New answers tagged

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An electron being a ball of uniform mass and charge is not consistent with its observed gyromagnetic ratio. The charge must be pushed out and the mass must be pushed comparatively inwards to satisfy the existing ratio of about 2. See Classical proof of the gyromagnetic ratio $g=2$


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Any observer outside the Schwarzschild radius sees the same thing: matter approaching the Schwarzschild radius at slower and slower (asymptotically zero) speed, forming a thin shell around the event horizon. The matter takes an apparently infinite time to collapse, and infinity is infinitely larger than a large finite the same way it's infinitely larger than ...


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BHs can carry charge - so you squirt some electrons into it to charge it and then use an electrical charge on the parabolic reflector to couple it to the ship.


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The conservation of $\vec{k}\cdot\vec{u}$ only holds in the test particle limit. That is, it considers the metric to be unaffected by the motion of the particle. In this limit, there are no gravitational waves, since the metric has no time-varying quadrupole. If you want to see gravitational waves, you need to allow the metric to evolve dynamically, ...


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There is a treatment of lowering a string through a Rindler horizon here, (which contains a brief discussion on the extent to which the approximation is representative).


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It is not a coincidence. It has to work like that. The deficit angle has to be zero. It's most convenient to see it in the Feynman's path integral approach to quantum mechanics. One works in the Euclideanized spacetime to calculate the temperature $T=1/\beta$ partition sum. Let us consider the full finite-size black hole; the Rindler geometry is a local ...


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That's fairly small for an object. It wouldn't have any significant gravitational effect on the moon or the earth. Tidal effects go as the cube of the distance. So the sun has about half the tidal effects of the moon. If this object were in low earth orbit (400km altitude), then the relative tidal effects on the surface when it is overhead would be about ...


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To answer this we need to talk a bit about how particles are described in quantum field theory. For every type of particle there is an associated quantum field. So for the electron there is an electron field, for the photon there is a photon field, and so on. These quantum fields occupy all of spacetime i.e. they exist everywhere in space and everywhere in ...


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@JohnDuffield: I can give you both a correct answer in simple terms and the fairy tale, together with references to an explanation how the fairy tale is related to the real thing! The dry facts are that two real particles (e.g., two photons, or an electron and a positron) are created from the energy in the very strong gravitational field near the horizon of ...


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Let us for simplicity work in units where the speed of light $c=1$ is equal to one, and assume that there is no cosmological constant $\Lambda=0$. A spherically symmetric vacuum solution to the EFE of the form $$\tag{1} ds^2~=~g_{tt}(r)dt^2 + g_{rr}(r)dr^2 +r^2 d\Omega^2,$$ such that it asymtotically becomes Minkowski space $$\tag{2} ...


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Suppose you have two systems $S_1,S_2$ with Hilbert spaces $H_1,H_2$ with a density matrix $\rho$ on $H_1\otimes H_2$. The partial trace of $\rho$ over the Hilbert space of one of the systems, $H_1$ say gives you a reduced density matrix $\rho_2$. The reduced density matrix predicts the expectation values of all the measurements you can conduct on $S_2$ ...


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Since everybody seems to need the kid who cries that the emperor has no clothes, I am more than happy to make the same statement in an answer: the question posed by the black hole complementarity paradox is unphysical. Information is always lost in any physical systems. Thermodynamics is about nothing else than information loss. Whether it's melting ice ...


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Conserved quantities in GR In GR, energy (or mass) is typically an ill-defined concept. In flat spacetime, we define energy as the conserved quantity corresponding to time translational symmetry. Extending this to GR is quite tricky mainly because, what one is calling time is already observer dependent (this is of course also true in flat spacetime, but at ...


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Is there another way to conclude the Schwarzschild solution has a mass M It's not so much a conclusion as a definition. From Schutz in "A first course in general relativity", section 8.4 "Newtonian gravitational fields", pages 207 - 208: Any small body, for example a planet, that falls freely in the relativistic source's gravitational field ...


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Utilising Black Holes as a potential energy source Have I got a surprise for you! I'm aware of the Penrose process and the basic physics behind that. Be wary of Penrose. He has a habit of appealing to Einstein's authority then flatly contradicting the guy. And then he'll tell you about the parallel antiverse and other fairy tales: Also, I ...


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For the simple case of a spherically symmetric, uniform, pressureless ball we have an analytic solution to describe the collapse called the Oppenheimer-Snyder metric. In this case the event horizon starts at the centre before the singularity is formed and grows outwards. The matter remains as a uniform sphere that eventually shrinks to a point. At no point ...


