10}^{24}$.

Noncommutative gravitational quantum well

We conjecture that, because of color confinement, the physical vacuum forms an event horizon for quarks and gluons, which can be crossed only by quantum tunneling, i.e., through the QCD counterpart of Hawking radiation at black holes. Since such radiation cannot transmit information to the outside, it must be thermal, of a temperature determined by the chromodynamic force at the confinement surface, and it must maintain color neutrality. We explore the possibility that the resulting process provides a common mechanism for thermal hadron production in high energy interactions, from e+e- annihilation to heavy ion collisions.

Thermal hadronization and Hawking–Unruh radiation in QCD

We perform a systematic comparison of the statistical model parametrization of hadron abundances observed in high-energy pp, AA and e
 +
 e
 − collisions. The basic aim of the study is to test if the quality of the description depends on the nature of the collision process. In particular, we want to see if nuclear collisions, with multiple initial interactions, lead to “more thermal” average multiplicities than elementary pp collisions or e
 +
 e
 − annihilation. Such a comparison is meaningful only if it is based on data for the same or similar hadronic species and if the analyzed data has quantitatively similar errors. When these requirements are maintained, the quality of the statistical model description is found to be the same for the different initial collision configurations.

A comparative analysis of statistical hadron production

The thermal multihadron production observed in different high energy collisions poses two basic problems. (1) Why do even elementary collisions with comparatively few secondaries (e
 +
 e
 − annihilation) show thermal behavior? (2) Why is there in such interactions a suppression of strange particle production? We show that the recently proposed mechanism of thermal hadron production through Hawking–Unruh radiation can naturally account for both. The event horizon of color confinement leads to thermal behavior, but the resulting temperature depends on the strange quark content of the produced hadrons, causing a deviation from full equilibrium and hence a suppression of strange particle production. We apply the resulting formalism to multihadron production in e
 +
 e
 − annihilation over a wide energy range and make a comprehensive analysis of the data in the conventional statistical hadronization model and the modified Hawking–Unruh formulation. We show that this formulation provides a very good description of the measured hadronic abundances, fully determined in terms of the string tension and the bare strange quark mass; it contains no adjustable parameters.

The thermal production of strange and non-strange hadrons in e + e − collisions

We consider noncommutative quantum mechanics with phase space noncommutativity. In particular, we show that a scaling of variables leaves the noncommutative algebra invariant, so that only the self-consistent effective parameters of the model are physically relevant. We also discuss the recently proposed relation of direct proportionality between the noncommutative parameters, showing that it has a limited applicability.

Paolo Castorina

Papers

Noncommutative gravitational quantum well

Thermal hadronization and Hawking–Unruh radiation in QCD

A comparative analysis of statistical hadron production

The thermal production of strange and non-strange hadrons in e + e − collisions

Scaling of variables and the relation between noncommutative parameters in noncommutative quantum mechanics