# Tagged Questions

Vector-fields are vector valued functions which define a vector at each point in space. Examples of the vector field include the electric field and the velocity of a fluid.

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### How to show flat FRW metric has a time-like conformal Killing vector?

I would like to derive the fact that the flat FRW metric has a time-like conformal Killing vector. Is there an easy way to do this? @ValterMoretti showed how one can do this for metrics with a ...
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### Conformal time-like Killing vector near null geodesics in all spacetimes?

Is it true that in all spacetimes there is some conformal time-like Killing vector $\tau^a$ in the vicinity of null geodesics? If the above statement is true then can one argue that, for all ...
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### What exactly is conservative vector field?

I'm studying calculus, but since the example involved a physical concept. I will ask here: This is how it goes: This means that in a conservative force field, the amount of work required to ...
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### Books on Liouville Operator

I am looking for a good book doing classical mechanics and statistical mechanics in terms of the Liouville operator. I have not found a lot on this subject and even books like Mathematical Methods of ...
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### Is a vector field not a vector quantity?

I'm trying to make sense of Poisson bracket relation $$\{L_i,A_k\}_{PB}~=~\epsilon_{ikl}A_l,\tag1$$ where $L_i$ is $i$th component of angular momentum, $A_k$ is $k$th component of an arbitrary ...
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### Momentum of stationary electron in a curl free vector potential

The essence of this question is simplicity itself: There is an electron in a curl-free $\vec{A}$ field. The electron is stationary so its m$\vec{v}$ momentum is 0. However, it has "momentum" from ...
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### Vector fields of a physical quantity [closed]

I had this small confusion - The components of a vector field representing a physical quantity must have the same physical dimension right? for example- the radius vector has the unit of length along ...
Can someone explain why this two equation are equivalent? $\nabla_T$ denotes the transverse two-dimensional nabla operator: $\nabla_T=\hat{x}\frac{\partial}{\partial x}+\hat{y}\frac{\partial}{\... 1answer 81 views ### Duality and 1 forms How is a dual map defined if we are talking about partial derivatives and 1 forms? 3answers 257 views ### If a Killing vector field is timelike, can it be set to$\partial/\partial t$? If one has a Killing vector that turned out to be a timelike Killing vector field because of negative norm. Can we set this Killing vector field equal to$\partial/\partial t$? 0answers 40 views ### The first term of Stokes Vector of natural light is zero? Consider the electric field of a beam of natural light: $$E(r,t) = E_0 \cos(k·r+wt)$$ Since this beam of light is natural, the vector E has all the components possible that satisfies: ... 0answers 136 views ### Norm of Killing vector field Let us suppose we have a Killing vector field with$X^a = 1/2$and$X^b = 1/3$and$g_{ab}=1$where the other$c$and$d$components are zero. Now we want to find its norm: The formula for finding ... 2answers 67 views ### EM waves and fields According to wikipedia, electromagnetic waves are "synchronized oscillations of electric and magnetic fields that propagate at the speed of light". I understand what it means in theory. But in ... 2answers 231 views ### Advection operator How are exactly$u_j\partial_ju_i$and$u_i\partial_j u_i$related? And what is their relation to ($\boldsymbol{u}\cdot\nabla)\boldsymbol{u}$and$\boldsymbol{u}\cdot(\nabla\boldsymbol{u})$? I ask ... 1answer 252 views ### What is an “Einstein transformation” in general relativity? When introducing the vielbein formalism in general relativity, I came across the use of an infinitesimal general transformation, or Einstein transformation. The latter term seems not to be covered on ... 3answers 607 views ### How to visualize the gradient as a one-form? I am reading Sean Carrol's book on General Relativity, and I just finished reading the proof that the gradient is a covariant vector or a one-form, but I am having a difficult time visualizing this. I ... 1answer 105 views ### How to get the linear and angular acceleration generated by a force vector field? I am working on a physics simulation and I have to calculate the angular acceleration in degrees per seconds squared around the point on the object located relatively to the center of a vector field (... 1answer 197 views ### Can a spacetime solution in GR have no Killing vector fields? Sometimes Killing vector fields in a given spacetime are described as giving information about a symmetry of that particular spacetime solution. If I look at the requirement of a Killing vector field ... 1answer 284 views ### Conformal Killing fields on Schwarzschild I am trying to understand which are the conformal Killing Fields on the Schwarzschild spacetime. I say that$X$is a conformal Killing field on$S$($S$is Schwarzschild) if there exists a function$f:...
Question: What do the solutions of $\nabla_\mu A^\nu = 0$ look like? And is it possible for spacetime curvature to somehow restrict the solution to $A^\nu = 0$? Here is my current ...