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Great question. Black holes are some of the brightest objects in the universe. While we think they require the Blandford-Znajek (BZ) mechanisms to produce things like Relativistic Jets, the bulk of the light (emission) they produce is just the efficient thermalization of gravitational energy when material falls into (`accretes' onto) them. The simplest way ...


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For a given mass the gravitational attraction remains the same -- but only if you are far away. For example, the surface gravity of Sol, our sun, is $274$ $ m/s^2$, about 28 times the surface gravity of Terra, which is $9.8$ $ m/s^2$. But as the material is compacted, the surface gravity increases: this is because the effective mass can be treated as ...


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Density here is a bit misleading. For example density of galaxy cluster is low because there is so much space between it. It does not mean all the material inside has low density.. We cannot observe beyond Event horizon, so we use diameter of event horizon to measure volume. Actual matter will be in a smaller volume. To understand why large objects need ...


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This density is not possible that's why earth cannot become Black Hole. Larger masses need less density to convert into black hole. For example super massive black holes in the centre of glaxy need density of water to become black holes !!! link However stellar black hole have much less mass, thus very high density. Even removing all empty space in inside ...


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Is this analogy of Hawking Radiation correct? No. I know you read stuff like this on the internet, in pop-science articles, and even in textbooks. But it's not correct at all. Sorry. I'll go through it step by step: Within the ergosphere of the black hole, virtual pairs of particles and anti-particles are constantly appearing No they aren't. ...


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You have to consider the singularity and event horizon. By observing the orbits of nearby planets and such, we can calculate the approximate mass of the black hole, and thus where the singularity is. This then further gives us the Schwarzschild radius; $R_{Schwarzschild}=\frac{2GM}{c^{2}}$ This defines the event horizon, thus allowing us to then calculate ...


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$du,dv$ are light-like, i.e. they could, in principle, be viewed as some affine parameters of some light-rays. However, we will focus (in the spirit of the usual coordinate-nature analysis) on what is the nature of either $u,v$ constant. I.e., we want to know what is the nature of $u,v$ constant hypersurfaces and derive the nomenclature from this. We will ...


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As the comments have suggested, the problem is that your description of virtual particles appearing to vacuum fluctuations is wrong. Have a look at my answer to Black holes and positive/negative-energy particles for more on this. There isn't an explanation of what is really going on that is accessible to the non-quantum field theory nerd (though I have ...


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There are a few big differences: Tidal effects change the rate at which the orbit decays The neutron stars touch before the black holes would have merged Ejected matter can contribute to the gravitational-wave signal The merged neutron star can have "mountains" that keep radiating Probably the most important effect: the matter in NSs can emit photons and ...


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No, and certainly not by the mechanism you describe. The "orbits" of electrons around nuclei are structures created by the electromagnetic force. This force is mediated by photons, which cannot pass out of the event horizon by definition of the event horizon. So even in the highly implausible scenario in which an atomic structure existed within a black ...


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The statement that at the beginning of the universe energy/mass was concentrated in a single region under conditions of extreme temperature and density is usually extrapolated from experimental data on the energy/mass content of the universe and its expansion, which is then analyzed through the classical (i.e. non-quantum) theories of general relativity and ...


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Once you are inside the event horizon every form of energy just increases the gravity. For example when discussing the weak force you suggest: By being random over enough time has an expected value of having "lucky spurts" of weak force over large enough time may play a part in tearing apart a black hole. by which I assume you're thinking of a decay in ...


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A photon that escapes from black hole's neighborhood does work on the black hole. The photon causes the black hole not to be in the photon's gravity well after the photon has escaped. In other words the photon increases the potential energy of the black hole. The following paragraph may not be science, I just want to say something sane, as opposed to ...


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This is just ordinary potential energy from first semester physics -- when the photon is close to the black hole, it's deep in the potential well. As it goes away from the black hole, it picks up gravitational potential energy, so therefore, it must lose kinetic energy. For a photon, the kinetic energy is given by the Planck formula $E = hf$, so the photon ...


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Since due gravitational time dilation something takes forever to fall inside a black hole from the perspective of an outside observer, there is nothing in it yet that could come out. The light which is emitted from outside the horizon does reach an outside observer, but since it hasn't yet fallen in, it technically doesn't escape from inside the black ...


