Fossil fields as the name suggests are simply the gravitational field of a large star before it goes S/N and leaves a BH remnant...that also pertains to EMF's and explain how gravity and such "gets out" of a BH.Fossil fields are interstellar magnetic fields. https://en.wikipedia.org/wiki/Fossil_stellar_magnetic_field . Interstellar radiation field is EM radiation. https://en.wikipedia.org/wiki/Interstellar_medium .
I'm sure I also gave you a link confirming that.
http://math.ucr.edu/home/baez/physics/Relativity/BlackHoles/black_gravity.html
If a star collapses into a black hole, the gravitational field outside the black hole may be calculated entirely from the properties of the star and its external gravitational field before it becomes a black hole. Just as the light registering late stages in my fall takes longer and longer to get out to you at a large distance, the gravitational consequences of events late in the star's collapse take longer and longer to ripple out to the world at large. In this sense the black hole is a kind of "frozen star": the gravitational field is a fossil field. The same is true of the electromagnetic field that a black hole may possess.