# Tag Info

26

You can check this yourself using this very long link which will give you a list of Hawking's work that has been published in refereed journals, ordered by the number of times they have been cited in other papers (a measure of how influential they are on other scientists). This is a way of providing at least some non-opinion based answer to this question. ...

26

The two largest contributions that come to mind are both in the realm of general relativity. The first is his contribution to the singularity theorems. These are purely general relativistic results (i.e. no quantum mechanics involved), and they mathematically prove that generically one expects to find singularities in spacetime. That is, except in somewhat ...

13

First note that this is a fictional movie and the image is an artist's impression, not a detailed simulation. The public seems to think the movie is some sort of fictionalized documentary, which it never claimed to be. That said, the image is qualitatively conveying some of what happens near a black hole. The diagonal disk is the accretion disk -- this is ...

7

1.When they travel to the watery planet, they say that 1 hour on this planet is 7 yrs om earth. How is this possible? Is the planet moving at a speed close to c? Or does strong gravitational field influence time? Sure. This is gravitational time dilation. It's due to the gravitational field of the black hole. You can calculate it using $$\frac{d ... 6 There are many problems with this line of reasoning. The most common galaxy types are elliptical galaxies and spiral galaxies, and there might be a parallel with star systems, where the most common types are systems with a single star, and binary systems with two stars in the middle. There is simply no justification for this. The dynamics of stellar ... 5 This is explained thoroughly in Thorne's book "The Science of Interstellar". There were two scientific papers based on the simulations: One in physics and one in computer rendering. The two circles are caused by gravitational lensing by a very rapidly spinning black hole. The radius of this black hole is 150 million kilometers with a mass of 100 million ... 5 Have a look at the question Speed of light in a gravitational field ? as this shows you in detail how to calculate the speed of light in a gravitational field. I haven't flagged this as a duplicate because I'd guess you're not so interested in the details but rather how the speed of light can change at all. You've probably heard that the speed of light is a ... 5 You can get the time dilation factor by computing the redshift of a radial photon emitted by someone on a circular orbit, compared to the frequency measured by someone at rest at infinity. The derivation of this formula is a bit involved, but the answer is not too complicated:$$ ...

3

I tink your question is mostly answered by the answers to the question Universe being flat and why we can't see or access the space "behind" our universe plane?. The rubber sheet analogy gives the impression that there is an extra dimension in which spacetime is curved. Curvature in an extra dimension is called extrinsic curvature. However in ...

3

The conceptual key here is that time dilation is not something that happens to the infalling matter. Gravitational time dilation, like special-relativistic time dilation, is not a physical process but a difference between observers. When we say that there is infinite time dilation at the event horizon we don't mean that something dramatic happens there. ...

3

$$g_{\mu\nu} = \text{diag}(-A,B,r^2,r^2\sin^2\theta)$$ $$g^{\mu\nu} = \text{diag}\left(-\frac{1}{A},\frac{1}{B},\frac{1}{r^2},\frac{1}{r^2\sin^2\theta}\right)$$ $$T_{\mu\nu} = \text{diag}(-A,B,-r^2,-r^2\sin^2\theta)\times \frac{Q^2}{32\pi^2r^4}$$ $$g^{\mu\nu} T_{\mu\nu} = (1 + 1-1-1)\times \frac{Q^2}{32\pi^2r^4} = 0$$

3

multiple coordinates may refer to a single point Normally, the way we define this kind of thing in GR is that we have an atlas, and the atlas is made of charts. Each chart is required to be invertible, so no, we can't have multiple coordinates that refer to a single point. In any case, when we define dimensionality on a topological space, we do it in a ...

3

If you want a complete and consistent picture, I would recommend studying geodesics (orbits) in some black-hole solution of equations of GR (for reasons of simplicity, take the Schwarzschild metric). Almost all work is already done for you in this wikipedia article. Short answer: no, the speed would never reach or exceed the speed of light. The aspects of ...

3

You can find an explanation of scalar fields and associated quantum effects in the Schwarzschild background in chapter four of these lecture notes. The article also contains references which might be of use to you.

