Astrophysics (Index)About

general relativity

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

General relativity (GR) 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 that is virtually consistent with the observed effects of Newton's laws on our more familiar (Euclidean) space-time concept, and with special relativity. GR relegates gravitational force to be an artifact, like centrifugal force or Coriolis force. Einstein completed its development 1916 after years of effort, his earlier special relativity having been developed in 1905. 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 aka Einstein's equation:

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

μ and ν each indicate one of 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 equation'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.

GR is proven and accepted (current everyday technology requires GR theory to be taken into account, including your phone's GPS), and despite occasional news headlines announcing "Einstein was right again", physicists have long known that the workings of the real world are not explained without GR. However, modifications to GR are explored in hopes of meshing GR with quantum theory and in explaining various unexplained phenomena. Such modified GR theories are currently of interest because advances, such as those in observing black holes can offer tests that could confirm some modified version of GR (and "Einstein right again" announcements are made when proposed modifications fail to improve on existing GR in such a test). The term Einstein gravity is sometimes used to distinguish his version of GR from proposed modifications.


(equation,physics,relativity,geometry)
Further reading:
https://en.wikipedia.org/wiki/General_relativity
https://preposterousuniverse.com/wp-content/uploads/2015/08/grtinypdf.pdf
https://www.pitt.edu/~jdnorton/teaching/HPS_0410/chapters/general_relativity/
https://www.space.com/17661-theory-general-relativity.html
https://en.wikisource.org/wiki/Translation:The_Field_Equations_of_Gravitation

Referenced by pages:
alternative cosmologies
anti-de Sitter space (AdS)
areal coordinate system
Big Bang
bigravity
Birkhoff's theorem
black hole (BH)
black hole model
black-hole information paradox
Chern-Simons gravity
CMBFAST
core collapse supernova (CCSN)
correction term
cosmological constant (Λ)
cosmological model
cosmology
critical density (ρc)
curvature
dark energy (Λ)
dark matter (DM)
Doppler shift
effective field theory (EFT)
Einstein delay
Einstein-de Sitter model
ephemeris
ergosphere
f(R) gravity
Friedmann model
geodesic
GR1D
gravitational constant (G)
gravitational field
gravitational singularity
gravitational wave (GW)
graviton
gravity
Gravity Probe B (GP-B)
GW detection (GW)
Hartle-Thorne metric (HT metric)
Hawking radiation
Hubble time (tH)
Hulse-Taylor Binary (PSR B1913+16)
innermost stable circular orbit (ISCO)
Johannsen-Psaltis metric (JP metric)
Keplerian orbit
Kerr black hole
Lambda-CDM model (ΛCDM)
LARES
law of cosmic censorship
Legendre polynomials
light cone
Lovelock gravity
Mach's principle
magnetohydrodynamics (MHD)
mathematical field
metric
modified Newtonian dynamics (MOND)
no-hair theorem
numerical relativity (NR)
parameterized post-Newtonian formalism (PPN formalism)
post-Newtonian formalism (PN formalism)
redshift-angular size relation
relativistic momentum
relativity
scalar-tensor gravity
Schwarzschild radius (RS)
Shapiro delay
spacetime
SpEC
special relativity (SR)
strong-field gravity
supergravity (SUGRA)
supersymmetry (SUSY)
theoretical modified GR metric
Theory of Everything (TOE)
time dilation
Tolman VII object
Tolman-Oppenheimer-Volkoff limit (TOV)
wCDM
wide binaries (WB)
worldline
wormhole
ZAMO frame

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