Potential energy and annihilation

[Guywithquestions]

Let's assume an electron and an anti-electron are in a gravitational field so they both have potential energy.
What will become of this energy if they annihilate?
Will the momentum of the photons after the annihilation will increase so the total energy will be conserved?

Thanks for answering!

 

[Dale]

Will the momentum of the photons after the annihilation will increase so the total energy will be conserved?

Yes*. This is known as gravitational redshift.

*With the usual conventions (reference point “at infinity”) it is a decrease rather than an increase

 

[jartsa]

Doesn't light have potential energy?

If it has, then it sounds very intuitive that daughter particles would inherit the potential energy of the parents.