code id | Wiki id | meaning |
bSI | 3 physical constants in SI units | |
gu | Same units geometrized | |
c | c | speed of light |
bG | G | gravitational constant |
ke | 1/4πε_{0}c^{4} | Coulomb’s constant |
bM | M | Mass of BH |
bQ | Q | charge on BH |
bJ | J | angular momentum |
dtau2 | dτ | τ is proper time, measured locally.
dtau2 is a function of coordinates and differential vector. |
rs | r_{s} | Schwarzschild radius |
rQ2 | r_{Q}^{2} | a squared measure of the charge. |
a | α | common subexpression |
r | r | Schwarzschild radius, the r coordinate. |
th | θ | Latitude = (90−180*θ/π)°, a coordinate |
dt | dt | delta t where t is the coordinate time. |
dr | dr | delta r |
dth | dθ | delta θ |
dp | dφ | delta longitude. Longitude = 180*φ/π. |
rh2 | ρ^{2} | common subexpression |
del | Δ | common subexpression |
Three physical constants play a role here, c, bG and ke. These constants can be expressed in either SI units of geometrized units.
Three constants describe the particular black hole: M, Q and J.
The function dtau2 is of the relevant coordinates, r and th, and the differential vector, (dt, dr, dth, dp), separating the two events whose distance the metric defines.
This to compute r^{2} from x, y, z and a.
The plan: