SEKI wrote:On 5/5/18 8:50 AM, SEKI wrote:
> On Friday, May 4, 2018 at 4:59:21 PM UTC+9, Steven Carlip wrote:
>> On 5/1/18 1:41 PM, SEKI wrote:
[...]
>> First of all, what you've described is not the actual derivation
>> of Hawking radiation, but rather a hand-waving after-the-fact
>> description of the mathematics. If you were right, it wouldn't
>> mean Hawking radiation was unrealistic, it would just mean that
>> the description isn't a very good one. You really can't dodge
>> the math; reading pop sci descriptions can sometimes lead to
>> good questions, but it won't give you answers.
> I am sorry, I am neither a professional physicist nor young to
> become one. I merely would like to carry out a thought experiment.
>> But your argument is wrong, too. According to the equivalence
>> principle, the trajectory of an object in a gravitational field
>> is independent of its mass. In a vacuum, a hammer falls with the
>> same acceleration as a feather; a negative mass hammer would do
>> the same. It's simply not true that a negative mass particle
>> would be repelled by a black hole, in either general relativity
>> or Newtonian gravity.
> I am not sure this argument is right or not.
What would it take to make you "sure"?
>> It *is* true that a particle, of positive or negative mass, would
>> be repelled by a negative mass black hole.
> Isn't this inconsistent with what you wrote above?
No. A positive mass attracts everything (including both positive
and negative mass objects); a negative mass repels everything.
> Anyway, I acknowledge that mathematical models of modern physics
> is based on Einstein's equation as far as gravitation is concerned.
> As I wrote previously, Einstein's gravitational equation is
> presented in terms of linear expression of energy-momentum tensor.
> So, negative energy is considered to curve the space-time in the
> opposite direction to positive one. And, I suppose that particles
> with negative energy, if actually present, are to be repelled by
> the black hole.
Spacetime is four dimensional, and its curvature can't really be
described in terms of a "direction." You guess is roughly right,
though -- a positive mass source produces an attractive gravitational
field, and a negative mass source produces a repulsive gravitational
field (up to some subtleties about what counts in "mass").
The point, though, is that an attractive gravitational field attracts
*everything*, and a repulsive gravitational field repels *everything*.
In Hawking radiation, in particular, the black hole mass is positive,
and it's simply not true that it repels negative energy particles.
> If you give me a proof that my supposition is wrong, my question
> is to be resolved and it is really appreciated.
Again, what kind of "proof" do you want?
-- You could take the word of people who actually know general
relativity. (I've been teaching GR for more than 25 years, have
a textbook coming out soon, and have more than 100 published
papers, including a recent review paper on Hawking radiation,
https://arxiv.org/abs/1410.1486, with more than 50 citations in
Google Scholar.)
-- You could learn enough GR to see for yourself.
-- You could... well, I don't know. What else would be a "proof"
you'd accept?
Steve Carlip