# Velocity Term in Alcubierre Metric - Exploring its Significance

• redstone
In summary, the conversation discusses the inclusion and purpose of the velocity term, v, in Alcubierre's paper on the "warp" drive. The presence of this term is questioned and its potential value is explored. It is concluded that the term is not necessary for the metric to work, but simplifies the stress energy tensor. The purpose of the term is to make the coordinate speed of the bubble explicit. Furthermore, it is confirmed that equation 5 is preserved despite the inclusion of the v term.
redstone
Reading over Alcubierre's paper on his "warp" drive (http://arxiv.org/abs/gr-qc/0009013), the metric in equation 3 has a velocity term, v, that doesn't seem to be needed anywhere. Even in the one spot where it seems potentially valuable, equation 12, he just call it =1 and essentially ignores it. Also, it doesn't seem to have any mathematical connection to dx/dt (he just randomly says that's what it is after equation 5.

So I'm just wondering what it is I'm missing here? Why is the v term included at all? Is there some stronger need that requires it actually be equal to dx/dt? And finally, if v>0, doesn't that then destroy his equation 5 (i.e. 3-space would curve when a body has velocity)?

Any insight into that variable would be appreciated.

I guess nobody seems to know. So for posterity...
My own research into it, it appears to not be necessary for the metric itself to work, but when solving for the stress energy tensor, it looks like it makes terms, at least the T00 term, simpler, since there are d/dt terms that act on the x, giving new v's that cancels things out in a nice way. Haven't solved it without the v in there to verify, but guessing it would be more complicated.

The purpose is simply to make the coordinate speed of bubble explicit. If you just used a generic function for beta-x, you would then have to solve for the coordinate speed getting some messy function. By building it in as specified, you get to pick the coordinate speed of the bubble.

As to your second question, equation 5 is preserved just fine. This equation, in context, simply says that if you consider a t=0 3-surface, you have a Euclidean spatial metric. This is clearly true for his equation (8). Just consider dt=0 in the metric.

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## 1. What is the Alcubierre metric?

The Alcubierre metric is a theoretical solution to Einstein's field equations in general relativity. It was proposed by physicist Miguel Alcubierre in 1994 and describes a warped space-time that allows for faster-than-light travel.

## 2. What is the significance of the velocity term in the Alcubierre metric?

The velocity term, represented by the v variable, is a crucial component of the Alcubierre metric. It determines the speed at which the space-time is warped, allowing for faster-than-light travel. Without this term, the Alcubierre metric would not be able to achieve its intended purpose.

## 3. How does the velocity term affect the Alcubierre metric?

The velocity term directly affects the amount of energy required to create the necessary warp in space-time for faster-than-light travel. The higher the velocity, the greater the energy required. Additionally, the velocity term also influences the size and shape of the warp bubble.

## 4. Is the velocity term in the Alcubierre metric realistic?

No, the velocity term in the Alcubierre metric is not considered to be realistic. It violates the principles of causality and special relativity, making it impossible to achieve in our current understanding of physics. However, it remains a valuable theoretical concept for exploring the possibilities of faster-than-light travel.

## 5. What are some potential applications of the Alcubierre metric and its velocity term?

The Alcubierre metric and its velocity term have been used in science fiction as a way to explore the concept of faster-than-light travel. However, in the real world, there are currently no known practical applications for the Alcubierre metric. It remains a theoretical concept that may have implications for future advancements in physics and space travel.

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