- #1

ohwilleke

Gold Member

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## Summary:

- Are there are scientific names for the special cases of the stress-energy tensor in GR, for example, where all components of the stress-energy tensor of GR except the mass component, or where all components except the mass and pressure components, are zero?

**Background and Motivation**

The stress energy tensor of general relativity, as conventionally defined, has sixteen components.

One of those component, conventionally component T

_{00}, also called ρ, is mass-energy density, including the E=mc

^{2}conversion for electromagnetic fields.

The other components (three each for components in each of the three space dimensions) represent linear momentum, angular momentum, electromagnetic flux, sheer stress, and pressure.

In a static, pressureless case, without electromagnetic fields, however, all of these components except ρ are zero.

There are lots of physical situations where these fifteen components, while not actually zero, are small enough to be ignored in a quite good first order approximation of the gravitational forces that arise, but where it would be desirable to make a relativistic rather than a Newtonian calculation. And, with just one component, you have greatly simplified the computations involved.

Another case which would be considerably simpler and physical relevant for first order approximations in some cases, although not quite as simple, would be the static case without electromagnetic fields, but with both mass-energy density and pressure.

**Question**

My primary question is whether there is a special technical name or buzzword for this special case that would make it easier to search for and easier to talk about intelligently?

Also, is there a special technical name or buzzword for the slightly less simplified static case without electromagnetic fields, in which all elements not on the diagonal of the stress energy tensor are zero, but ρ and the three pressure components of the stress energy tensor are non-zero?

Finally, are there other special cases of the stress energy tensor similar to these cases that have special technical names?