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My earlier comments related specifically to Schwarzschild black holes - which are stationary, hence they don’t evaporate. Generalising this to the case of an evaporating black hole is not straightforward or trivial. Such black holes are called Vaidya black holes, and this represents an entirely different solution to the field equations, and thus a spacetime with a different geometry. While Schwarzschild is a vacuum solution, Vaidya is not, because now all of spacetime is filled with radiation, so we are no longer in a vacuum. Adding relative motion between observer and a Vaidya black hole does of course not yield the aforementioned Aichlburg-Sexl ultraboost, but some different metric, which I have not encountered in my studies. Like in the Schwarzschild case, that new metric would be related to the Vaidya metric by some coordinate transformation, but I suspect the transformation will be a lot more complex than in Schwarzschild spacetime, mostly due to the presence of off-diagonal terms in the metric tensor. I’m sure it can be done though, and probably has been, though a quick search does not immediately turn up anything. But the answer to your question will be “no” regardless, because in both cases we are in a curved spacetime, so you can’t naively use the transformation rules of SR. The total time dilation here has a kinetic component from relative motion, and a gravitational component from spacetime curvature. So the lifetime a specific observer calculates for the black hole will be subject not only to his relative speed, but also to the particulars of the geodesic he traces out (i.e. to the initial and boundary conditions of his motion), and where on this geodesic he is when he performs the calculation; so it will be some (probably quite complicated) function of his trajectory and the surface area of the horizon (which will itself be some complicated function, since the horizon is no longer spherical for such an observer). This is a common misunderstanding based on the fundamental error of using the wrong solution to the field equations for the scenario at hand. I know that countless papers have been published showing this calculation, but ultimately these results are not physically meaningful. If you naively go and consider free-fall observers in Schwarzschild spacetime, then yes, the maths will show you that they can’t detect Hawking radiation. However, evaporating black holes are by definition not Schwarzschild, so this point is moot. When done correctly using Vaidya spacetime, the free fall observer will definitely detect radiation (it is a non-vacuum spacetime after all!), just at a different temperature relative to other observers. The type of physical spacetime one is in is characterised by curvature invariants, which is something all observers always agree on, even if they use different coordinate charts to map that spacetime. Like I said, one must use the correct spacetime to model this scenario. How in-fall time is related to evaporation time of a black hole in Vaidya spacetime is a question I can’t answer off hand. It would likely depend on the initial mass of the black hole, its age (as calculated by the in-falling observer), and the in-fall geodesic. For solar-mass (at the time of in-fall) black holes though the lifetime of the black hole will be much longer than the length of most in-fall geodesics, by many orders of magnitude.2 points
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Generally speaking, I am on your side. In this specific case, they made a comment where it is difficult to interpret it in any way that isn't racist: The first part of this comment implies that the people that Hitler deliberately committed genocide against don't get to count as "people". The second part is so facially false in its misrepresentation of basic history that it indicates the writer is either a troll or such a committed racist that they don't even care about the genocide itself. Either way, a forum setting is not going to convince them to change their ways. Part of the difference is that they did more than express distaste. They used that distaste to make derogatory claims about black culture as a whole, and to dismiss the protests without even engaging with the basic claims of the protests, with a strong implication that black people don't deserve to protest. On a side note: I strongly disagree with the implication that "disrespect for authority" is necessarily a problem. To a large extent, the protests are about the claim that that authority is being abused - and authority being abused should not be respected.2 points
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How did the planet lose the excess kinetic energy, which would be required to be captured? What evidence do you have to support your hypothesis?1 point
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It wasn’t a compliment. It was an accurate answer to your query. Idiot Unsure how that’s gonna play in txt medium, but I mean it as a silly ribbing of a friend just so we’re clear1 point
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That's what I think. Art and/or symbolism certainly imply intelligence. But I would make the further qualification that first hints only too reasonably come later than the real thing. The excavations of Homo naledi (335,000–236,000 years ago) at the Rising Star cave in South Africa have shown that, very likely, a stray cousin of ours that looked very much like an upright ape and didn't use tools or made any kind of art, seemed to go to the trouble of carefully placing their dead in an almost inaccessible dead end of a cave where no other fossils of animals have been found. My suspicion is that some "human" attributes go farther back than we dare to postulate. Cautiousness is mandatory, of course.1 point
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I think the key words (e.g., for a Google search) here are "theory of mind" and "anthropology." IOW: Humans at some point started to realise other humas also thought and try to guess what the other human was thinking, in order to extend prediction to the context of the human mind itself. Some scholarly sources: https://evolutionaryanthropology.duke.edu/research/3chimps/research/theory-of-mind#:~:text=Theory of Mind,that differ from our own. https://www.youtube.com/watch?v=j-bUEgalv-8 https://www.youtube.com/watch?v=TFTe3z5ISGo1 point
