Calabi-Yau manifold + ideal gas + point disturbance?

In summary, the conversation discusses the possibility of filling a Calabi-Yau manifold with an ideal gas and considering sound waves from a point disturbance. It is suggested that this may be possible by having a brane wrapping the manifold and a gas of attached strings. The Ricci-flat condition of Calabi-Yau spaces may provide insights into sound propagation, but this is not yet known. A two-dimensional torus with a flat metric is given as an example of a Calabi-Yau space.
  • #1
Spinnor
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Because it is a closed space, can it make sense to fill a Calabi_Yau manifold with an ideal gas and consider waves from a point disturbance?

Would the Ricci-flat condition of Calabi-Yau manifolds have anything to say about possible sound waves?

Thanks!
 
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  • #2
If you are thinking of Calabi-Yaus in the usual context (as a model of the extra dimensions), remember that there is a copy of the Calabi-Yau at every point in macroscopic space-time. So if you had a "gas" filling just one of these CYs, the "molecules" would spill out into neighboring space.

One way around this, is to suppose that there is a brane wrapping one of the CYs, and that the gas consists of open strings attached to the brane. Some stringy black holes are like this - wrapped branes with a gas of attached strings. In such a case, the thermodynamics of the black hole comes from the thermodynamics of this string gas.
 
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  • #3
mitchell porter said:
If you are thinking of Calabi-Yaus in the usual context

Just a single Calabi-Yau manifold plus time. Of course this can only be done as a thought experiment.

So with our gas filled Calabi-Yau space I would expect that the wave front from a point disturbance would initially expand as a 5 dimensional spherical shell? Then things get complicated but I thought that the Ricci-flat condition of these spaces might allow one to make some general statements about sound propagation?

I guess sound propagation in curved spaces is complicated.

Thanks!
 
  • #4
Spinnor said:
I thought that the Ricci-flat condition of these spaces might allow one to make some general statements about sound propagation?
It probably does but I don't know what they are.

A two-dimensional torus with a flat metric is a Calabi-Yau space. So an ancient wraparound video-game like "Asteroids" is an example of "physics in a Calabi-Yau space".
 
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1. What is a Calabi-Yau manifold?

A Calabi-Yau manifold is a special type of manifold in mathematics that has important applications in string theory and complex geometry. It is a six-dimensional space with complex structure that is characterized by Ricci flatness and the absence of torsion.

2. How does an ideal gas behave on a Calabi-Yau manifold?

An ideal gas on a Calabi-Yau manifold behaves similarly to an ideal gas on a flat space. The particles in the gas move freely and independently of each other, and the pressure and volume of the gas can be described by the ideal gas law. However, the geometry of the Calabi-Yau manifold may affect the energy states of the particles and lead to different physical properties.

3. What is a point disturbance on a Calabi-Yau manifold?

A point disturbance on a Calabi-Yau manifold refers to the introduction of a localized disturbance or perturbation at a specific point on the manifold. This can be thought of as a point mass or a localized source of energy that affects the surrounding geometry and may cause changes in the behavior of particles or fields on the manifold.

4. How is the behavior of an ideal gas affected by a point disturbance on a Calabi-Yau manifold?

The behavior of an ideal gas on a Calabi-Yau manifold may be affected by a point disturbance in several ways. The energy states of the particles in the gas may be altered, leading to changes in temperature, pressure, and other physical properties. The geometry of the manifold may also be modified, which could affect the motion of the gas particles and lead to deviations from the ideal gas behavior.

5. What are the implications of studying Calabi-Yau manifolds and ideal gases with point disturbances?

The study of Calabi-Yau manifolds and ideal gases with point disturbances has important implications in both mathematics and physics. In mathematics, it helps us understand the properties of complex geometry and the behavior of manifolds in higher dimensions. In physics, it provides insights into the behavior of particles and fields in curved spaces and their interactions with localized disturbances, which has implications for theories such as string theory and quantum gravity.

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