By Michael Petri
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Additional resources for The holographic solution - Why general relativity must be understood in terms of
Example text
If the pressure is gravitational in origin, one would expect the cross-sectional area to be roughly equal to the Planck-area. For the following discussion I will assume, that σ and m (or rather the ratio σ/m) remain constant in the geodesically moving frame. Note, that this must not necessarily be so. Quantum field theory predicts, that the cross-sectional areas of the strong, weak and electro-magnetic force vary with energy and that the particle mass varies with energy. As the local temperature in the interior holostar space-time depends on r, one cannot rule out a priori that σ/m = const.
Small fluctuations will displace the particle from its equilibrium position. Whenever r >≈ ri the outward directed geodesic acceleration will dominate over the inward directed pressure-induced acceleration, as g ∝ 1/r3/2 and aP ∝ −1/r2 (for low velocities). As the motion becomes more and more geodesical the ratio aP /g quickly approaches an inverse square law, which means that the pressure-induced acceleration becomes negligible with respect to the geodesic acceleration whenever r >≈ (2 − 3)ri .
Then the number density n(r) of particles in the shell, as it moves inward or outward, is given by the respective change of the shell’s volume: n(r) = 1 Ni Ni Ni ri = = √ 3 = n(ri ) 2 δV 4πr δl 4π ri δli r 2 r 3 2 (50) Under the assumption that the interior matter-distribution of the holostar is (quasi-) static, and that the local composition of the matter at any particular r-position doesn’t change with time, self-consistency requires that the number density of zero rest-mass particles per proper volume should be proportional to the number density predicted by equation (50).
The holographic solution - Why general relativity must be understood in terms of by Michael Petri
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