The discovery of the relation between the quantum energy-momentum tensor (EMT) and General Parton Distributions [1, 2] provides a unique way to study the EMT of the nucleon [3,4].  

It was shown that the expectation value of the EMT for an unpolarized proton target in the forward limit has the same structure as that of a perfect fluid [5]. The generalization of this result to a more general class of frames [6] leads to a more general EMT structure similar to that of an anisotropic perfect fluid density in the Breit frame. In this case additional terms can be related to the internal energy and transverse/radial pressure inside an unpolarized proton target.

We illustrate these results using current phenomenological knowledge of the EMT form factors.

References
[1] X.-D. Ji; Phys.Rev. D55 (1997) 7114-7125.
[2] X.-D. Ji; Phys.Rev.Lett. 78 (1997) 610-613.
[3] M.V. Polyakov; Phys.Lett. B555 (2003) 57-62.
[4] M. Burkardt; Int.J.Mod.Phys. A18 (2003) 173-208.
[5] C. Lorce'; Eur.Phys.J. C78 (2018) no.2, 120.
[6] C. Lorce', L. Mantovani, B. Pasquini; Phys.Lett. B776 (2018) 38-47.