A Brief History of Time

The updated and expanded tenth anniversary edition
Stephen Hawking
Bantam Books, 1988-1996

Chapter 2 - Space and Time, p 19

The fact that light travels at a finite, but very high, speed was first discovered in 1676 by the Danish astronomer Ole Christensen Roemer [Rømer]. [...] Nevertheless Roemer's achievement [...] was remarkable--coming as it did eleven years before Newton's publication of Principia Mathematica.

Chapter 3 - The Expanding Universe, p 42

In 1922, several years before Edwin Hubble's discovery, Friedmann predicted exactly what Hubble found!

Chapter 7 - Black holes ain't so black, p 109

How is it possible that a black hole appears to emit particles when we know that nothing can escape from within its event horizon? The answer, quantum theory tells us, is that the particles do not come from within the black hole, but from the "empty" space just outside the black hole's event horizon!

p 110

Because energy cannot be created out of nothing, one of the partners in a particle/antiparticle pair will have positive energy, and the other partner negative energy. The one with negative energy is condemned to be a short-lived virtual particle because real particles always have positive energy in normal situations. [...] However, a real particle close to a massive body has less energy than if it were far away, because it would take energy to lift it away against the gravitational attraction of the body. Normally, the energy of the particle is still positive, but the gravitational field inside the black hole is so strong that even a real particle can have negative energy there. It is therefore possible, if a black hole is present, for the virtual particle with negative energy to fall into the black hole and become a real particle or antiparticle. In this case, it no longer has to annihilate with its partner. Its forsaken partner may also fall into the black hole as well. Or, having postive energy, it might also escape from the vicinity of the black hole as a real particle or antiparticle. to an observer at a distance, it will appear to have been emitted by the black hole. The smaller the black hole, the shorter the distance the particle with negative energy will have to go before it becomes a real particle, and thus the greater the rate of emission, and the apparent temperature, of the black hole. [...]
A flow of negative energy into the black hole [...] reduces its mass. As the black hole loses mass, the area of the event horizon gets smaller, but this decrease in the entropy of the black hole is more than compensated for by the entropy of the emitted radiation, so the second law is never violated.
Moreover, the lower the mass of the black hole, the higher its temperature. So as the black hole loses mass, its temperature and rate of emission increase, so it loses mass more quickly. What happens when the black hole eventually becomes extremely small is not clear [...]

Chapter 10 - Wormholes and Time Travel


Physics, Essays
Marc Girod
Last modified: Wed Apr 7 11:52:08 EEST 2004