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General Relativity

(formula relating gravity, space, time, and mass)

General Relativity is a description of Gravity in terms of space-time geometry, characterizing acceleration due to gravitational force as constant motion within a curved space-time. In other words, what I feel as the Earth's gravitational force is an artifact of the space I'm occupying moving in that direction relative to the Earth.

General Relativity consists of the mathematical equations that provide such a characterization consistent with Newton's laws and Special Relativity. It relegates gravitational force to be an artifact, like centrifugal force or Coriolis Force. It was developed by Einstein in 1916 following his earlier development of Special Relativity. General Relativity remains the current favored model of gravity, based on its unique ability to explain the common, intuitive behavior of gravity as well as observed extreme cases that defy the common behavior.

The formula is known as Einstein's Field Equation or Einstein's Equation:

      1               8πG
Rμν - —— gμνR + gμνΛ = ———— Tμν
      2                c4

μ and ν each indicate the four dimensions of space-time, i.e., R, g and T each indicate a relationship between the four individual scalar values.

  • Rμν - Ricci curvature tensor.
  • R - scalar Curvature.
  • gμν - metric tensor.
  • Λ - Cosmological Constant.
  • G - Newton's gravitational constant.
  • c - speed of light.
  • Tμν - stress energy tensor.

Of interest is Λ, the Cosmological Constant, which Einstein included to compensate for the formula's implication that the universe would otherwise be expanding or contracting. Upon Edwin Hubble's later discovery of the visible expansion of the universe, Einstein no longer saw reason to include it. More recent observations showing expansion not following General Relativity's predictions has induced physicists to revive the "constant", as a rug under which they can sweep the unexplained visible phenomena, also known as Dark Energy.


Referenced by:
Birkhoff's Theorem
Black Hole (BH)
Core Collapse Supernova
Cosmological Constant (Λ)
Critical Density (ρc)
Dark Energy
Dark Matter
Doppler Shift
Einstein-de Sitter Model
Gravitational Wave (GW)
Law of Cosmic Censorship
Legendre Polynomials
Light Cone
Numerical Relativity (NR)
Hulse-Taylor Binary (PSR B1913+16)
Strong-Field Gravity
Time Dilation