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Thread: Hawking radiation: time passing in and outside the EH?

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    Hawking radiation: time passing in and outside the EH?

    With Hawking radiation,radation is emitted by a black hole over billions of years, yet it is said that there is no time inside the event horizon...so how are these spread out(in time) HR emissions separated, as events, inside the EH?

    Is the answer something to do with the coordinate system inside the EH..?
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    Quote Originally Posted by WaxRubiks View Post
    With Hawking radiation,radation is emitted by a black hole over billions of years, yet it is said that there is no time inside the event horizon...so how are these spread out(in time) HR emissions separated, as events, inside the EH?

    Is the answer something to do with the coordinate system inside the EH..?
    This comes up if you google 'time inside a black hole':

    http://www.hawking.org.uk/into-a-black-hole.html

    Straight from Hawking.

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    There is time inside the event horizon.

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    Yes, it has to do with how tricky it is to get a coordinate system that works normally across the event horizon. When people say time stops at the EH, they really mean they are attempting to cover the global spacetime from them, at large distance from the black hole, to the EH, using a single coordinate system called Schwarzschild coordinates. This is vaguely analogous to trying to extend your own local north-south-east-west coordinate system all the way to the north pole. You say that you can take a step in any of those four directions, but that someone at the north pole cannot-- any step they take will be south. So it sounds like north, east, and west have somehow vanished at the north pole, yet a person at the north pole feels no different from you, and feels like they can take a step in any of four distinct directions just like you do. Similarly, the person a great distance from the black hole may choose coordinates that make it seem like the time direction goes away at the EH, but the person at the EH thinks time is acting perfectly normally.

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    Quote Originally Posted by WaxRubiks View Post
    With Hawking radiation,radation is emitted by a black hole over billions of years, yet it is said that there is no time inside the event horizon...so how are these spread out(in time) HR emissions separated, as events, inside the EH? Is the answer something to do with the coordinate system inside the EH..?
    I think the answer is no. I think the answer is that Hawking radiation totally ignores gravitational time dilation. I don't say that lightly, I've read all Hawking's papers on the subject, and other material.

    Hawking’s first paper on Hawking radiation was arguably the four laws of black hole mechanics, co-authored with Brandon Carter and Jim Bardeen in 1973. But I'd say his most significant paper was black hole explosions? which appeared in Nature in 1974. That’s where Hawking claimed that "any black hole will create and emit particles such as neutrinos or photons at just the rate that one would expect if the black hole was a body with a temperature of (κ/2π)(ħ/2k) ≈ 10−6 (M /M)K where κ is the surface gravity of the black hole”. He made further claims, saying the temperature will increase as the hole loses energy, and a smaller black hole would end its life in an explosion "equivalent to about 1 million 1 Mton hydrogen bombs". He talked about a massless Hermitian scalar field in an asymptotically flat spacetime. He referred to the Heisenberg operator ϕ with ai and ai+ interpreted as creation and annihilation operators. He talked about outgoing waves and waves crossing the event horizon and positive and negative frequencies. He said the number of particles created and emitted in a gravitational collapse can therefore be determined. He also talked about a wave propagating backward in spacetime from future null infinity to past null infinity. But there's no mention of gravitational time dilation.

    Edit: anybody, what's the score re attachments? Hawking's paper was freely available, now it appears to be paywalled, so I've attached a copy below.
    Last edited by The Physics Detective; 2019-Jan-24 at 02:23 PM.

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    Quote Originally Posted by WaxRubiks View Post
    With Hawking radiation,radation is emitted by a black hole over billions of years, yet it is said that there is no time inside the event horizon...so how are these spread out(in time) HR emissions separated, as events, inside the EH?
    Hawking radiation does not come from inside the event horizon.
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    Quote Originally Posted by The Physics Detective View Post
    I think the answer is no. I think the answer is that Hawking radiation totally ignores gravitational time dilation.
    So, you're saying that a photon of Hawking radiation would follow a different spacetime trajectory from a photon that did not originate as Hawking radiation? Which would imply that, in principle, we should be able to separate Hawking radiation photons for other photons with the same trajectory, simply by passing them through a strong gravitational field.

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    Quote Originally Posted by The Physics Detective View Post
    Edit: anybody, what's the score re attachments? Hawking's paper was freely available, now it appears to be paywalled, so I've attached a copy below.

    The Physics Detective: Your attached article appears to be a copyrighted article from Nature, and as such cannot just be scanned and posted here, therefor it was removed. Please don't do this again.
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    And, actually, the fact that time passes inside the event horizon is important in the "virtual pair" model of Hawking radiation. It's that fact that the time axis is directed radially within the event horizon that allows the infalling member of the pair to have negative energy as measured at infinity.

    Grant Hutchison
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    Interesting point, I never could see where the negative energy idea was coming from!

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    Quote Originally Posted by Ken G View Post
    Interesting point, I never could see where the negative energy idea was coming from!
    Yeah - I may be pushing things too far, but my understanding is that because the time axis has swapped with a spatial axis, energy can correspondingly behave "momentum-like", and so can have negative values for that famed distant observer.

    Grant Hutchison
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    During life, we all develop attitudes and strategies to make our interactions with others more pleasant and useful. If I mention mine here, those comments can apply only to myself, my experiences and my situation. Such remarks cannot and should not be construed as dismissing, denigrating, devaluing or criticizing any different attitudes and strategies that other people have evolved as a result of their different situation and different experiences.

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    That sounds perfectly reasonable to me.

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