# 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 ${\displaystyle \rho _{m}}$ 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

${\displaystyle T^{\mu \nu }=\left(\rho _{m}+{\frac {p}{c^{2}}}\right)\,U^{\mu }U^{\nu }+p\,\eta ^{\mu \nu }\,}$

where U is the 4-velocity vector field of the fluid and where ${\displaystyle \eta _{\mu \nu }=\operatorname {diag} (-1,1,1,1)}$ 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

${\displaystyle T^{\mu \nu }=\left(\rho _{\text{m}}+{\frac {p}{c^{2}}}\right)\,U^{\mu }U^{\nu }-p\,\eta ^{\mu \nu }\,}$

where U is the 4-velocity of the fluid and where ${\displaystyle \eta _{\mu \nu }=\operatorname {diag} (1,-1,-1,-1)}$ is the metric tensor of Minkowski spacetime.

This takes on a particularly simple form in the rest frame

${\displaystyle \left[{\begin{matrix}\rho _{e}&0&0&0\\0&p&0&0\\0&0&p&0\\0&0&0&p\end{matrix}}\right]}$

where ${\displaystyle \rho _{\text{e}}=\rho _{\text{m}}c^{2}}$ is the energy density and ${\displaystyle p}$ 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

${\displaystyle T^{\mu \nu }=\left(\rho _{m}+{\frac {p}{c^{2}}}\right)\,U^{\mu }U^{\nu }+p\,g^{\mu \nu }\,}$

where U is the 4-velocity vector field of the fluid and where ${\displaystyle g_{\mu \nu }}$ 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

## Saturday, May 16, 2020

### Gaslighting in America

Gaslighting is a form of psychological manipulation in which a person or a group covertly sows seeds of doubt in a targeted individual, making them question their own memory, perception, or judgment, often evoking in them cognitive dissonance and other changes such as low self-esteem. Using denial, misdirection, contradiction, and misinformation, gaslighting involves attempts to destabilize the victim and delegitimize the victim's beliefs. Instances can range from the denial by an abuser that previous abusive incidents occurred to the staging of bizarre events by the abuser with the intention of disorienting the victim.
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I must say having been involved in the consumption of the news of late and the pandemic forcing us into stay at home so I started to wonder.

## The creation of the Artemis Accords

The ability to extract and utilize resources on the Moon, Mars, and asteroids will be critical to support safe and sustainable space exploration and development.

The Artemis Accords reinforce that space resource extraction and utilization can and will be conducted under the auspices of the Outer Space Treaty, with specific emphasis on Articles II, VI, and XI.

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# Outer Space Treaty of 1967

#### Outer space, including the moon and other celestial bodies, is not subject to national appropriation by claim of sovereignty, by means of use or occupation, or by any other means.

Article VI
States Parties to the Treaty shall bear international responsibility for national activities in outer space, including the moon and other celestial bodies, whether such activities are carried on by governmental agencies or by non-governmental entities, and for assuring that national activities are carried out in conformity with the provisions set forth in the present Treaty. The activities of non-governmental entities in outer space, including the moon and other celestial bodies, shall require authorization and continuing supervision by the appropriate State Party to the Treaty. When activities are carried on in outer space, including the moon and other celestial bodies, by an international organization, responsibility for compliance with this Treaty shall be borne both by the international organization and by the States Parties to the Treaty participating in such organization.

#### Article XI

In order to promote international co-operation in the peaceful exploration and use of outer space, States Parties to the Treaty conducting activities in outer space, including the moon and other celestial bodies, agree to inform the Secretary-General of the United Nations as well as the public and the international scientific community, to the greatest extent feasible and practicable, of the nature, conduct, locations and results of such activities. On receiving the said information, the Secretary-General of the United Nations should be prepared to disseminate it immediately and effectively.