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Now, with special relativity applied to the scenario of me getting closer and closer to light speed, my mass would increase with respect to the observer, and also my length would contract in the direction of motion, again with respect to the observer. Now, if this is allowed to continue, there certainly would come a point where my mass would be observed to be very very high, and my length contracted to below my Schwarzschild Radius, now what would happen in this scenario? Would the observer observe a black hole while observing me? if not, what would the observer actually see?(If the observer sees me as a black hole, shouldn't that technically not happen since nothing is different to me from my own point of view!? )

Would I turn into a black hole? and if not, what would the observer see if I do not turn into a black hole? Would the observer notice any gravitational effects from me?

Hritik Narayan
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  • I've deleted an extended comment discussion. That sort of thing should be held in [chat]. – David Z Dec 21 '14 at 16:14
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    @DavidZ: Fair. I think what's not fair is to close the question. The question is interesting and I think the answers given in the other post are false or, as the OP mentioned, completely insufficient. – CuriousOne Dec 21 '14 at 16:19
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    @CuriousOne then post a better answer to the other question. If the questions are really not asking the same thing, such that an answer to this one would not constitute an answer to the other one, then this question should be edited to show exactly what sets it apart from the other question, i.e. what this one is asking that the other one is not, and then it can be considered for reopening. – David Z Dec 21 '14 at 16:21
  • @DavidZ: I did post an answer. Given the overwhelming sentiments on the other post I don't feel like going back there and start discussions about it. It seems a little futile. – CuriousOne Dec 21 '14 at 16:24
  • OK... my final comment on this one: this paper might help and contains citations of the original publication dealing with the problem. I think the paper makes it obvious that intuition doesn't get one too far: http://arxiv.org/pdf/gr-qc/0110032v1.pdf – CuriousOne Dec 21 '14 at 17:01
  • I think my question is mostly about what kind of gravitational effects the observer would see, and hence it is different from the other one mentioned @DavidZ – Hritik Narayan Dec 21 '14 at 17:30
  • I thing the question gets reopened because what I intend to ask for is different from the question this has been marked duplicate to. I ask whether or not the observer would observe any gravitational effects at all, and not only about the black hole part of it! – Hritik Narayan Dec 23 '14 at 13:46

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OK... I can't give a definitive answer to the problem. My intuition tells me that any massive particle or macroscopic mass, boosted high enough, has to look like a black hole. Why? Because it is very hard to see why/how gravity, if we believe in the equivalence principle, should be able to distinguish between kinetic energy and other forms of internal energy (which, by the way, for the case of baryonic matter are also largely kinetic because of relativistic quarks inside the nucleons).

I think the real bummer here is the question what properties a highly boosted Schwarzschild metric really has and what that means to a test particle that gets caught in the near field of such an object.

CuriousOne
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  • could you provide me some sources to study Schwarzschild Metrics? (I'm not too well versed with General Relativity.) preferably basic beginner stuff! – Hritik Narayan Dec 21 '14 at 15:02
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    @HritikNarayan: This is certainly not "beginner stuff". I would love to provide you with a link, but I have not seen a paper like that. Did you try a literature search? – CuriousOne Dec 21 '14 at 15:09
  • I shall, okay!. – Hritik Narayan Dec 21 '14 at 15:14
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    Thought experiment time: Say there's an object travelling along at high enough velocity to make it a "black hole" ala your intuition. If I fire a light pulse at this object such that it is perpendicular to the object's trajectory and strikes the object at the point of closest approach (I have good timing), what happens? There is no doppler shifting of the light pulse; shouldn't it merely reflect off the side of the object and return to me? If so, how can this be a black hole? – Jim Dec 21 '14 at 15:16
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    @Jim: What makes you believe that the light will be reflected? You state implicitly that it will be, but what's the evidence for that? – CuriousOne Dec 21 '14 at 15:21
  • I asked if it should be reflected, and I guess the evidence for it would be mostly intuitive. Much like you admit your evidence for it looking like a black hole is intuition – Jim Dec 21 '14 at 15:24
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    @Jim: I am an experimentalist: my only evidence for this case comes from the equivalence principle and thermodynamics. If you can make microscopic black holes and bounce light off of them, good for you. I can't, and if I can't do experiments, I am not using my intuition to guesstimate what the result should be. All I know about equivalence tells me that an outside observer can't tell one form of energy from another. All the theorists that I have heard talking about it seem to think the same. I will go with that. – CuriousOne Dec 21 '14 at 15:29
  • @Jim: I don't have an intuition about what happens directly at the object. Honestly, I don't think anybody does, or we would have an answer to what's inside a black hole, already. – CuriousOne Dec 21 '14 at 16:20
  • @CuriousOne http://cds.cern.ch/record/428066/files/0002076.pdf Here is a paper about apparent horizons for boosted black hole frames. In it, as I've been trying to explain, they state that the event horizon itself remains invariant under boosts and that, in fact, the apparent horizon for a boosted Schwarzschild black hole is Lorentz contracted. There's a nice figure on page 22 that shows the apparent horizon of the boosted black hole against the apparent horizon of the un-boosted black hole. The horizon gets smaller. So you cannot boost to become a black hole – Jim Dec 21 '14 at 16:25
  • GR uses the rest mass of an object to define the radius of the event horizon of a black hole because whether or not a null ray can escape is entirely dependent on if it can escape in a frame that is fixed on the object. – Jim Dec 21 '14 at 16:35
  • @Jim: And every little bit of a black hole evaporates. We are turning in circles. Your purely geometric description of black hole physics stops somewhere around 1965, when we still thought that black holes can violate the third law of thermodynamics. Today we don't think that any longer. – CuriousOne Dec 21 '14 at 16:38
  • That paper was written in 2000 – Jim Dec 21 '14 at 16:40
  • Evaporation is irrelevant. If it doesn't have an event horizon, it isn't a black hole. The event horizon is invariant under boosts and we define its size using the rest mass of the object to determine at what radius a null ray cannot escape. Even though evaporation can decrease that radius, it is not relevant to the fact that a boosted object is not considered a black hole because we use the rest mass to determine if it is one. – Jim Dec 21 '14 at 16:47
  • @Jim: The problem is known and solved. The metric is called Aichelburg-sexl and the paradoxes resulting from it have also been discussed. And why wouldn't they have be? http://en.wikipedia.org/wiki/Aichelburg%E2%80%93Sexl_ultraboost – CuriousOne Dec 21 '14 at 16:54