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Spacetime isn't an object, like some sort of elastic jelly, that galaxies move through churning it up as they go. Spacetime is a mathematical object that we use for calculating observables in relativity. So there isn't any sense in which a singularity twists up spacetime. The treatment of singularities is quite subtle in relativity. We describe spacetime as ...


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To understand the origin of black body radiation, which is what every material body with a temperature T has been measured to emit, one has to go to quantum statistical mechanics. Atoms and molecules, to start with, in any ensemble, interact with the electromagnetic radiation. At that level, the processes are quantum mechanical. In quantum mechanics the ...


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Stephen Hawking says that black holes emit radiations known as Hawking Radiations. This is not yet proven but tachyons might be Hawking Radiation particles since they travel faster than light.


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The field of quantum black holes is an hot topic of research right now, and the firewall proposal is still being debated. I have the feeling that no one really take the proposal seriously. By saying this I don't mean that it was a bad paper, on the contrary it's a nice thought experiment that forced us to think even more about the black hole information ...


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Black holes don't form. And you should keep your hand on your wallet when the word clearly is involved. If you have a spherically symmetric star and a spherically symmetric shell around it and you are inside the shell but outside the star then you notice the mass of the star but not the shell. When the shell contracts and gets to where you are it changes ...


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A theory that describe the black hole interior is intended to give some predictions that is testable even outside the horizon. For instance the internal "dynamics" could be relevant to tell what is the final state of the hole after the evaporation and what are, if there are, the correlation in the Hawking radiation. If the putative theory gives the right ...


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According to the cosmic censorship hypothesis all singularities are assumed to be behind horizons. This is not the same as saying "all horizons contain a singularity". The black hole solutions to Einstein's equations (which contain singularities) are all stationary, vacuum spacetimes. Stationary means that the spacetime does not explicitly depend on time. ...


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I was considering this question as well. Neither matter/energy can be created or destroyed, only converted from one form to the other. Consumption of star stuff by a singularity would convert that star stuff into star energy, but with no other way of expressing that energy there seems no choice but for nature to convert with 100% efficiency that matter into ...


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The first equation present the Einstein-Hilbert action field equation proportionality form , the second one presents the interval of of four space-time dimensions and exactly a solution for differential equation by solving it at the method of zero matrices


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If black holes can swallow any object, Black holes have a very strong gravitational field, this field from a distance attracts any other matter and the Newtonian approximation when there is a distance is adequate. When two strong gravitational fields get close enough General Relativity equations have to be used, but the "attraction" is there and very ...


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Yes, an observer inside the (Schwarzschild) black hole region may receive signals from the external region if the BH is sufficiently large. The motion of an internal observer is arbitrary, it is pictured by a generic timelike curve. The only constraint is that, within a finite interval of proper time, the curve reaches the internal singularity (roughly ...


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"Does a black hole really slow down time?" No. Gravitational time dilation is an absurd concept. General relativity predicts that gravitational time dilation occurs even in a HOMOGENEOUS gravitational field ("the homogeneous gravitational field is the gravitational field which, in every point, has the same gradient of the potential. Such a field is produced ...


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Your statement is not true. First, note Sofia's point that $J = Ma$, where $a$ is the angular momentum parameter inserted into the standard Kerr solution. Then to see that the claims in the OP are wrong, simply note that as $a\rightarrow 0$, the angular momentum goes to zero, but the mass does not. Meanwhile, the radius of the black hole horizon (I ...


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Suppose you crossed the event horizon. But you will never make up to the singularity. What happens at the singularity is still unanswered. Hawking's radiation is solely explained based on thermodynamic basis. Hawking assumed the blackhole as a black body. It could absorb any wavelength radiation. So at a low temperature the black body should emit radiations. ...


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Technically/mathematically correct answer Here's an example of a black hole that is technically inside another black hole: the maximally extended Reissner-Nordstrom solution. In this case, what we mean by being "inside" the black hole is that the event horizon for one black hole is completely to the future of the other (see below for why this isn't ...


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Anything inside the event horizon of a black hole, is destined to fall into the singularity. If one event horizon is totally inside a bigger event horizon, then two singularities will merge quickly.


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Yes it's falsifiable and indeed has been falsified. The geometry of spacetime is described by an equation called the metric that we get by solving Einstein's equation. We can get some information about the metric that describes the universe by studying the motion of objects like galaxies, galaxy clusters etc. When we do this we find the observations are ...



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