Zamicol's Relativity Playground

Name Symbol Value
Gravitational Constant G `6.67408 × 10^-11 m^3 kg^-1 s^-2`
Speed of Light c 299,792,458 m/s
Plank Constant h `6.62607015 × 10^-34 J⋅s`

Lorentz Transformation and Velocity Time Dilation

`gamma = 1/root()(1-v^2/c^2)`
Stationary Frame
Time:
Space x:

β:

Moving Frame
Time':
Space x':

Einstein Field Equations (EFE)

`R_(munu) - 1/2Rg_(munu) + Lamdag_(munu) = (8piG)/c^4T_(munu)`

Einstein gravitational constant: `kappa = (8piG)/c^4`

Gravitational Time Dilation

`"dilated time" / "observer time" = root()(1-(r_s)/r)`

Escape Velocity

`"Escape Velocity" = root()((2GM)/r)`

Schwarzschild radius

`"Schwarzschild radius" = (2GM)/c^2`

Bekenstein bound

`S ge (2pikRE)/(ℏc)`

Shanon Entropy

`H(X) = -sum_(i=1)^n P(x_i)logP(x_i)`






Important Concepts

Major Interesting or Surprising Things

Minor Interesting or Surprising Things

Learning Resources







TODO:

  • Gravitational Redshift Calculator (give mass, r, distance and get redshift)
  • Below surface gravitational time dilation (give m, r, and distance get t)
  • Above surface gravitational time dilation (give m, r, and distance get t)