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vacuum example
====Example 1: Stress-energy tensor for a vacuum====
The simplest possible stress-energy tensor is, of course, one in which all the values are zero.
:<math>T_{\mu \nu }\ =\ 0</math>
This tensor represents a region of space in which there is no matter, energy or fields, not just at a given instant, but over the entire period of time in which we're interested in the region. Nothing exists in this region, and nothing happens in this region.
So one might assume that in a region where the stress-energy tensor is zero, the gravitational field must also necessarily be zero. There's nothing there to gravitate, so it follows naturally that there can be no gravitation.
In fact, it's not that simple. We'll discuss this in greater detail in the next section, but even a cursory qualitative examination can tell us there's more going on than that. Consider the gravitational field of an isolated body. A test particle placed somewhere near but outside of the body will move in a geodesic in spacetime, freely falling inward toward the central mass. A test particle with some constant linear velocity component perpendicular to the interval between the particle and the mass will move in a conic section. ''This is true even though the stress-energy tensor in that region is exactly zero.'' This much is obvious from our intuitive understanding of gravity: gravity affects things at a distance. But exactly ''how'' and ''why'' this happens, in the model of the Einstein field equations, is an interesting question which will be explored in [[#The left side of the equation: the Einstein curvature tensor|the next section]].
====Example 2: Stress-energy tensor for an ideal dust====
