Pure Geometric Horizon Mechanics of Black Holes

ABSTRACTIn standard theoretical astrophysics, black hole thermodynamics, Hawking radiation, and event horizon optics are formulated using complex expressions dependent on mass (M), gravitational constant (G), and reduced Planck constant (h_bar). This paper demonstrates that all physical properties of black holes can be derived strictly from linear geometry within a tensioned elastic space lattice defined by wave velocity (c = 299,792,458 m/s), minimum pixel length (l_P = 1.616255 * 10^-35 m), clock tick (t_P = 5.391253 * 10^-44 s), and lattice tension force (F_lattice = 1.210256 * 10^44 N). By modeling a black hole through its outer spatial indentation radius (Schwarzschild radius, Rs) and its conjugate inner quantum vortex radius (Rv), mass and G cancel out completely. We show that Hawking temperature scales inversely with Rs (T * Rs = 1.82223 * 10^-4 Km), radiative luminosity scales inversely with Rs^2 (L * Rs^2 = 1.9645 * 10^-22 Wm^2) and directly with the square of the inner quantum vortex radius (Rv^2), complete evaporation lifetime scales with the cube of the Planck pixel count spanning the horizon radius (t_evap = 640 * Pi * t_P * (Rs / l_P)^3), and the observable photon capture shadow radius equals 2.5981 * Rs. Step-by-step arithmetic verifications are presented for three observed black holes across nine orders of magnitude in mass: stellar-mass Cygnus X-1 (21.2 solar masses), Milky Way galactic center Sagittarius A* (4.3 million solar masses), and supermassive M87* (6.5 billion solar masses), showing exact consistency with Event Horizon Telescope (EHT) shadow measurements and all eight universal space-lattice invariants.