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I'm trying to understand the connection between The Equivalence principle and the Rindler space. According to Einstein the inhabitants of the elevator should feel the acceleration. However, for an observer in outer space (far the homogeneous field) should observe the elevator (and its inhabitants) as free-falling objects in the curvature of spacetime. This implies the they dont accelerate and thus describe the motion of a geodesic. Shouldn't the observer obtain a geodesic equation With vanishing Christoffel symbols ?

is there something wrong with my reasoning? if not, How to obtain such geodesic equation for an observer in outer space for which the Christoffel symbols vanish and thus represents a 'free-falling' object.

M91
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  • Please describe the “inhabitants of the elevator”. Is this elevator at rest on earth, accelerating on a rocket in deep space, in free fall near the earth, or floating in deep space – Dale Oct 07 '20 at 14:03
  • The elevator accelarates with $g$ in the $z$ direction in space. The inhabitants expirience a force $mg$. But they dont know wether they stand on earth or just being free falling in an homogeneous gravitational field in $z$ direction or even accelarating (equivalance principle?). – M91 Oct 07 '20 at 14:27
  • Sorry I was unclear. I meant for you to please put that necessary extra information in the question itself. – Dale Oct 07 '20 at 15:35
  • Also relevant is my answer to Curvature gravity and a falling apple? – John Rennie Oct 07 '20 at 15:52

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