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True, which is why it is better to define the event horizon in terms of the geodesic structure of the spacetime in question. If there is relative motion at relativistic speeds between observer and black hole, then we need to label events in that spacetime in a different way. The relevant metric for this case is called the Aichlburg-Sexl Ultraboost. In these coordinates the black hole is not spherically symmetric, so the horizon area is different, and hence also the Hawking temperature (which is consistent with the Unruh picture of this scenario). Generally speaking, temperature is an observer-dependent quantity. It should be noted though that we are still in the same physical spacetime - Schwarzschild and Aichlburg-Sexl are related by a (more or less) simple coordinate transformation, i.e. the observer just labels events in that same spacetime differently, from his own point of view. And of course it needs to be that way, because obviously relative motion cannot affect the geometry of spacetime. The event horizon itself is not merely an artefact of coordinates, it originates in the geodesic structure of the spacetime in question, which is of course something all observers agree on. What is an artefact of the coordinates is the (coordinate) singularity, which, in the Schwarzschild metric, happens to coincide with the physical location of the event horizon. There is no physical reason that this must be so, other than the boundary conditions of this particular metric. Once could simply choose a different coordinate chart, which eliminates the singularity, but leaves the event horizon. Spacetime itself is smooth, continuous, and geodesically complete at the horizon, which is easily shown by looking at the curvature invariants of the Riemann tensor. Below the event horizon, there are no stationary rest frames - all geodesics are incomplete, i.e. must terminate at the singularity. This is true regardless of what coordinate chart you use to cover this spacetime, and the horizon is always at the same physical location (which of course will have different coordinate labels in different charts). Yes, it is the “point of view” (so to speak) of an observer at rest at asymptotically flat infinity. Schwarzschild coordinates also cover only parts of this spacetime, namely the exterior region above the horizon, excluding the horizon itself and everything below it. If one needs to examine spacetime at or below the horizon (in the classical picture of course), a different coordinate chart is needed, usually Kruszkal-Szekeres, or Gullstrand-Painleve, depending on the problem at hand.1 point
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When you speak, it’s not hateful. When we reply, you respond reasonably. When you mention black peoples, it doesn’t sound like you equate them with cockroaches.1 point
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Good answers to you both however the correct answer gets more complex. @md65536 the Schwartzchild metric though it is still a horizon breaks down on different observers. The coordinate system cannot accurately describe the causal nature of events. @Endy0816 the radius of the null surface would change afiak however the mass determines the radius so it would not be an inverse relation. However the null surface isn't necessarily the event horizon..... (more on that later) ( I could very well be wrong on this) This is where we can finally get back to the Ops misunderstanding on Hawking radiation. There is another horizon called the Apparent horizon which represents the trapped surface. This trapped surface may or may not coincide with the event horizon described by R_s=2GM. Here is an article covering this. https://www.google.com/url?sa=t&source=web&rct=j&url=https://arxiv.org/pdf/hep-th/9501071&ved=2ahUKEwixr5mr7IzqAhWHvZ4KHZhcA44QFjABegQICRAB&usg=AOvVaw2CyhOXTEPO_MkckNS8tQqE Now the Apparent horizon definitely changes according to the observer. I'm unclear if the Schwartzchild event horizon does due to its limitations of valid observers and being a coordinate singularity that doesn't truly describe causality for all observers. (Future past lightcones etc) Let's readdress this question now that we are looking at apparent horizons being involved in causal relations. @rjbeery Don't get discouraged the Penrose diagrams are extremely confusing with regards to causal connections even with lightcones. Hawking radiation is described in more detail in the last link but note which region it occurs. @everyone involved I am far more familiar with cosmology and particle physics than black hole dynamics. Lol unlike many I studied them to a certain extent but it's never been a focal point in my studies. 🤔 Anyways here is another article covering horizons in regards to BH's Black hole Boundaries. https://arxiv.org/abs/gr-qc/05081071 point
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What you may have overlooked was Essereio's clear association of certain distasteful social tendencies (ex: loud music and voices, disrespect, drugs, and gun) specifically with "black people." His rap music references were a means to characterize his perspective of a people rather than his or our dislike for a certain music genre. "A good portion of black people", using Essereio's words, aren't anymore inherently loud, disrespectful, misogynistic, or into drugs and guns than a good portion of people of other racial distinctions. It wasn't what he said about the music that's important here, it was how he used that music reference to describe a people. Rap, as I understand, is a culture that engages people of multiple races. Admittedly, I'm no more a fan of rap music than my parents were fans of rock and roll. It a generational thing and one I accept as the sound of all young people and not just people of color.1 point
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Your "freedom" will surely carry you along whatever incoming currents determine... we are but twigs in the shoulders of a mighty stream.1 point
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! Moderator Note That’s out of place here. “Can X happen” is a very different question from “Can X happen under conditions A, B and C” If you don’t give specifics you’re wasting peoples’ time. Threads like this are arguably in violation of our “good faith” rule. If you have physics questions ask them in the correct forum. If you post in speculations you are expected to actually post your speculation and provide the rigor we require.1 point
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It is an important issue. Carbon dioxide is important for life to flourish. Right now we have too little carbon dioxide. Watch the video below by the scientist William Happer. William Happer is an American physicist who has specialized in the study of atomic physics, optics and spectroscopy. He is the Cyrus Fogg Brackett Professor of Physics, Emeritus, at Princeton University, and a long-term member of the JASON advisory group, where he pioneered the development of adaptive optics. From 1991 to 1993, Happer served as director of the Department of Energy's Office of Science as part of the George H.W. Bush administration. In 2018, Happer joined the National Security Council of the Trump Administration. https://youtu.be/U-9UlF8hkhs-2 points