We use mass as a property of objects that relates to the deformation that this object causes into the field that embeds this object. In black holes the scale of its boundary is proportional to its mass. For spherical black holes this means that their mass is proportional to their radius.
Far from a massive object with mass m, the gravitation potential of the object g(r) equals g(r)≈ mG/r
The shape of the Green's function of the field is f(r)=1/r
This means that a relation exists between the Green's function and the gravitation potential at far enough distance r
The Green's function has some volume and the spherical black hole also has some volume. If the volume of an extra Green's function is added to the black hole, then that volume is added to the volume of the black hole in an isotropic way. Its radius appears to scale with the number of added Green's function volumes.
This raises the idea that the internals of the black hole are optimally filled with Green's function volumes and that the mass of the black hole is proportional to the number of Green's functions that in this way determines the volume of the black hole.
Spherical pulse responses can inject the volume of the Green's function into a field. Thus, when the injection takes place within the internals of a black hole, then the scaling rule becomes manifest.
Spherical pulse responses act as spherical shock fronts. The above story implies that spherical shock fronts cannot pass the boundary of a black hole. That boundary is known as the event horizon.
Usually the event horizon is interpreted as the place where the escape velocity equals the light speed or as the place where the energy of a photon equals the gravitational energy.
@Hans van Leunen
Hi Hans.
If that is the case, then how can we explain the gamma-ray plumes that have been detected on some black-holes?.
Is there some kind of photonic tunneling effect caused by the shock fronts at the event horizon?
Ian
Ian,
The story that describes the internals of black holes says nothing about what happens just outside the border of the black holes. There some violent processes may occur that can be observed from a distance.
Also from Hawking radiation is suggested that part the volume of what is normally injected in free space is injected inside of the black hole and the other part is injected outside of the border. The stochastic process that generates the footprint of an elementary particle is active in a significantly wide region that can partly overlap the region of black hole. The Hilbert Book Model states that each elementary particle resides on a private quaternionic separable Hilbert space that manages a private quaternionic parameter space. Part of the spatial part of that parameter space determines the region of activity of the private stochastic process that under normal conditions generate the footprint of the elementary particle. The characteristic function of the stochastic process determines its activity region. It is the Fourier transform of the location density distribution that the process produces under normal conditions.
If the geometric center of the activity region cannot pass the event horizon, then the activity region can still partly overlap the black hole region. If the black hole attracts elementary particles then its border will be covered with partly overlapping elementary particle platforms.
Of course this is pure speculation, but it might explain some features of black holes.
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