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In a previous series of articles, I posed the question “Does Gravity Gravitate?” and explained how, depending on how you interpreted the terms “gravity” and “gravitate”, one could answer the question, either way, yes or no. This article will similarly treat its title question. :-)
To be sure, this case is a bit simpler than the previous one because there is only one term that can be given more than one meaning. The term “pressure” is clear: it means the spatial diagonal components of the stress-energy tensor. (More precisely, it means those components in the rest frame of the fluid, but we won’t delve into such technical details very much in this article.) The ambiguity is in the term “source of gravity”. What does that term mean?
The standard answer to that question in GR is that the source of gravity is the stress-energy tensor, the thing that appears on the RHS of the Einstein Field Equation. So anything...
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