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- Asking how GR treats gravitational potential energy, which is typically described in a Newtonian context.

Hi, folks. Several years ago I made a YouTube video with a new demonstration of GR for a general audience ("How Gravity Makes Things Fall"). It won a pretty prestigious physics award. I still get comments and questions on it. One today stumped me: "How do we account for potential energy if gravity is not a force field?"

I consulted my Hartle textbook, but the index said, "See Newtonian gravity." There, Hartle talks about how gravitational potential is an analog of electrostatic potential. So that won't help me answer the viewer's question.

How is gravitational potential energy described within the context of curved spacetime? In Newtonian gravity, we describe a test particle's potential as a specific quantity, in terms of masses and distance. But in GR, it seems that a test particle in a curved spacetime could be described as having various potentials, depending upon the masses and distance associated with the curvature. So is PE meaningless in the context of GR?

Thank you very much for your help!

I consulted my Hartle textbook, but the index said, "See Newtonian gravity." There, Hartle talks about how gravitational potential is an analog of electrostatic potential. So that won't help me answer the viewer's question.

How is gravitational potential energy described within the context of curved spacetime? In Newtonian gravity, we describe a test particle's potential as a specific quantity, in terms of masses and distance. But in GR, it seems that a test particle in a curved spacetime could be described as having various potentials, depending upon the masses and distance associated with the curvature. So is PE meaningless in the context of GR?

Thank you very much for your help!