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Assume a space contains one black hole and two electrons $e_1$ and $e_2$ only. The distance between the black hole and electron $e_1$ is $10^6$ km, and the distance between the black hole and $e_2$ is $10^{15}$ km (about 100 light years). Relative velocities of two electrons to the black hole are zero. There is no other interaction between the black hole and two electrons, except gravitational force.

My question is : Is $e_2$'s mass is greater than $e_1$'s mass because of gravitational potential energy difference?

Because I am an engineer, not a physicist, my question may have some defects. What I want to know is : if the potential energy is indeed in the object, the mass of the object can vary because of the potential energy difference?

pdh0710
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Potential energy certainly contributes to mass. For example the mass of the hydrogen atom contains proton and electron masses as well as their kinetic and potential energy. However an external potential energy does not contribute to the mass. Mass is simply the energy of a system at rest. The interaction with another object is not included. The interaction does contribute to the mass of the combined object of black hole plus electron.

By the way, why bring up black holes at the risk of starting a discussion on general gravitation? The electron could also be in an electric field, which is more close to your expertise.

my2cts
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