Can a time-varying gravitational field produce photons?

Our critique of Hawking radiation contains a conjecture that a time-varying gravitational field cannot produce photons if there is no ordinary matter present. Ordinary matter is coupled to the electromagnetic field, and can produce photons when the gravitational field pushes its particles around.

If a time-varying gravitational field is a gravitational wave, or it is produced by hypothetical dark matter, then photons cannot be produced, according to our conjecture.

This is at odds with the fact that a time-varying electromagnetic fields, or photons, create a time-varying gravitational field. If there is a coupling to that direction, why not to the other direction?

If we have a small random quantum fluctuation in the electromagnetic field, can a time-varying gravitational field make it to grow to real photons? Can the gravitational field give enough energy?

Let us study an analogous situation. The Dirac electron-positron field is coupled to the electromagnetic field. A time-varying Dirac field will always create a time-varying electromagnetic field.

In the Schwinger process, an electric field will create electron-positron pairs. That is, even a static electric field creates a permanent disturbance of the Dirac field, if the potential difference in the electric field is at least 1.022 MV.

In the coupling of the Dirac field and the electromagnetic field, there is an asymmetry: any small disturbance in the Dirac field always produces photons, but only a relatively large 1.022 MV potential difference in the electric field creates a permanent disturbance to the Dirac field. The quantum of the Dirac field has an energy 511 keV, while a photon can have any energy.

We have a conjecture that electromagnetic waves really are waves in the polarization of virtual electron-positron pairs. There is really just one field, the electron-positron field, whose temporary polarization manifests as photons, and permanent polarization as electrons and positrons. A big difference in the electric potential can turn a virtual electron-positron pair into a real one.

What about the gravitational field?

Conjecture 1. Gravitational waves really are polarization of virtual pairs, one having a positive mass-energy and the other having the opposite negative mass-energy.


Can a strong static gravitational field create pairs of photons?

Suppose that a quantum fluctuation creates a transient pair of wavelength b virtual photons. One photon hass mass-energy E and the other -E. The E photon travels down the gravitational potential. Let its wavelength get shorter by some ratio R. It gains energy from gravitational pull, so that it has energy R * E. If the photon did not have enough energy to be real at the start, it cannot gain enough energy to become real as it travels down.

The -E photon will travel up (?). It gains positive energy from the gravitational push. Its mass-energy will approach zero but can never become zero. Thus, creation of photons by this process seems to be prohibited by quantum field theory.

Can a static gravitational field create electron-positron pairs?

Suppose we have a virtual electron e- with mass-energy E and a positron e+ with mass-energy -E.

The electron will travel downward and gain momentum and mass-energy from the gravitational pull. If it gains the 511 keV, do we have then a real electron?

The positron has the same problem as the photon: its negative mass-energy will diminish, but can never reach zero. It cannot become a real particle.

Looks like a static gravitational field cannot create pairs of particles. The difference to the Schwinger process is that the mass-energy of the negative energy particle can never become positive.