3

The answer is it depends on which observer we are talking about - an observer "with" the collapsing mass sees it and them crushed to a singularity; an external observer "sees" (though see below) the mass frozen just at the event horizon. In GR and a standard black hole, there is only one future for a mass that finds itself at or inside the event horizon, ...

3

I think the following image sums up why your model, at least for our galaxy, is wrong rather nicely: These are the orbits for 6 stars in the inner region of the galaxy. The orbital period for S2, for instance, is 15 years for an orbit that is roughly twice the size of Sedna's orbit--which takes it 12 thousand years to complete its orbit. Using Kepler's ...

3

The horizontal circle is probably the accretion disc of the black hole. The vertical circle might depict the effect of gravitational lensing (although I am not sure this depiction is accurate).

2

You are correct that physicists think a black hole is a link to another universe. No, not really, that's just an attention grabbing headline. Physicists (most of them) don't believe black holes are links to other universes, apart from some fringe theories that I'll come back to. But let me explain where this misconception comes from. This absolutely ...

2

Indeed photons are massless particles, so they follow "quickest paths" during their propagation in space-time; these are called "geodesics". However, general relativity doesn't simply says how the way masses attract each other is modified, it most of all says that mass (and energy density) curve space-time; this also curves the geodesics, which photons (in ...

2

It is said that photons have zero rest mass so how can gravitational force of a black hole affect light? Photons have zero rest mass so when they are at rest they have no mass. They are never at rest so this is a little misleading. And if photons do have some effective mass while traveling at speed of light then only can a black hole's ...

2

You're focusing too much on the stuff at the center of the hole. The thing about general relativity is that lots of mass in any form will alter the space and time around it. If you bend things enough, the direction we used to unambiguously call "forward in time" bends into "toward the singularity at the 'center' of the black hole." So there is a region -- ...

2

One thing to note is that this horizon would only be present in an idealized eternal black hole, for a realistic non-rotating black hole formed by a collapsing star the Kruskal-Szekeres diagram would look more like the right-hand diagram below (from Gravitation by Misner, Thorne and Wheeler), where the gray area represents the interior of the star and the ...

2

If you solve the geodesic equation in Schwarzschild space-time then you will obtain, for the freely falling particle, the coordinates of its worldline $x^{\mu}(\lambda)$ in say the (global) Schwarzschild coordinate system; here $\lambda$ is an affine parameter such as proper time $\tau$ for a massive particle. The $x^i(\lambda)$ will be the spatial ...

2

I believe that the math covering condensed matter physics are very similar to that describing black holes and some high energy physics. So what was seen was an experimental result verifying the maths. Whether the maths really applies to a BH is unknown. In a way, it is more like solving equations experimentally using condensed matter as an analog computer. ...

2

The spacetime geometry around a rotating uncharged black hole is described by the Kerr metric. I'll give this below, and it will look terrifying, but bear with me because there's only one small bit of the equation we need to see why the horizon disappears. Anyhow, the Kerr metric is: \begin{align} ds^2 &= -(1 - \frac{r_s r}{\rho^2})dt^2 \\ ... 1 The size of a black hole is defined by the radius of its event horizon, instead of the "size" of the singularity. Plus, a singularity is not a point, but a spacelike hypersurface. As long as you are far away from the singularity, there is no difference that you can tell from a star. The gravity is the same. Gravity being massive is because the surface ... 1 The metric of the Schwarzschild black hole is ds^2=\left(1-\frac{2M}{r}\right)dt^2-\left(1-\frac{2M}{r}\right)^{-1}dr^2-r^2(d\theta^2+\sin^2\theta d\phi^2). $$Therefore, the Lagrangian of a particle in this background is (with proper time \tau)$$ ...

1

It's not just the mass that matters or just the radius. It's $r/m$. If $r/m$ is less than $2G/c^2$, then you have a black hole. Black holes can theoretically have big masses or small masses. It's theoretically possible to have a black hole with a mass of 1 kg -- we just don't know of any processes in nature that would compress a 1 kg mass enough to make it ...

1

$R$ in the formula for escape velocity is simply distance from the center of the object, not necessarily the radius of the object. If the object is something with a well-defined and nearly-spherical surface, like a planet, then we can let R be the radius of that surface, and speak about the escape velocity from the surface, but you can also talk about the ...

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