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Correct, the standard Schwarzschild metric is asymptotically flat and indeed the time co-ordinate $t$ is the local time of an observer infinitely removed from the black hole and sitting in this flat space and so there is no pair of points outside the black hole's event horizon which ultimately cannot causally reach or signal each other. The de ...


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Actually its perfectly possible within standard GR to do so! The question then becomes at what point does GR break down, and if it formed a mass at that point would it have time to decay via hawking radiation down to a Planck remnant? Many types of matter exhibit what is called type II critical collapse where if you carefully tune initial data, you can ...


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If I understand correctly, you are just asking about the relation between energy and distances in both radiation and matter (and cosmological constant) dominated eras of the expansion of the universe. Consider the Einstein equation $$ G_{\mu\nu} = 8\pi G T_{\mu\nu} \ ,$$ where $G$ is Newton's constant. In a FLRW unverse $G_{\mu\nu}$ is diagonal and using ...


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I don't think I can explain all the technical stuff, but first things first. Primordial means "at the creation", so if it was created today it wouldn't be primordial. Now "Primordial size" black hole, is probably what you mean and even that is a bit vague as estimates vary on the possible sizes of Primordial black holes, (and there's some uncertainty as ...


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If people brought all the trash in the galaxy to a single place and dumped it, a black hole could eventually form from the ever-increasing density without ever forming a star. Hypothetically, a bunch of heavier elements (incapable of starting a fusion/fission process to hold the gravitational collapse at bay) could happen to end up in the same region of ...


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Cosmic rays have a de Broglie wavelength. The de Broglie wavelength is redshifted by the expansion of space in the same way that the wavelength of light is redshifted. Another way of saying this is that their peculiar momenta with respect to a co-moving local volume decrease as the inverse of the scale factor. This means that the energies of any cosmic rays ...


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The critical density is an observable quantity. $$\rho_C = \frac{3H_0^2}{8\pi G},$$ where $H_0$ is the present-day value of the Hubble parameter. $H_0$ is known (observationally) from a variety of methods to be 69 km/s per Mpc, with an accuracy of about 1 per cent. So to answer your question as posed, the critical density has a confidence interval of about ...


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You are approaching the question from the wrong end. The expansion of the universe is described by a particular solution to Einstein's equation called the FLRW metric. To derive this metric we have to make some assumptions, and the key assumptions are that the universe is isotropic and homogeneous i.e. that it is the same everywhere. So the universe being ...


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Expansion of space is allowed by General Relativity. Which has made quite specific predictions that passed. So it seems valid to have solutions with an expanding space on the table (and leave it to observation to exclude them or to favor them). And there are two different situations where it comes up. A cosmological context where the expansion is the ...


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Yes. You can make a model where you have coordinates $t, x,y,z$ where for any $x,y,z$ the universe looks the same. The metric ends up looking e.g. like $$ds^2=dt^2-(a(t))^2(dx^2+dy^2+dz^2)$$ and you can move your $x,y,z$ to have any value and everything looks the same (those things do loom different for different cues of $t$). You end up with the densities ...


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You are not travelling faster than light in the sense that if you send some light to your destination it gets there before you do. It can be faster than light in the sense that if space is isotropically and homogeneously distributed with energy and such then there is an obvious global frame and distance in the global frame between two points can decrease ...


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My understanding is that Hubble said the farther our we look into the Universe, the higher the redshift, therefore the faster things are moving. Pretty much. If you were some raisin in a rising cake, you'd say the same of the other raisins. But my question is, why is this surprising? It isn't. What was surprising is that the expansion rate is ...


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The first thing is to change your cartoon picture of Big Bang (an exploding egg of matter and energy). Big bang was not an explosion it was the start to expansion and the big bang theory tells the aftermath of this i.e. How the Universe evolved with time.What Hubble did observe was that the farther the galaxy or the source of light was faster it seemed to ...


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If you don't want to violate causality then you can only have a few types of faster than light travel. One is to not allow it to slow down. Another is to only allow it to go in one direction and hope the universe is infinite. Otherwise it is rather trivial to use regular slower than light motion between some FTL trips to generate a time machine. As for ...


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good strategy! Hubble Constant = Ho = [d/s]/[d/1] in basic variables, thus it reduces to 1/s which is time inversed, that is, the inverse of the age of the universe at whatever Ho constant value used and further adjustments from the Standard Model equations. The big adjustment is U. acceleration [ and significant deceleration during first 2 billion years]. ...


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The de Broglie wavelengths of freely propagating particles (i.e. forget interactions) are redshifted by the expansion of the universe. Another way of saying this is that their peculiar momenta with respect to a co-moving local volume decrease as the inverse of the scale factor. As neutrinos have a non-zero mass (perhaps 0.1 eV - see Battye & Moss 2014, ...


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At the moment there does not exist a quantized unified theory of gravitation and the standard model. The only candidate to date is string theories which are at a research level, and in which I am not able to form an answer. There exist effective quantizations of gravity and effective models including the standard model in the studies of cosmology and the ...


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Does the accelerated rate of expansion of the Universe have any effect on the velocity of light? This is the subject of some debate. Check out the Wikipedia Variable Speed of Light article: "The idea from Moffat and the team Albrecht–Magueijo is that light propagated as much as 60 orders of magnitude faster in the early universe, thus distant regions ...


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The expansion of the Universe has no effect on the local speed of light. Any local measurement of $c$ will yield $c$, and $c$ won't change. There is one thing that often causes confusion about the speed of light or faster-than-light travel. A photon moving in an expanding space-time appears to move at an average speed faster than $c$. Consider a ...


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The Michelson-Morley experiment indicated (contrarily to it's original intent), that the speed of light perceived by an observer is not dependent on their speed relative to anything. Along these lines, our movement in space with respect to any arbitrary point has no impact on the speed of light measured in the earth system. Disclaimer: did not hear a ...



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