UNIVERSITY OF CAMBRIDGE
Department of Applied Mathematics and Theoretical Physics
Silver Street, Cambridge CB3 9EW
Telephone: Cambridge (0223) 337900. Direct Line: (0223) 337844
S. W. Hawking, C.B.E. F.R.S.
Lucasian Professor of Mathematics

June 3,1988
Dear Andy,
Thank you for your letter, and I am glad that you have enjoyed "A brief history of time" so much. As to your questions, I will answer these below:

Close to the event horizon, pairs will be produced. One will have negative energy and be an antiparticle the other with positive energy, normally, from which is now subtracted a huge amount of energy due to their proximity. Thus you could have 1 very negative energy anti-particle, and 1 particle which may have positive or negative total energy. In your example I believe you want the anti-particle to fall in first. This leaves a particle with negative energy. It has two options: either it falls in through normal gravity, or it flies away, gaining total energy as it goes, and thus becoming a positive energy particle again. If it falls in, then it's energy will become even less, as it is getting nearer the black hole. However if it had a huge energy at the beginning it might never get near enough (due to the uncertainty principle) to the black hole (inside the event horizon) to cancel all of it out. Thus it can have positive energy, though it's more likely it will go negative eventually.

The reason why black holes do exert a gravitational attraction is because of the curvature of space time. The event horizon stops particles, and light from travelling along space-time, but the surface is still there. Imagine throwing a rock in the air. You will never be able to throw it up more than 200m, thus you could say that 200m is the "Event horizon for rocks". This doesn't mean that space stops 200m up.

I hope this answers your questions,
yours sincerely
N.B.P. Phillips,
Assistant to Professor Hawking.

UNIVERSITY OF CAMBRIDGE
Department of Applied Mathematics and Theoretical Physics
Silver Street, Cambridge CB3 9EW
Telephone: Cambridge (0223) 337900. Direct Line: (0223) 337844
S. W. Hawking, C.B.E. F.R.S.
Lucasian Professor of Mathematics

September 11,1988
Dear Andy,
Thank you for your far too flattering response to my answers, usually I speak gibberish!. Anyway I'm sorry to have left two of your questions unanswered, and will try to make ammends now. Negative energy particles do not, I'm afraid, have negative gravity or inertia. This is because they have a total negative energy, which is made up of one part which is negative and another positive. The positive part is due to their mass, binding energy etc (all this energy gives them inertia and acts on gravity) and another negative part due to their position in the gravitational well. The deeper into a black hole that they go, the more negative energy they acquire, which in turn causes their TOTAL energy to decrease, eventually going negative and causing a negative energy particle! Thus, though their TOTAL energy is now negative, the energy that makes them suseptible to gravity is, and has always been positive, perhaps even increasing a little as they achieve great speeds on their fall into the black hole.

If there was a singularity in the center of a black hole, then these particles would continue to fall forever towards it, gaining negative energy all the time, and thus all particles would eventually attain negative total energy, regardless of however much positive (mass etc) energy they had at the beginning. However, if, as suspected, small-scale quantum mechanical effects come into play prohibiting a singularity, then there would be a maximum amount of negative energy that any particle could gain. So, lighter particles with less positive energy would end up with negative total energy, while the more massive (high positive energy particles) would, even after the addition of the maximum negative energy, still have positive total energy. I hope that isn't too confusing.

As to your last question, I think it's about an attribute called "Helicity" that photons carry h = ~1. It's rather like spin, and can point in either clockwise or anti-clockwise direction, along the photons path. The interaction of the helicity with the incident particle causes either a repulsion or attraction. However, it's ages since I took HEP courses, and I couldn't be sure !!!

Lastly, thank you for the great photos, were they taken with a Celestron C8 ? I studied Astronomy in my second degree and was perpetually looking through various telescopes at the great beauty of the stars. However these are some of the best photos I've seen, especially of Halley's comet, as Scotland didn't get too good a view! Once agaln, thank you, and I hope this is all useful,

yours sincerely,
N.B.P. Phillips,
Assistant to Professor Hawking