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According to GR, how do changes in the mass of an energy density become reflected in its gravitational field?

Is the dissemination of the change in mass throughout the gravitational field c-limited?

If so, what geodesic does the dissemination of the change travel. Is the geodesic the same as that of a photon?

If the geodesic is different than that of a photon, then does gravitational flux travel outside the manifold of space-time as described by GR?

If the geodesic is the same, then may the gravitational flux travel faster than c?

Please consider this problem of gravitational flux within the context of a black hole:

In a black hole, photons cannot escape the event horizon due to the curvature of space-time (the geodesic). Can gravitational flux travel beyond the event horizon? If so, how? Does gravitational flux travel a different geodesic from photons, i.e., "outside" of the space-time manifold? Does gravitational flux travel faster than c? What gives?

Is the dissemination of the change in mass throughout the gravitational field c-limited?

If so, what geodesic does the dissemination of the change travel. Is the geodesic the same as that of a photon?

If the geodesic is different than that of a photon, then does gravitational flux travel outside the manifold of space-time as described by GR?

If the geodesic is the same, then may the gravitational flux travel faster than c?

Please consider this problem of gravitational flux within the context of a black hole:

In a black hole, photons cannot escape the event horizon due to the curvature of space-time (the geodesic). Can gravitational flux travel beyond the event horizon? If so, how? Does gravitational flux travel a different geodesic from photons, i.e., "outside" of the space-time manifold? Does gravitational flux travel faster than c? What gives?

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