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Hot answers tagged general-relativity

21

Energy (in any form) falling into a black hole contributes to the mass of the hole, and mass is one of the many forms that energy can take, using the usual conversion factor: $E = mc^2$.

9

To expand on @dmckee's answer, if we have a speacetime that has the matter concentrated in a central area, we can definte an overall conserved energy-momentum vector called the ADM energy. It can be further shown that the ADM energy does not change when the matter falls into the black hole.

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Start by considering the ordinary Newtonian gravity. This tells us that the acceleration of a test mass due to our planet of mass $M$ is: $$a = \frac{GM}{r^2}$$ The acceleration is the rate of change of velocity with time. A fast moving object spends less time near the planet than a slow moving object so its velocity changes less. That means fast moving ...

7

It is not true that there is a unique geodesic through every point. To understand it, imagine a point on a sphere (where geodesics are just great circles) or even on a plane (here geodesics are straight lines). Through that point you can draw infinitely many geodesics, e.g. infinitely many straight lines passing through this point. However, if you restrict ...

4

It is rather the other way around: our understanding of physics has enabled us to build GPS systems in the first place. It is correct however that GPS was direct confirmation of not only the theory of special relativity, but also of general relativity. Neglecting the time dilation from the difference in gravitational fields between the satellite's position ...

3

Is there any other scientific theory that proves that big bang is the origin of time ? Here is a gross misunderstanding of what a scientific theory is. A scientific theory can never be proven. It is successful if it fits data and observations, then one says it is validated, and if its predictions are always validated. An invalid prediction requires drastic ...

2

It loses organization, e.g. matter changes into pure energy or some such thing. It's not entirely clear what form there is (some suggest there is no form at all, but it's obvious that it doesn't follow Pauli's exclusion principle). This is nothing special, it happens all the time - when you burn carbon, for example, you get a bit of disorganised energy (heat)...

2

No. When they merge their horizons will change shape, and eventually become the static or stationary shape of a BH horizon. Nothing inside either horizon while this is happening can escape. At all times the timelike curves stay inside, and the deformed horizons are where the lightlike curves end up. In each, and after they merge. The area of each horizon ...

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I think I have a misunderstanding for the KK theory. In the KK theory, we are living in, say, a 5-dimensional spacetime with one dimension compactified. What's different from the brane-world theory is that, in brane-world theory, we are living on a 4-dimensional brane which is embedded in the 5-dimensional spacetime. So in the post, I can not assume that the ...

2

So the answer is no. An electric field has energy and energy generates a gravitational field, just like any mass. See the charged black hole solution is the Wikipedia article https://en.m.wikipedia.org/wiki/Charged_black_hole The charge of a black hole, if nonzero, changes the metric and solution to account for the charge and electric field. That ...

1

The quote you give from Carroll about the covariant derivative is right: it quantifies the rate of change of a tensor field relative to parallel transport. The covariant derivative of a tensor at a point doesn't make sense. However, the commutator of covariant derivatives acting on a point does. The situation is analogous to the vector field commutator. ...

1

Consider a region in the manifold where a tensor field is everywhere well defined. Consider a point $x$ and a neighbouring point $x+dx$. The tensor field, say $V^\mu$ is given at both points as $V^\mu(x)$ and $V^\mu(x+dx)$. We can parallel transport the tensor(vector in this case) from $x$ to $x+dx$. This parallel transported vector $V_P^\mu(x+dx)$ is in ...

1

Object can't go with the speed of light on the Special Relativity, on which the General Relativity is based upon. The gravitational waves are predicted and calculated by the General Relativity, i.e. if you are talking about them, you are using the terminology of a theory which closes out the things going with the speed of the light. But we can talk about an ...

1

Toward position y. Gravity couples to itself (Einstein's equations are nonlinear), so yes, gravity can cause itself to curve. Another way to see it is that photons and gravitons are both massless and so they both travel along identical null geodesics, so wherever you see light coming from, you'll feel the gravity from the light source pulling you in the ...

1

This depends on how you do the analysis -- If you do it in the Kruskal spacetime, which is the more physical way, It's hard to talk about what "$r = 0$" is, and the question becomes somewhat ill-posed. If you naïvely do it in Schwarzschild coordinates, you'll find that $R$ has terms involving constants multiplied $\nabla^{2}\frac{1}{r}$, which an analysis ...

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If we want to be formal, at $r=0$ there is a manifold singularity. So no tensor/scalar quantities are well defined there (i.e. our mathematical formalism does not work there). On the other hand, as physicists, we can look for different examples that behave in a similar manner. Also the (classical) electromagnetic field generated by a point-like charged ...

1

DISCLAIMER: I have never seen the below conlcusion made explicitly, but it seems to me to be a straight-forward consequence of established theory. I cannot find any error in my thinking, whence I will post it and await your judgement. The equivalence theorem, proved e.g. in Cartan's Leçons sur la géométrie des espaces de Riemann, states that in a rigid ...

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The brief answer is 'yes’. Here is a thought experiment which I think makes it easy to see that the answer must be yes. Consider the standard twin 'paradox': twin a hangs around in free-fall; twin b zooms off on their spaceship at some enormous speed with respect to twin a, turns around (in some smooth way, undergoing acceleration), and returns. Well, ...

1

Suppose there is a flash event that we can represent as a light cone as the flash expands. There are three shutters with detectors around this flash event. The shutters open and close only once and this is almost instantaneous. One shutter opens in spacetime outside the light cone. One Shutter opens in spacetime inside the lightcone and the third opens ...

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