# Perfect fluid

The stress–energy tensor of a perfect fluid contains only the diagonal components.

In physics, a perfect fluid is a fluid that can be completely characterized by its rest frame mass density $\rho _{m}$ and isotropic pressure p.

Real fluids are "sticky" and contain (and conduct) heat. Perfect fluids are idealized models in which these possibilities are neglected. Specifically, perfect fluids have no shear stresses, viscosity, or heat conduction.

In space-positive metric signature tensor notation, the stress–energy tensor of a perfect fluid can be written in the form

$T^{\mu \nu }=\left(\rho _{m}+{\frac {p}{c^{2}}}\right)\,U^{\mu }U^{\nu }+p\,\eta ^{\mu \nu }\,$ where U is the 4-velocity vector field of the fluid and where $\eta _{\mu \nu }=\operatorname {diag} (-1,1,1,1)$ is the metric tensor of Minkowski spacetime.

In time-positive metric signature tensor notation, the stress–energy tensor of a perfect fluid can be written in the form

$T^{\mu \nu }=\left(\rho _{\text{m}}+{\frac {p}{c^{2}}}\right)\,U^{\mu }U^{\nu }-p\,\eta ^{\mu \nu }\,$ where U is the 4-velocity of the fluid and where $\eta _{\mu \nu }=\operatorname {diag} (1,-1,-1,-1)$ is the metric tensor of Minkowski spacetime.

This takes on a particularly simple form in the rest frame

$\left[{\begin{matrix}\rho _{e}&0&0&0\\0&p&0&0\\0&0&p&0\\0&0&0&p\end{matrix}}\right]$ where $\rho _{\text{e}}=\rho _{\text{m}}c^{2}$ is the energy density and $p$ is the pressure of the fluid.

Perfect fluids admit a Lagrangian formulation, which allows the techniques used in field theory, in particular, quantization, to be applied to fluids. This formulation can be generalized, but unfortunately, heat conduction and anisotropic stresses cannot be treated in these generalized formulations.[why?]

Perfect fluids are used in general relativity to model idealized distributions of matter, such as the interior of a star or an isotropic universe. In the latter case, the equation of state of the perfect fluid may be used in Friedmann–Lemaître–Robertson–Walker equations to describe the evolution of the universe.

In general relativity, the expression for the stress–energy tensor of a perfect fluid is written as

$T^{\mu \nu }=\left(\rho _{m}+{\frac {p}{c^{2}}}\right)\,U^{\mu }U^{\nu }+p\,g^{\mu \nu }\,$ where U is the 4-velocity vector field of the fluid and where $g_{\mu \nu }$ is the metric, written with a space-positive signature.

## Monday, November 23, 2020

### Solar Panel Revolution in the Wind? By AleSpa - Own work, CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=29290121

I am encouraged by some research that is currently going on that is improving the efficiency of solar panels up and coming. This encouragement is based on designs I have seen in corollary manufacturing processes that could created a whole new industry.

It is a whole new research path that could greatly improve the energy retention otherwise seemingly at a standstill,  although these manufacturing processes for solar panels are currently inexpensive.

I have been pondering these ideas for sometime now and since the move to electrics for transportation is now more important then ever as I open the door to the studious and bright innovators who wonder about these potentials.

# Dr. Christian Schuster, researcher from the Department of Physics, told The Week news “We found a simple trick for boosting the absorption of slim solar cells. Our investigations show that our idea actually rivals the absorption enhancement of more sophisticated designs, while also absorbing more light deep in the plane and less light near the surface structure itself. Our design rule meets all relevant aspects of light trapping for solar cells, clearing the way for simple, practical, and yet outstanding diffractive structures, with a potential impact beyond photonic applications.” He added, “This design offers potential to further integrate solar cells into thinner, flexible materials and therefore create more opportunity to use solar power in more products.”

## Thursday, August 20, 2020

### Everyday Einstein: GPS & Relativity

See also: Everyday Einstein: GPS and Relativity  @Perimeter Institute for Theoretical Physics

## Wednesday, August 05, 2020

### Automated for the Future

Automated for the Future -Perimeter Institute for Theoretical Physics