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