# Tagged Questions

The variables used in general relativity to describe the shape of spacetime. If your question is about metric units, use the tag "units", and/or "si-units" if it is about the SI system specifically.

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### Can we exit the event horizon of merging black holes?

I have an intuitive scenario. Consider we have a spaceship just below the event horizon of a BH, which is merging with another black hole. Finally, the singularities merge and we have a single black ...
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### Are black holes perfect spheroids?

What I know about black holes (correct me if I'm wrong) is that they are the most compact objects in the universe that have been discovered. Due to all that gravity, wouldn't black holes be a perfect ...
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### Parenthetical tensor notation [on hold]

Just out of curiosity, what does it mean to be a type $(n,m)$ tensor? For instance in the context of special and general relativity, the Minkowski metric $\eta$ is considered a type $(0,2)$ tensor. I ...
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### Is there energy output when mass moves between two spacetimes [closed]

Is there energy output when mass $m$ moves between two spacetimes? Say, it starts in a flat spacetime and then falls into a black hole (other examples don't come to mind, but this doesn't mean they ...
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### Solving the Friedmann Equation [closed]

Through substituting for values of $\rho$ and $k$, I have: $$H^2=\left(\frac{\dot{a}}{a}\right)^2=\frac{8\pi G C}{3a^4} + \frac{\Lambda c^2}{3}$$ $a=a(t)$, and $a(t=0)=0$. Note that $C$ is a ...
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### Riemann tensor for a diagonal metric [closed]

Is it correct that for a diagonal metric tensor, the Riemann tensor with one contravariant ( upper ) index, $R^\mu_{\phantom{a}\nu\theta\phi}$, is anti-symmetric for interchange of the two first ...
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### What is the measure of distance in higher dimensions?

In our world we are using kilometers to measure distance. What measurement is used to measure distance in higher dimensions?
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### A question about metric tensor and their minors and cofactors in general relativity

In Einstein's book- 'the meaning of relativity', he says- The equation 55 mentioned is this one- I don't understand what the equation (62) means or how it can be proved. I know that the metric tensor ...
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### Effective Potential in General Relativity

I would like to clarify a concept about the Effective Potential in General Relativity when the kinetic energy term is not unitary. Suppose (in spherical coordinates) one has a generic line element of ...
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### Given a metric of a torus can we measure it's thickness?

What I mean is, if you have a metric of a torus $T_2$, and you want to distinguish between say very thin stringy tori and very thick tori with the same surface area, is there a nice formula for this ...
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### Age of universe from Hubble's constant

Assume the Robertson-Walker metric: $$g = -d\tau^2 + a^2(\tau)\gamma$$ where $\gamma$ is the flat, spherical or hyperbolic spatial metric and $a$ is the scale factor. Wald seems to calculate the age ...
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### What is the relation between the metric tensor and the graviton?

In Zee's quantum theory in a nutshell, at the end of chapter I.10, he states that the graviton is of course the particle associated with the field $g_{\mu\nu}$. My understanding of quantum ...
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### Derivation of Christoffel Symbols

So I am reading a book on relativity & differential geometry and in the text, they gave the Christoffel symbols in terms of the metric and its derivatives, but I wanted to derive it myself. ...
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### The form of the metric after a dimension is compactified

Upon the compactifiation of one spatial dimension, it is said (as though an axiom) that the 5 dimensional spacetime metric separates into a 4 dimensional metric, a vector, and a scalar, (4D gravity, ...
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### The most general way to write flat space metric [closed]

What is the most general way to write flat space (in d=4 in particular), but still preserving some isometries? In particular I'm interested in the case with 2 isometries, basically by using explicitly ...
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### Ground state metric?

In kaluza-klein theory, there's a notion of a "ground state metric" after compactification. What is the meaning of the term "ground state metric"?
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### How much Gravity is required to stop time?

Clocks free of gravitational influence run faster than those experiencing gravity. Is it possible for gravitational influence to bring time to a stop? Additionally can acceleration affect clocks in ...
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### EFE and Local Minkowski

Suppose we view the Einstein Field Equations (EFE) in the context of a boundary value problem with a given stress-energy tensor and boundary conditions. The problem is solved by finding a pseudo-...
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### Spacetime background of Quantum mechanics [closed]

Why is it said that the Schrodinger equation suggests a fixed, non-dynamical background spacetime, with time as an external parameter? How does this interpretation come about from the Schrodinger ...
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### Why are dimensions regarded as square/perpendicular?

Starting from the second dimension, the dimensions are basically represented by a square, cube, tesseract, and so on. I don't know if this is a stupid question or not, but is there an obvious or less-...
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### Do any two points in Minkowski spacetime determine a unique line?

Any two points in a Euclidean space determine a unique line, but I wasn't sure if this result generalized to Minkowski spacetime given that the latter is not a Euclidean 4-space, but is, instead, a ...
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### What is the difference between time and space in general relativity?

I know that similar questions have been asked before, I will try to be specific. In special relativity time is the coordinate with minus sign in metric tensor. In general relativity the components of ...
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### Coordinate time difference between emiting and detecting a photon in bent spacetime

Consider an arbitrary non-trivial metric $g_{ij}$ - like the Schwarzschild metric. Now, consider two observers $A$ and $B$, staying at fixed radii $R_A$ and $R_B$, respectively, with $R_A > R_B$. ...
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### Scalar Curvature of a Conformally Flat Metric

Suppose that you have a metric $g_{\mu\nu}=\phi^2\eta_{\mu\nu}$ for some function $\phi$. There is a standard formula for what the scalar curvature $R$ looks like in terms of $\phi$, which is given by ...
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### Orbits around the Photon sphere of a black hole (Schwarzschild coordinates)

This is a follow-up question to the answer given at What is the exact gravitational force between two masses including relativistic effects?. Unfortunately the author hasn't been online for a few ...
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The geodesic equation used in general relativity is the following: $${\mathrm d^2 x^\mu \over \mathrm ds^2} =- \Gamma^\mu {}_{\alpha \beta}{\mathrm d x^\alpha \over\mathrm ds}{\mathrm d x^\beta \... 1answer 70 views ### Signature of f: \Lambda^2(\mathbb{R}^4) \times \Lambda^2(\mathbb{R}^4) \to \mathbb{R}, f(\omega, \omega') = \omega \wedge \omega' [closed] Define$$f: \Lambda^2(\mathbb{R}^4) \times \Lambda^2(\mathbb{R}^4) \to \Lambda^4(\mathbb{R}^4) \cong \mathbb{R}, \quad f(\omega, \omega') = \omega \wedge \omega'.$$What is the signature of f? ... 0answers 36 views ### Induced metric is a scalar for transformation from x\to x'? (Poisson E.A p.62) I have a (simple) question about the induced metric h_{ab}. In Poisson E.A. (a relativist toolkit) it says in p. 62 that the induced metric$$h_{ab}=g_{{\alpha}{\beta}} \frac{\partial x^{\alpha}}{\...
If you are moving at $c$ in 3D space and $c$ in time axis too, What would be your total speed? Edit: Since question has been voted to be closed, I shall make an Edit. In 4D world all objects move ...
The geodesic equation used in general relativity is the following: $${d^2 x^\mu \over ds^2} =- \Gamma^\mu {}_{\alpha \beta}{d x^\alpha \over ds}{d x^\beta \over ds}.$$ It states that the ...