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## Main Question or Discussion Point

Classically if you lift up a body, say a brick, you are doing work against the gravitational force, this work is then 'stored' as Gravitational Potential Energy and released when the body is dropped.

Energy is conserved so GPE (and other forms of PE) + KE = Constant.

In GR the problem is that there is no gravitational force as such. Gravitation is explained as the effect of space-time curvature. Free-falling bodies travel along straight lines (geodesics) through curved space-time. Like two ants crawling across the dip around the stalk of an apple, the geodesics of a dropped brick and the Earth converge because the Earth's mass (and to a much lesser extent the brick's) has curved the space-time through which they both 'fall'.

The force of 'weight' is a non-inertial force perturbing the brick from its free-falling geodesic. Release it and the brick suffers no weight at all, it is weightless.

The problem arises when you try to work out where the energy used to lift the brick goes to.

Lift a brick and put it on a shelf. The rest energy of the brick has not changed, so where has the GPE, the work expended lifting it, gone to?

The standard answer is "into the field", the presence of the brick higher up in the Earth's gravitational field has altered it slightly, the components of the GR Riemannian tensor describing that field has changed.

However if the brick now falls off the shelf it is momentarily still stationary but accelerating downwards. In that free-falling state the space-time locally around becomes flat. This is called the Einstein Equivalence Principle, "the physics of a small enough volume around a free-falling test particle becomes indistinguishable from that of SR", its coordinate system locally is Lorentzian.

So what has happened to the GPE now?

Energy is conserved so GPE (and other forms of PE) + KE = Constant.

In GR the problem is that there is no gravitational force as such. Gravitation is explained as the effect of space-time curvature. Free-falling bodies travel along straight lines (geodesics) through curved space-time. Like two ants crawling across the dip around the stalk of an apple, the geodesics of a dropped brick and the Earth converge because the Earth's mass (and to a much lesser extent the brick's) has curved the space-time through which they both 'fall'.

The force of 'weight' is a non-inertial force perturbing the brick from its free-falling geodesic. Release it and the brick suffers no weight at all, it is weightless.

The problem arises when you try to work out where the energy used to lift the brick goes to.

Lift a brick and put it on a shelf. The rest energy of the brick has not changed, so where has the GPE, the work expended lifting it, gone to?

The standard answer is "into the field", the presence of the brick higher up in the Earth's gravitational field has altered it slightly, the components of the GR Riemannian tensor describing that field has changed.

However if the brick now falls off the shelf it is momentarily still stationary but accelerating downwards. In that free-falling state the space-time locally around becomes flat. This is called the Einstein Equivalence Principle, "the physics of a small enough volume around a free-falling test particle becomes indistinguishable from that of SR", its coordinate system locally is Lorentzian.

So what has happened to the GPE now?