Does Pressure Increase or Decrease Active Gravitational Mass Density?

Details Does Pressure Increase or Decrease Active Gravitational Mass Density? Does Pressure Increase or Decrease Active Gravitational Mass Density?

2006-07-21

arxiv.org/abs/gr-qc/0607087v4

Phys. Lett. B. 685(1), 8-11 (2010)

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

The originally accepted journal version, subsequent modifications removed

Scientific paper

It is known that, for a static fluid sphere, the GeneralRelativistic (GR) Effective Mass Energy Density (EMD) appears to be (rho + 3 p), where rho is the bare mass density, p is the isotropic pressure, from a purely localized view point. But 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 Gravitational Mass Energy Density (AGMD) is sqrt{g_{00}} (rho + 3 p) and which is obviously smaller than (rho + 3p) because g_{00} < 1. Then we show that the AGMD eventually is (rho - 3p), 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 intersting property, we obtain the GR virial theorem in terms of appropriate ``proper energies''.

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