# Questions tagged [general-relativity]

A theory that describes how matter interacts dynamically with the geometry of space and time. It was first published by Einstein in 1915 and is currently used to study the structure and evolution of the universe, as well as having practical applications like GPS.

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### Can I form a scalar with coordinates in general relativity?

There is no position vector in general relativity. I was wondering whether a quantity like $$k_\mu x^\mu$$ where $k_\mu$ are covariant vector components is to be treated like a scalar i.e. invariant ...
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### David Tong's definition passive transformation of the fields looks wrong

David Tong's definition of active transformation is clear. Under active transformation coordinates (basis vectors) are not changed but rather the field is. I denote the old and new fields as $\phi$ ...
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### Why is “Gravity as a result of space-time curvature” not accepted as a fact? [duplicate]

Now that gravitational waves are confirmed. Not to mention the other numerous experimental verifications. Why do we still need an elusive graviton? Isn't there not enough evidence that the space-time ...
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### What is the connection between topology and physics? [closed]

I'm a physics undergrad student, but this year I had the chance to take general topology course. It is a wonderful topic, and I have read it has some applications in physics.
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### Why does the flow of time slow down as the space-time curvature gets deeper?

According to General Relativity and its experimental tests, a clock far above Earth ticks faster than it does on the surface of Earth. Because near the surface of the Earth space-time curvature is ...
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### Einstein summation and square roots

It has occurred to me I don't know if there is a general rule about this or not. If I have an expression like: $$\int \sqrt{g_{ij}\frac{dx^i}{dt}\frac{dx^j}{dt}} dt$$ I take the summation inside the ...
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### Metric field equations for the Jordan-Brans-Dicke action

Considering the Jordan-Brans-Dicke action: $$S=\int d^4x\sqrt{-g}\left(\phi R+\frac\omega\phi(\partial\phi)^2+\mathfrak{L_{m}}(\psi)\right).$$ I was trying to get the metric field equations by varying ...
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### General treatment of connections and covariant derivatives

Hi have been following an introductory course on quantum gravity and we are covering the basics of free quantum field theory in curved spaces. I have been introduced to how spin connections play a ...
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### Does the energy density of space create cause gravitational attraction beyond what would be computed from an object's mass alone?

I am starting from the assumption that the gravitational warping of spacetime increases its volume, so a spherical region of space with a fixed surface area would be able to fit a larger number of ...
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### Spherical collapsus according to a running observer [closed]

Imagine that a spherically symmetric body goes through a gravitational collapsus. In $t_1$ event horizon builds up instantly. Then say that somebody runs next to the collapsing body with ...
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### Conceptual problem with general relativity

According to Einstein, mass curves spacetime and objects in the nearby field tends to travel in the shortest possible path to reach their heavier counterparts. My question is was not Newton's ...
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### Locally Flat Understanding

I wanted to make sure that I was definitely understanding the proof of locally flat correctly. I can't see to find a similar proof to the one in the book, so I'm not super sure if my understanding/...
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### Is spacetime curvature and the shape of the planet is the same?

Let's say you're telling the story about two people starting walking toward the north pole from two different points (one from LA the other from NY), they going to walk straight line, but nevertheless ...
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### How can Earth accelerate toward US and China with no expanding? [duplicate]

In this video it's explained that there is no gravity force, it's all acceleration: Earth moving toward us, but how that's possible without expanding (toward people standing on the opposite sites of ...
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### What does a rotating universe look like?

If everything in the universe were revolving around an axis, how would that affect space-time? In my mind it would be no different from a normal universe since it would look normal in a comoving frame,...
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### $R=0$ solution in field equations

I am dealing with some General Relativity extensions and I am not sure about my knowledge in basic GR since I am having some weird troubles with what I think are basic concepts. As far as I know, if ...
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### Conditions on one forms [closed]

I am trying to solve exercise 8.3 from Lightman's problem book, but I don't know where to start to get a sufficient and necessary condition on a field of one forms $\tilde\sigma$ for there to exist a ...
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### Describing spacetime with qubits

Susskind in one of his lectures at PiTP 2018 on Complexity and Gravity talks about describing black holes as a qubit system, comprising qubits of the order of the entropy of the black hole. This is ...
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### Apparent horizon buildup in a BH merger

I just read some articles about binary BH merger simulation. These state that at a certain instant a common apparent horizon(or MOTS) appears, surrounding the two BHs. This instant is called the ...