Confusion about relativistic fluids

In summary, according to Schutz's book, fluids in the MCRF are characterized by no bulk flow of the fluid element and no spatial momentum in the particles. However, there is still heat flow present, which is why the energy-momentum tensor T0i is not zero. This also explains why the other elements Ti0 and Tij are not null, as there can still be momentum flux across boundaries even without particle motion. In the case of perfect fluids in the MCRF, there is no heat flow or particle motion, but there is still pressure due to the random motion of particles. This motion is not considered when it is said that there is no particle motion in the MCRF, as it only refers to bulk
  • #1
Marco Melo
1
0
According to Schutz book, in special relativity general fluids in the MCRF (Momentarily Commoving Reference Frame) are characterized by no bulk flow of the fluid element and no spatial momentum in the particles. The energy-momentum tensor elements T0i (flux of energy across i-surface) are not zero because, although there is no spatial momentum in the particles (no motion since we are in the MCRF), there is heat flow. But how can the other elements Ti0 (momentum density) be not null if the there isn’t particle motion inside the fluid element? Also, T_ij is not null either, so there is momentum flux across the boundaries even with no particle motion?
In the case of perfect fluids in the MCRF there isn’t heat flow and also there isn’t particle motion, so T0i is now zero. However the pressure, due to the random motion of particles is not zero.
Is this random motion not taken into account when it’s said that there isn’t particle motion in the MCRF? In order words, when it is said that motion doesn’t exist in the MCRF do they mean that CM motion or bulk motion only do not exist? So that the energy transfer (for non-perfect fluids) and pressure (for all fluids) are not due to particles transfer (since we are in the MCRF) but only collisions between particles in the fluid element with particles in its neighboring elements (in the case of non-perfect fluids)?
 
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  • #2
Marco Melo said:
Also, T_ij is not null either, so there is momentum flux across the boundaries even with no particle motion?

Maybe they balance each other out, something like the "vector sum" being zero?
 
  • #3
atyy said:
Maybe they balance each other out, something like the "vector sum" being zero?

I think that's wrong. It seems more like the fluid being at momentarily rest, but it could have an acceleration.
 

1. What is a relativistic fluid?

A relativistic fluid is a fluid that follows the principles of special relativity, which describes the behavior of objects moving at high speeds or in strong gravitational fields. In this context, a fluid is a substance that can flow and change its shape, such as gases or liquids.

2. What are the key differences between classical and relativistic fluids?

Classical fluids, which are described by Newton's laws of motion, assume that the speed of the fluid particles is much smaller than the speed of light. Relativistic fluids, on the other hand, take into account the effects of special relativity, such as time dilation and length contraction, which become significant at high speeds.

3. How are relativistic fluids used in scientific research?

Relativistic fluids are used in a variety of fields, including astrophysics, plasma physics, and high-energy physics. They are also important in the study of black holes and neutron stars, as well as in the development of new technologies, such as nuclear fusion reactors.

4. Can relativistic fluids be observed in everyday life?

No, relativistic effects are only noticeable at very high speeds or in strong gravitational fields, which are not typically encountered in everyday life. However, they can be observed and studied in experiments or simulations.

5. What are some current challenges in understanding relativistic fluids?

One of the main challenges is accurately modeling and simulating the behavior of relativistic fluids, especially in extreme conditions such as those found in the early universe or in the vicinity of black holes. Another challenge is reconciling the principles of relativity with quantum mechanics, which is necessary for a complete understanding of relativistic fluids.

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