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general relativity

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

General relativity is a description of gravity in terms of spacetime geometry, characterizing acceleration due to gravitational force as constant motion within a curved spacetime. 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 (and since I'm standing still on Earth, I'm moving "upward" relative to that space, and in fact, accelerating).

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 that "common" behavior. It is encapsulated in 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 spacetime, i.e., Rμν, gμν and Tμν each indicate a relationship between the four individual scalar values (a tensor, e.g., a 4×4 matrix).

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 term to make the equation to match observed reality, hypothesizing dark energy to explain it.

Further reading:

Referenced by pages:
alternative cosmologies
anti-de Sitter space (AdS)
areal coordinate system
black-hole information paradox
black hole model
Big Bang
Birkhoff's theorem
black hole (BH)
Chern-Simons gravity
core collapse supernova (CCSN)
cosmological constant (Λ)
critical density (ρc)
dark energy
dark matter
Doppler shift
effective field theory (EFT)
Einstein-de Sitter model
f(R) gravity
Friedmann model
gravitational constant (G)
gravitational field
gravitational wave (GW)
GW detection (GW)
Hawking radiation
Hubble time (tH)
innermost stable circular orbit (ISCO)
Johannsen-Psaltis metric (JP metric)
Kerr black hole
law of cosmic censorship
Legendre polynomials
light cone
Lovelock gravity
Mach's principle
mathematical field
no-hair theorem
numerical relativity (NR)
post-Newtonian formalism (PN formalism)
parameterized post-Newtonian formalism (PPN formalism)
Hulse-Taylor Binary (PSR B1913+16)
scalar-tensor gravity
Schwarzschild radius (RS)
Shapiro delay
gravitational singularity
special relativity (SR)
strong-field gravity
supergravity (SUGRA)
supersymmetry (SUSY)
theoretical modified GR metrics
time dilation
Theory of Everything (TOE)
Tolman-Oppenheimer-Volkoff limit (TOV)
wide binaries (WB)
ZAMO frame