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accdd
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Why in general relativity do we need the physics of perfect fluids?
Because some physicists like to go for a pint of beer after a hard day's theorising.accdd said:Why in general relativity do we need the physics of perfect fluids?
"A mathematician is a machine for turning coffee into theorems", as a double-espresso drinking mathematician friend once told me.PeroK said:Because some physicists like to go for a pint of beer after a hard day's theorising.
Ken Ribet got a math book he didn't need, went to the local used book store, sold it, and on the way back bought himself a cup of coffee. Then realized he had just turned theorems into coffee.Ibix said:"A mathematician is a machine for turning coffee into theorems", as a double-espresso drinking mathematician friend once told me.
You'd be lucky to get a coffee for the money you'd get for an unwanted maths book.martinbn said:Ken Ribet got a math book he didn't need, went to the local used book store, sold it, and on the way back bought himself a cup of coffee. Then realized he had just turned theorems into coffee.
The story goes back to the 80s I think, but I wasn't clear. He didn't want the book or didn't have a use for it, it may have been wanted in general. It may have been a book he has.PeroK said:You'd be lucky to get a coffee for the money you'd get for an unwanted maths book.
Just to point out that the reverse is also true, given the expansion history you can figure out how the relation between pressure and energy density has evolved historically as fixing the metric fixes the stress-energy tensor.vanhees71 said:The equations of motion get closed by just choosing a simple equation of state (usually "cold/non-relativistic" matter, "radiation/relativistic matter", and "dark energy").
Certainly in the case of pressureless dust, since there exists a coordinate system in which the fluid isn't moving even on a micro level. FLRW spacetime is an example. In a fluid with pressure there can be a coordinate system where there's no bulk motion (may also be one with no motion at all), so that works too. However, I think once you get to fluids with convection then you can't really use the notion anymore.cianfa72 said:Btw, is there any useful application of perfect fluids in GR as a 'physical realization' of coordinate systems ?
They're basically a simple approximation, that's usually sufficient.accdd said:Why in general relativity do we need the physics of perfect fluids?
wiki said:In physics, a perfect fluid is a fluid that can be completely characterized by its rest frame mass density and isotoropic pressure.
Real fluids are "sticky" and contain (and conduct) heat. Perfect fluids are idealized models in which these possibilities are neglected.
An ideal fluid is a theoretical concept used in fluid mechanics to describe a fluid that has no viscosity, is incompressible, and has no internal friction or heat transfer. It is a simplified model that allows for easier analysis of fluid flow.
The concept of an ideal fluid is needed because it provides a simplified model for understanding the behavior of real fluids. While real fluids have properties such as viscosity and heat transfer, these can be difficult to account for in mathematical equations. The ideal fluid model allows for easier analysis and prediction of fluid behavior.
The concept of an ideal fluid is not directly related to general relativity. However, the equations used to describe the behavior of ideal fluids are often used in the study of general relativity to describe the behavior of matter and energy in the universe.
Ideal fluids are used in a variety of real-world applications, such as in the design of aircraft and cars, the study of ocean currents and weather patterns, and the analysis of blood flow in the human body. They are also used in the study of astrophysical phenomena, such as the behavior of gases in stars and galaxies.
An ideal fluid is a simplified model that does not account for real-world properties such as viscosity and heat transfer. In contrast, a real fluid takes into account these properties and may exhibit behaviors such as turbulence and dissipation. Additionally, ideal fluids are considered incompressible, while real fluids may have varying degrees of compressibility.