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49 votes

Why would black hole rip me apart?

You don't need GR to see this effect. It's due to tidal forces. Suppose you are 2 meters tall. Then the force of the Earth on your feet is $GMm/r^2$, and the force on your head is $GMm/(r+2)^2$. The ...
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43 votes
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Why would black hole rip me apart?

The problem is that when you are falling, all of you can't be in the same inertial frame. That is, whilst your centre of mass might be inertial, parts of your body will be feeling accelerating forces ...
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3 votes

Why would black hole rip me apart?

There are nice answers by @fraxinus and @profrob, I would like to add a little side note about the balance between the forces. It arises because the gravitational field exerted on one body by another ...
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3 votes

Why would black hole rip me apart?

As a complement to the other answers: Not every black hole is capable of ripping you apart tidally. Too small black hole will burn and blow you away you with its Hawking radiation way before you are ...
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3 votes

What is the component of gravity other than curvature?

The spatial part of the trajectory is sharply curved, but the trajectory in spacetime is much less. If you throw a rock and it takes one second to rise and hit the ground, the parabola is sharply ...
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3 votes
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How velocity affects different orbits?

Yes there is. Total energy is, in polar coordinates in the plane where the movement occurs: $$E=\frac{1}{2}\,mv^2-G\frac{Mm}{r}=\frac{1}{2}\,m(\dot{r}^2+(r\dot{\theta})^2)-G\frac{Mm}{r}$$ A short ...
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3 votes

Is the volume in general relativity independent or dependent on the coordinates?

The actual volume should be independent from the way we measure it. Untrue. As an example, one can mention the metré des archives, since that is easier to understand than dealing with volumes. The ...
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2 votes

Is the volume in general relativity independent or dependent on the coordinates?

On any orientable pseudo-Riemannian manifold you have naturally defined volume n-form. You can integrate this to get a coordinate independent volume. However, you are asking about spatial volume, not ...
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2 votes
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State of the art on Modified gravity : going beyond the 2nd order differential equations, diffeomorphism invariance breaking, extra degrees of freedom

Going beyond second order means considering theories that contain terms that contain higher than second order derivatives of the metric in the equations of motions. E.g. a term like $\partial_{\mu} \...
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2 votes

What is the real world interpretation of $E = mc^2$?

The path of any particle, irrespective of mass, is given by the geodesic equation: $$\frac{d^2 x^\mu}{d\lambda^2}+\Gamma^\mu_{\alpha\beta}\frac{dx^\alpha}{d\lambda}\frac{dx^\beta}{d\lambda}=0$$ where $...
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2 votes
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What is the real world interpretation of $E = mc^2$?

The text of your question differs somewhat from the title. I'll tackle the title first: the "real world" interpretation of the equation is given by the title of Einstein's original paper, &...
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2 votes

The speed of time

Are time and gravity the same thing? No, they are not. Could there be a speed of gravity (cause and effect)? Gravitational waves travel at the same speed as light. In quantum theory both as ...
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2 votes

Why would black hole rip me apart?

It's also worth nothing that in the case of many black holes of which we have knowledge, the radiation from the accretion disk is so intense that you would be blasted into plasma long before you ...
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1 vote

Why would black hole rip me apart?

The inertial frame that falls towards the mass freely is only approximately an inertial frame. Around the Earth the approximation is almost perfect agreement. In the ISS, if you place marbles ...
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1 vote

How compact can a thin shell be without collapsing?

Thin shell could be even more compact than the fluid ball of the same mass. Assuming reasonable energy conditions on the shell matter, the minimal radius of a shell with mass $M$ is: $$ R_\text{min}=\...
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