You are over thinking it .. start where we all started including Einstein
You have a perfect fluid consider the pressure on an individual molecule in the fluid.
http://www.zweigmedia.com/diff_geom/Sec12.htmlYou don't even have to really follow the mathematics just follow they are describing the pressure at a specific point and trust there mathematics.
The key point here is it is a calculation in general you can never actually measure but it doesn't mean it's useless
In the real world the fluid would be less than ideal so it may compress, change viscosity etc which is the reason the calculation was first done.
Do you remember the post I calculated the pressure at the centre of the earth ... very similar
I smile because good luck ever measuring it.
To make electomagnetism relativistic you give it the same treatment
https://en.wikipedia.org/wiki/Electromagnetic_stress-energy_tensorYou will see it ends up having the same properties
What we are dealing with has a scientific name called a body force.
https://en.wikipedia.org/wiki/Body_forceA body force is a force that acts throughout the volume of a body, in contrast to contact forces. Gravity and electromagnetic forces are examples of body forces. Inertial spin forces such as the Centrifugal force, Euler force, and the Coriolis effect are also examples of body forces.
It's that issue that leads to most of the complications from what many did with contact forces at school.
When you throw the frame of reference stuff in on top it gets very complicated.
