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Linear perturbations to solutions of nonlinear Einstein field equations
linearized gravity is an effective method for modeling the effects of gravity when the gravitational field is weak. The usage of linearized gravity is
Linearized_gravity
Field-equations in general relativity
spacetime as having only small deviations from flat spacetime, leading to the linearized EFE. These equations are used to study phenomena such as gravitational
Einstein_field_equations
Theory of gravitation as curved spacetime
Approximate solutions may also be found by perturbation theories such as linearized gravity and its generalization, the post-Newtonian expansion, both of which
General_relativity
Attraction of masses and energy
In physics, gravity (from Latin gravitas 'weight'), also known as gravitation or a gravitational interaction, is a fundamental interaction, which may
Gravity
Aspect of relativity in physics
a gravitational wave has a very small amplitude (as formulated in linearized gravity). However, they help illustrate the kind of oscillations associated
Gravitational_wave
Region in spacetime from which nothing can escape
Rindler coined the term in the 1950s. In 1784, John Michell proposed that gravity can be strong enough in the vicinity of massive compact objects that even
Event_horizon
Two interrelated physics theories by Albert Einstein
Special relativity applies to all physical phenomena in the absence of gravity. General relativity explains the law of gravitation and its relation to
Theory_of_relativity
Compact astronomical body
A black hole is an astronomical body so compact that its gravity prevents anything, including light, from escaping. Albert Einstein's theory of general
Black_hole
Condition in which spacetime itself breaks down
singularity, or simply singularity, is a theoretical condition in which gravity is predicted to be so intense that spacetime itself would break down catastrophically
Gravitational_singularity
Type of potential in electrodynamics
-\mathbf {r} '|}}\mathrm {d} ^{3}\mathbf {r} '} The retarded potential in linearized general relativity is closely analogous to the electromagnetic case. The
Retarded_potential
Measured time difference as explained by relativity theory
velocity time dilation equation in the presence of motion and absence of gravity, i.e. β e = 0 {\displaystyle \beta _{e}=0} . It reduces to gravitational
Time_dilation
Theorem in general relativity
by Dain and Moreschi that a corresponding theorem will not hold in linearized gravity, that is, given a solution of the linearised Einstein field equations
Goldberg–Sachs_theorem
Classical statement of gravity as force
Newton's law of universal gravitation describes gravity as a force by stating that every particle attracts every other particle in the universe with a
Newton's law of universal gravitation
Newton's_law_of_universal_gravitation
Hamiltonian formulation of general relativity
of general relativity that plays an important role in canonical quantum gravity and numerical relativity. It was first published in 1959. The comprehensive
ADM_formalism
Description of gravity using discrete values
Quantum gravity (QG) is a field of theoretical physics that seeks unification of the theory of gravity with the principles of quantum mechanics. It deals
Quantum_gravity
Hypothesis that inertial and gravitational masses are equivalent
of gravity, the equivalence principle is viewed as an observation, an accident of nature encoded in empirical law. In Einstein's model of gravity, the
Equivalence_principle
Hypothetical quantum cosmological effect
flow of an approximately perfect fluid is analogous to gravity. (See analog models of gravity.) Observations of Hawking radiation were reported in sonic
Hawking_radiation
Theory extending Einstein gravity
Quadratic gravity (QG) is an extension of general relativity obtained by adding all local quadratic-in-curvature terms to the Einstein–Hilbert Lagrangian
Quadratic_gravity
Use of circular rotational force to mimic gravity
experienced in linear acceleration, which by the equivalence principle is indistinguishable from gravity. In a more general sense, "artificial gravity" may also
Artificial_gravity
Hypothetical object of spacetime
Acceleration due to gravity is the greatest on the surface of any body. But since black holes lack a surface, acceleration due to gravity increases exponentially
White_hole
Theory of gravity in which the graviton has nonzero mass
can be seen as an extension of linearized gravity in the following way. Linearized gravity is obtained by linearizing general relativity around flat space
Massive_gravity
Solution to the Einstein field equations
gravity that corresponds to the gravitational field around a point particle. Even at the surface of the Earth, the corrections to Newtonian gravity are
Schwarzschild_metric
English mathematician, mathematical physicist (born 1931)
networks, which later came to form the geometry of spacetime in loop quantum gravity. He was influential in popularising what are commonly known as Penrose
