# SCRIPT: BH-MATCHED-12
# The horizon as a matched load. Source: The Membrane Model of Black Holes and Applications (astro-ph/9711276),
# Eq. (70): the horizon surface resistivity R_H = 4 pi in Gaussian units with c = 1, equal to the vacuum impedance.
# Kill conditions, written before the run:
#  M1  4 pi / c converted from Gaussian (s/cm) to SI ohms equals mu_0 c to better than 1e-6 relative.
#  M2  the Cayley map S = (Z - 1)/(Z + 1) is zero exactly at the normalised impedance Z = R_H / Z_0 = 1, and is
#      negative below and positive above (a mismatched membrane reflects).
import math
c_cgs=2.99792458e10; statohm_per_s_per_cm=8.987551787368e11
RH=4*math.pi/c_cgs*statohm_per_s_per_cm; Z0=4e-7*math.pi*299792458
print(f'R_H = {RH:.7f} ohm, Z_0 = mu_0 c = {Z0:.7f} ohm')
ok1=abs(RH/Z0-1)<1e-6
S=lambda z:(z-1)/(z+1)
ok2=S(1.0)==0 and S(0.5)<0 and S(2.0)>0
print(('PASS' if ok1 else 'FAIL'),'M1 horizon resistivity equals the vacuum impedance', f'ratio {RH/Z0:.9f}')
print(('PASS' if ok2 else 'FAIL'),'M2 zero reflection exactly at the matched value', f'S(1) = {S(1.0)}, S(1/2) = {S(0.5):.4f}, S(2) = {S(2.0):.4f}')
print('ALL PASS' if ok1 and ok2 else 'SOME FAILED')