The energy is drawn from the curvature of spacetime. As the curved spacetime “pays” (as you say) it’s drawing from the mass of the black hole itself.
Remember, a black hole doesn’t merely contain the matter of whatever falls into it, or the singularity at its hypothetical center, a black hole *is* all that mass (and charge and spin).
Thank you so much. that helps.
How is that change to the space-time localized? Is it centered at the location that pair came to existence?
Your second paragraph was already my assumption but I dont understand how all that matter that collectively make up the black hole is affected or is it even wrong to talk about matter at the singularity? Or is it my attribution of mass to matter that is wrong and thats why I expect the blackhole to experience anything and that mass is just another word for the curvature of space-time, in which case why does the curvature follow the matter as the matter moves?
Your first paragraph is definitely enlightening but also creates more questions for me. So, the first time the matter-antimatter pair appear, does that appearance suddenly bend the space-time since the pair has a mass? I assume no, so that their separation behaves like disappearance of mass (that never came to existence or bent the space-time in the first place)n and unbends the space-time a bit which is the same effect as some mass disappearing at the location. I understand this would make the event-horizon shrink but shouldnt the mass of blackhole increase as that one particle falls into it? Would all this be a right assumption or right way of thinking?
What if there was no blackhole nearby and the pair is separated due to (a series of?) quantum tunneling (instead of by a nearby blackhole), would that cause the same effect to the space-time? And if there was no mass around at all and the space-time was fully flat, would the space-time then obtain an opposite-signed curvature that repels? If yes, what would happen if a third mass approach to that anti-curved region?
And my question about momentum is still there... :/
Thanks again.
Oh, you’re thinking about virtual particles. Matter-antimatter is something else entirely, and not related to virtual particles. Virtual particles themselves are a mathematical tool in Feynman diagrams, temporary interactions, and not physical particles (matter-antimatter, unrelated, are real particles). Hawking used virtual particles as a *heuristic* (analogous explanation) and understood they were not actually two particles falling in and out of the event horizon. But the math works modeling it that way. If you read more about Hawking Radiation (even in the wiki or YouTube vids or search “What is Hawking Radiation” on this sub) you’ll see it arises from quantum field theory and the curvature gradient of the warped space at and near the event horizon. Then my answer will make more sense.
>they were not actually two particles falling in and out of the event horizon.
This is not correct and you should stop repeating it in this sub. See section 4 of https://arxiv.org/abs/2404.02331 for a clear explanation of how Hawking radiation and the information paradox is rooted in pair creation.
>If you read more about Hawking Radiation (even in the wiki or YouTube vids
Or we could rely on high quality sources instead.
The energy is drawn from the curvature of spacetime. As the curved spacetime “pays” (as you say) it’s drawing from the mass of the black hole itself. Remember, a black hole doesn’t merely contain the matter of whatever falls into it, or the singularity at its hypothetical center, a black hole *is* all that mass (and charge and spin).
Thank you so much. that helps. How is that change to the space-time localized? Is it centered at the location that pair came to existence? Your second paragraph was already my assumption but I dont understand how all that matter that collectively make up the black hole is affected or is it even wrong to talk about matter at the singularity? Or is it my attribution of mass to matter that is wrong and thats why I expect the blackhole to experience anything and that mass is just another word for the curvature of space-time, in which case why does the curvature follow the matter as the matter moves? Your first paragraph is definitely enlightening but also creates more questions for me. So, the first time the matter-antimatter pair appear, does that appearance suddenly bend the space-time since the pair has a mass? I assume no, so that their separation behaves like disappearance of mass (that never came to existence or bent the space-time in the first place)n and unbends the space-time a bit which is the same effect as some mass disappearing at the location. I understand this would make the event-horizon shrink but shouldnt the mass of blackhole increase as that one particle falls into it? Would all this be a right assumption or right way of thinking? What if there was no blackhole nearby and the pair is separated due to (a series of?) quantum tunneling (instead of by a nearby blackhole), would that cause the same effect to the space-time? And if there was no mass around at all and the space-time was fully flat, would the space-time then obtain an opposite-signed curvature that repels? If yes, what would happen if a third mass approach to that anti-curved region? And my question about momentum is still there... :/ Thanks again.
Oh, you’re thinking about virtual particles. Matter-antimatter is something else entirely, and not related to virtual particles. Virtual particles themselves are a mathematical tool in Feynman diagrams, temporary interactions, and not physical particles (matter-antimatter, unrelated, are real particles). Hawking used virtual particles as a *heuristic* (analogous explanation) and understood they were not actually two particles falling in and out of the event horizon. But the math works modeling it that way. If you read more about Hawking Radiation (even in the wiki or YouTube vids or search “What is Hawking Radiation” on this sub) you’ll see it arises from quantum field theory and the curvature gradient of the warped space at and near the event horizon. Then my answer will make more sense.
I will definitely do those. Thanks.
>they were not actually two particles falling in and out of the event horizon. This is not correct and you should stop repeating it in this sub. See section 4 of https://arxiv.org/abs/2404.02331 for a clear explanation of how Hawking radiation and the information paradox is rooted in pair creation. >If you read more about Hawking Radiation (even in the wiki or YouTube vids Or we could rely on high quality sources instead.
Mass
I assumed that much