Roger_Penrose
Theory in modern physics that describes gravity as an entropic force
Entropic gravity, also known as emergent gravity, is a theory in modern physics that describes gravity as an entropic force—a force with macro-scale homogeneity
Entropic_gravity
Analogies between Maxwell's and Einstein's field equations
radiation Gravity Probe B Kaluza–Klein theory Linearized gravity Modified Newtonian dynamics Non-relativistic gravitational fields Speed of gravity § Electrodynamical
Gravitoelectromagnetism
Theory of gravity
Mark Robert; Kuzmin, Sergei (2019), "A connection between linearized Gauss–Bonnet gravity and classical electrodynamics", Int. J. Mod. Phys. D, 28 (7):
Gauss–Bonnet_gravity
Wave where gravity is the main restoring force
In fluid dynamics, gravity waves are waves in a fluid medium or at the interface between two media when the force of gravity or buoyancy tries to restore
Gravity_wave
Physics concept expressed as E = mc²
refers to the inertial mass. However, already in the context of Newtonian gravity, the weak equivalence principle is postulated: the gravitational and the
Mass–energy_equivalence
Hypothetical FTL transportation by warping space
physicists have presented arguments to suggest that a theory of quantum gravity (which would incorporate both theories) would eliminate those solutions
Alcubierre_drive
Precession of a gyroscope due to a nearby celestial body's rotation affecting spacetime
popular in some circles to use the gravitoelectromagnetic approach to the linearized field equations. The reason for this popularity should be immediately
Lense–Thirring_precession
Diagram of different points in spacetime
Formulation ADM formalism BSSN formalism Einstein field equations Linearized gravity Post-Newtonian formalism Raychaudhuri equation Hamilton–Jacobi–Einstein
Penrose_diagram
Theory of quantum gravity merging quantum mechanics and general relativity
Loop quantum gravity (LQG) is a theory of quantum gravity that incorporates matter of the Standard Model into the framework established for the intrinsic
Loop_quantum_gravity
Theories of higher-dimensional general relativity
Higher-dimensional Einstein gravity is any of various physical theories that attempt to generalize to higher dimensions various results of the standard
Higher-dimensional Einstein gravity
Higher-dimensional_Einstein_gravity
Theory of gravity
S2CID 119370540. Berry, C. P. L.; Gair, J. R. (2011). "Linearized f(R) gravity: Gravitational radiation and Solar System tests". Physical Review
F(R)_gravity
Unified field theory
like ordinary gravity in free space, except that it is phrased in five dimensions instead of four. The equations governing ordinary gravity in free space
Kaluza–Klein_theory
Exact solution for the Einstein field equations
first measurement of this frame dragging effect was done in 2011 by the Gravity Probe B experiment. Roughly speaking, this effect predicts that objects
Kerr_metric
Physical constant equal to the speed of light
gravitational field which it produces. In the relativistic sense, the "speed of gravity" refers to the speed of a gravitational wave, which, as predicted by general
Speed_of_gravity
1984 graduate textbook by Robert M. Wald
throughout the book. However, he considered that the material on linearized gravity was too short, and recommended Gravitation by Charles Misner, Kip
General_Relativity_(book)
German-born theoretical physicist (1879–1955)
concept of a finite speed of propagation of the physical interactions of gravity with it. By contrast, gravitational waves cannot exist in the Newtonian
Albert_Einstein
Hypothetical particle found in supergravity
massless spin-2 field with a Proca field. The dual formulations of linearized gravity are described by a mixed Young symmetry tensor T λ 1 λ 2 ⋯ λ D − 3
Dual_graviton
Equations in physical cosmology
The winner depends upon the k value in the total energy: if k is +1, gravity eventually causes the universe to contract. These conclusions will be altered
Friedmann_equations
reproduces general relativity in the classical limit, but only at the linearized level and postulating that the conditions for the applicability of Ehrenfest
History of gravitational theory
History_of_gravitational_theory
Set of spacetime events, light-connected to a given event
Formulation ADM formalism BSSN formalism Einstein field equations Linearized gravity Post-Newtonian formalism Raychaudhuri equation Hamilton–Jacobi–Einstein
Light_cone
Key results in general relativity on gravitational singularities
theorem is weak: it says that light rays are always focused together by gravity, never drawn apart, and this holds whenever the energy of matter is non-negative
Penrose–Hawking singularity theorems
Penrose–Hawking_singularity_theorems
Light bending by mass between source and observer
von Soldner in 1801 (published in 1804) had pointed out that Newtonian gravity predicts that starlight will bend around a massive object as had already
Gravitational_lens
Effect of general relativity
