Does pressure increase or decrease active gravitational mass density

At first sight, for a static fluid sphere, Effective Mass Energy Density (EMD) appears to be (ρ+3p/c2)(ρ+3p/c2), where ρ is the bare mass density, p is the isotropic pressure and c   is the speed of light. But it is pointed out that such a direct increase in EMD is valid only for a purely local point of view. And since there is no truly local definition of “gravitational field”, such a notion could actually be misleading. On the other hand, by using the Tolman mass formula, we point out that, from a global perspective, the Active Mass Energy Density is g00(ρ+3p/c2) and which is obviously smaller than (ρ+3p/c2)(ρ+3p/c2) because g00<1g00<1. Then we show that the AGMD eventually is (ρ−3p/c2)(ρ−3p/c2), i.e., exactly opposite to what is generally believed. We further identify the AGMD to be proportional to the Ricci Scalar. By using this fundamental and interesting property, we obtain the GR virial theorem in terms of appropriate “proper energies”.