Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics. It's 100% free.

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

If we had a positive point charge of incredible quantity, does there exist an imaginary sphere about it, such that regardless of the initial speed and direction of any electron, that electron could not escape spiraling into the positive point charge?

Conversely, regardless of the initial speed and direction of a proton (even if it's position starts from within the imaginary shell), it's path could never intersect with the position of the point charge?

share|cite|improve this question

No, because the kinetic energy of an electron can be increased without limit by accelerating it close to the speed of light. It will always be possible to increase the kinetic energy of the electron to the point where it matches the potential energy due to the positive charge, so the electron can always escape to infinity.

Similarly you can accelerate an incoming proton to arbitrary energy, so you could get it to within any specified distance of the central positive charge.

By contrast you cannot get the electron out from inside an event horizon because the electron's energy will contribute to the stress-energy tensor and hence the curvature.

share|cite|improve this answer
I'm not sure that is the most pedagogical way to formulate why an electron cannot escape an event horizon. – BjornW Jul 26 '12 at 21:02
Yes, I'd have to agree, but it's hard to explain why, for example, an electron can't escape from a black hole without resorting to the maths. I did this in my answer to, but I don't think an answer of this nature would help the OP get a grasp of what's going on. If you can find a more elegant way to restate my final paragraph please do post it as an answer - I'd certainly upvote it! – John Rennie Jul 27 '12 at 5:59

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.