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

The Search for Supersymmetry: Probing Physics Beyond the Standard Model

Extended Theories of Gravity

Vacuum configurations for superstrings

I provide a pedagogical introduction to supersymmetry. The level of discussion is aimed at readers who are familiar with the Standard Model and quantum field theory, but who have had little or no prior exposure to supersymmetry. Topics covered include: motivations for supersymmetry, the construction of supersymmetric Lagrangians, superspace and superfields, soft supersymmetry-breaking interactions, the Minimal Supersymmetric Standard Model (MSSM), R-parity and its consequences, the origins of supersymmetry breaking, the mass spectrum of the MSSM, decays of supersymmetric particles, experimental signals for supersymmetry, and some extensions of the minimal framework.

A Supersymmetry Primer

On Kaluza-Klein theory

Super-gauge transformations

Spontaneous Compactification in Six-Dimensional Einstein-Maxwell Theory

Super-symmetry and non-Abelian gauges

A Lagrangian theory is formulated describing the intrinsic mixing of the graviton with a massive ${2}^{+}$ $f$ meson which interacts universally with hadrons through the stress tensor. The theory is developed as an analog of the well-known $\ensuremath{\rho}\ensuremath{-}\ensuremath{\gamma}$ model of hadron electrodynamics, and in particular a field-current identity is exhibited which equates the massive ${2}^{+}$ meson with the hadronic energy-momentum tensor. An Einstein-type Lagrangian is used for both spin-2 particles, and general covariance is preserved throughout. The nonlinear coupling of the hadrons to the $f$ meson leads, within the framework of nonpolynomial field theories, to a universal cutoff for strong-interaction physics.

J.A. Strathdee

Papers

On Kaluza-Klein theory

Super-gauge transformations

Spontaneous Compactification in Six-Dimensional Einstein-Maxwell Theory

Super-symmetry and non-Abelian gauges

f -Dominance of Gravity