- #1

Jonathan Scott

Gold Member

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## Main Question or Discussion Point

As I'm sure I've mentioned before, I've heard people say that stress and pressure terms in the energy tensor act as a gravitational source, but I don't understand how this could be, given that these terms can simply appear or disappear (in a non-stationary situation), unlike energy and momentum.

I understand that in GR we normally discuss either static cases or fluid equilibrium, where this problem does not occur, but surely the fact that pressure or stress can vanish in this way does not fit with what we know about gravitational sources.

For example, if two small masses are held apart in a stationary configuration by a couple of rigid rods end to end, then the integral of the pressure in the rods is mathematically equal to the potential energy of the configuration (both by Newtonian physics and via the GR Komar mass expression). If one rod then one slips past the other, then the pressure in the rods drops to zero instantly (well, technically, at the speed of sound in the rod), but the potential energy of the configuration is surely initially unchanged (at least in the Newtonian view), and one would also expect the gravitational field to be essentially unchanged at first.

In the Newtonian view the integral of the pressure in the static case is

Have I missed something? As far as I can see, these terms could only be a gravitational source if they are replaced in dynamic situations by some other equal terms involving rates of change, in a similar way to mechanical simple harmonic motion.

I understand that in GR we normally discuss either static cases or fluid equilibrium, where this problem does not occur, but surely the fact that pressure or stress can vanish in this way does not fit with what we know about gravitational sources.

For example, if two small masses are held apart in a stationary configuration by a couple of rigid rods end to end, then the integral of the pressure in the rods is mathematically equal to the potential energy of the configuration (both by Newtonian physics and via the GR Komar mass expression). If one rod then one slips past the other, then the pressure in the rods drops to zero instantly (well, technically, at the speed of sound in the rod), but the potential energy of the configuration is surely initially unchanged (at least in the Newtonian view), and one would also expect the gravitational field to be essentially unchanged at first.

In the Newtonian view the integral of the pressure in the static case is

**equal to**the potential energy, but it cannot actually**be**the potential energy, as is illustrated by what happens when the rod slips. The corresponding opposite tension of the field through space is however unaffected, and remains equal to the potential energy even in a dynamic situation. However, although the total force through a given plane is known, the location of this potential energy is not predetermined; a simple mathematical solution would be to copy electrostatics and model the energy density of the field as ##g^2/8\pi## where ##g## is the Newtonian field. But the GR view does not include "energy density" in the field.Have I missed something? As far as I can see, these terms could only be a gravitational source if they are replaced in dynamic situations by some other equal terms involving rates of change, in a similar way to mechanical simple harmonic motion.