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Hi all - first post at PF. As a 'science enthusiast' with no training in the tensor math of GR, was initially bewildered by the common assertion that still hypothetical 'dark energy' would act as a source of 'negative gravity' despite having positive energy density. Finally grasped that pressure in GR acts as a source of gravity 'all by itself' -

All well and good, but when visiting a Wikipedia article http://en.wikipedia.org/wiki/Stress-energy_tensor" [Broken] noticed that energy density and pressure are just some of the terms contributing to the energy-momentum stress tensor T

My question is this: what role do shear stresses play as source of gravity? What seems so strange is that it is well known that shear stress can be resolved into orthogonal acting tensile (negative pressure) and compressive (positive pressure) components of equal amplitude. As the diagonal pressure terms are in the first power only of p, to my mind shear stress should therefore make NO net contribution! Remember these stresses are supposed to contribute 'all by themselves' - NOT as shorthand for the associated elastic/hydrostatic energy density. So, are the shear stress terms just 'padding' or can someone explain what a chunk of matter under static shear stress contributes to the gravity of that chunk?

*quite additional*to any hydrostatic energy density associated with that pressure. As 'dark energy' is supposed to exert negative pressure, that term wins out as source of gravity (space-time curvature).All well and good, but when visiting a Wikipedia article http://en.wikipedia.org/wiki/Stress-energy_tensor" [Broken] noticed that energy density and pressure are just some of the terms contributing to the energy-momentum stress tensor T

^{ab}, which in GR is the total source of gravity. There is also energy flux, momentum flux, and most curiously, shear stress terms (the off-diagonals).My question is this: what role do shear stresses play as source of gravity? What seems so strange is that it is well known that shear stress can be resolved into orthogonal acting tensile (negative pressure) and compressive (positive pressure) components of equal amplitude. As the diagonal pressure terms are in the first power only of p, to my mind shear stress should therefore make NO net contribution! Remember these stresses are supposed to contribute 'all by themselves' - NOT as shorthand for the associated elastic/hydrostatic energy density. So, are the shear stress terms just 'padding' or can someone explain what a chunk of matter under static shear stress contributes to the gravity of that chunk?

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