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Tagged with warp-drives metric-tensor
13
questions
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Killing Vectors in The Alcubierre Metric
According to this article about the Alcubierre metric, the metric can be transformed in a way that results in "spherical symmetry" about the x-axis. I have to assume they meant to say ...
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1
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Volume Elements Inside The Warp Bubble
I'm trying to understand how to calculate proper spacelike volumes of metric tensors that have off-diagonal terms. Right now I'm considering a slower-than-light Alcubierre metric:
$ds^2=(v^2f^2-1)dt^2-...
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Is observing (superluminal) velocity independent of choice of coordinates for asymptotically flat spacetimes?
Alcubierre's warped metric in ($1+1$)D is typically given in the form of:
$$ds^2 = -dt^2 + [dx-v(t)f(r) dt]^2 \ \ .$$
Then it is nicely discussed how manipulating:
$$-dt^2 + [dx-v(t) f(r) \ dt]^2=0$$
...
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2
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Calculating proper volume in the Alcubierre spacetime
I'm trying to calculate the proper volume of a portion of the alcubierre spacetime to see how it compares to the euclidean volume element. As I understand it, the proper volume element in cartesian ...
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3
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Shift Vector in Warp Equation
In the Alcubierre metric, why is there a beta with subscript multiplied by a beta with superscript? I know beta with subscript is the shift vector, but what is the difference between the two?
$$\text ...
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1
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Late time behaviour of the Alcubierrie warp drive metric
The Alcubeierrie Warp Drive metric looks like $$ds^2 = -dt^2+(dx-Xdt)^2+dy^2+dz^2$$ where $X = v_s(t)f(r_s)$ and $r_s = [(x-x_s(t))^2+y^2+z^2]^{1/2}$. Now, $f(r_s) \approx 1 \quad 0 < r < R$ ...
- 1,200
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Geodesics in an Alcubierrie Warp Drive metric
The geodesics in an Alcubierrie Warp Drive metric are given by
$$\dot{t} = 1 \quad \dot{x} = X\dot{t} \quad y, z = \text{constant}$$ where $X = \dot{x}_s(t) f(r_s)$. Here $f(r_s)$ is a shape function ...
- 1,200
2
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What would a Natario Warp Drive look like, outside & inside the warp bubble?
Within a Natario Warp Metric, all mass in front of the ship is pushed outwards by it's negative energy density, this means no light would interact with the front of the ship at all. And since the ...
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Computing Riemann tensor components for Alcubierre metric
I am currently trying to compute the Riemann tensor components for the Alcubierre metric, and already, on the computation of the first component, I'm running into some issues.
The trouble component in ...
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2
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1
answer
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Alcubierre metric without geometrized units
In the beginning of Alcubierre's paper, he defines his metric with the use of geometrized units ($G = c = 1$). While it makes the math simpler, it seems to hide the physical numbers away, leaving me ...
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9
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Einstein field equations to the Alcubierre metric
I was wondering how Alcubierre derived the metric for the warp drive? Sources have said it's based on Einstein's field equations, but how did he go from this to the metric?
3
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1
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How can I understand $\mathrm ds^2 = -c\,\mathrm dt^2 + [\mathrm dx-v_s(t)f(r_s)\mathrm dt]^2 +\mathrm dy^2 +\mathrm dz^2 $ in the simplest way?
How can I understand this equation $$\mathrm ds^2 = -c\,\mathrm dt^2 + [\mathrm dx-v_s(t)f(r_s)\mathrm dt]^2 +\mathrm dy^2 +\mathrm dz^2 $$ in the simplest way?
I am a 13 year old boy who is totally ...
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Is every spacetime metric physically realizable?
Is every spacetime metric physically realizable? I know that given any spacetime metric, you could work out a stress-energy tensor for each position that would result in that metric.
However, I also ...
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