Fuzzy 'Gaussian Prime' Number Force Fields

 

A Black Hole Toy Model 

Let Figure 1 capture a black hole event horizon’s black body surface patch area power spectrum function mole fraction n^{log(e^t )} = P•V/R•T [mol], P = GPn(force)/dV [nt/m²], V = ∫4•ℼ•t²•dt [m³], #points n ^{log (e^t )}…Let’s count exponential power point t =  t + 1→ t = 23 and see n ^{log (e^t )} = 1 mole of points become a gravitating cluster of n²³ =  GPn/dV•∫4•ℼ•t²•dt / R•T pseudorandom mass boundary points #GPn = GPn /log(GPn), gravitating an event horizon surface area patch’s populated by #GPn =  n^th Gaussian prime number complex endpoint predicted by using a Prime number Theorem extension PNText  that can place limits on light cone’s vertical ‘Time’ direction [second], and horizontal space ‘X’ direction [meter], and (X+dX) • (t+dt) light cone’s product point extensions.  

 PNText:  #GPn = GPn / log(GPn) = (#n/#Pn) = 1 ≡  (#eletron^mass(n)^- / #proton^mass (Pn)⁺)

Corollary:  PNText   ≡   (#eletron^mass(n)^- / #proton^mass (Pn)⁺) ≈  1836

Figure 1: A vacuum free energy Joule GP(E(X, t), ~E(X, t)) surface energy plane graph with rest mass origin point at coordinate point (Y(t(0)), X(½+ n•|dt|)) that extends to a cosmic boundary with a 4•ℼ solid angle that contains orbits for spectrum of 2^№ line endpoints length√(GP(X,t)² ) as drawn on Light Cone or  momentum map

 The model described, involves a detailed analysis of the event horizon's black body surface patch area and its power spectrum integral zeta product function, and has several profound implications for black hole physics. Firstly, it provides a framework for understanding the thermodynamics of black holes, particularly how they emit radiation, known as Hawking radiation. This phenomenon suggests that black holes are not entirely black but emit radiation due to quantum effects near the event horizon.

Moreover, the constraints and boundary conditions specified in the model could help refine our understanding of the quantum mechanics of black holes. By defining precise mathematical relationships, the model may offer insights into the behavior of particles and energy near a black hole's event horizon. This is crucial for testing theories of gravity and quantum mechanics in extreme conditions.