Hecht, Jeff. "Gravity Probe B scores 'F' in NASA review". New Scientist. Retrieved 2023-09-17. "Gravity Probe B – MISSION STATUS". "Gravity Probe B finally
Frame-dragging
Black holes are characterized only by mass, charge, and spin
mathematicians refer to it as the no-hair conjecture. Even in the case of gravity alone (i.e., zero electric fields), the conjecture has only been partially
No-hair_theorem
Hypothetical topological feature of spacetime
resort to exotic matter. For example, this is possible with R2 gravity, a form of f(R) gravity. The impossibility of faster-than-light relative speed applies
Wormhole
Precession of satellite orbits due to a celestial body's presence affecting spacetime
angular momentum of a gyroscope orbiting the Earth, as carried out by the Gravity Probe B experiment. The geodetic effect was first predicted by Willem de
Geodetic_effect
Hypothetical physical concept
fundamental interactions: electromagnetism, strong and weak nuclear forces, and gravity. Finding such a theory is one of the major unsolved problems in physics
Theory_of_everything
American physicist, writer, and Nobel Laureate (born 1940)
contributions, which center on the general nature of space, time, and gravity, span the full range of topics in general relativity. Thorne's work has
Kip_Thorne
Speed of electromagnetic waves in vacuum
(2003). Gravity: An Introduction to Einstein's General Relativity. Addison-Wesley. pp. 52–59. ISBN 978-981-02-2749-4. Hartle, J. B. (2003). Gravity: An Introduction
Speed_of_light
Approximation method for general relativity in physics
parameters. It is used as a tool to compare non-linear Einsteinian gravity to simpler Newtonian gravity in the limit in which the gravitational field is
Parameterized post-Newtonian formalism
Parameterized_post-Newtonian_formalism
Tensor field in Riemannian geometry
mathematical tool in the theory of general relativity, the modern theory of gravity. The curvature of spacetime is in principle observable via the geodesic
Riemann_curvature_tensor
Restatement of Newton's law of universal gravitation
In physics, Gauss's law for gravity, also known as Gauss's flux theorem for gravity, is a law of physics that is equivalent to Newton's law of universal
Gauss's_law_for_gravity
Branch of differential geometry
Formulation ADM formalism BSSN formalism Einstein field equations Linearized gravity Post-Newtonian formalism Raychaudhuri equation Hamilton–Jacobi–Einstein
Riemannian_geometry
General-relativistic effect
confirmed directly by the Pound–Rebka experiment in 1959, and later refined by Gravity Probe A and other experiments. Gravitational time dilation is closely related
Gravitational_time_dilation
Low-velocity approximation of special relativity
a Galilean transformation. In all inertial frames, Newton's laws, and gravity, hold. In comparison, the corresponding statements from special relativity
Galilean_invariance
Thought experiment in special relativity
ISBN 0-8018-8422-5. Schutz, Bernard (2003). Gravity from the Ground Up: An Introductory Guide to Gravity and General Relativity (illustrated ed.). Cambridge
Twin_paradox
Abstract coordinate system
centrifugal force, and gravitational force. (All of these forces including gravity disappear in a truly inertial reference frame, which is one of free-fall
Frame_of_reference
Hypothetical particle
theory's compactifications of extra dimensions. In Brans–Dicke theory of gravity, Newton's constant is not presumed to be constant but instead 1/G is replaced
Dilaton
Tensor describing energy momentum density in spacetime
relativity, just as mass density is the source of such a field in Newtonian gravity. The electromagnetic stress–energy tensor was introduced by Hermann Minkowski
Stress–energy_tensor
Differentiable manifold with nondegenerate metric tensor
Minkowski spacetime Metric tensor Equations Formalisms Equations Linearized gravity Einstein field equations Friedmann Geodesics Mathisson–Papapetrou–Dixon
Pseudo-Riemannian_manifold
Solution of Einstein field equations
Luongo, Orlando; Quevedo, Hernando (2014). "Characterizing repulsive gravity with curvature eigenvalues". Physical Review D. 90 (8) 084032. arXiv:1407
Kerr–Newman_metric
Mathematical model combining space and time
of gravity, is uniform throughout, and serves as nothing more than a static background for the events that take place in it. The presence of gravity greatly
Spacetime
Theorem in general relativity
Lovelock theory of gravity Vermeil's theorem Einstein tensor § Uniqueness Clifton, Timothy; et al. (March 2012). "Modified Gravity and Cosmology". Physics
Lovelock's_theorem
the Wheeler–Feynman absorber theory. Presumably the same holds in linearized gravity: e.g., see Gravitoelectromagnetism. Pretorius, Frans (2005). "Evolution
Two-body problem in general relativity
Two-body_problem_in_general_relativity
Field theory in physics that aims to unify the fundamental forces and particles
of field theory that allows all fundamental forces of nature, including gravity, and all elementary particles to be written in terms of a single physical
Unified_field_theory
Trace radiation from the early universe
S2CID 16825580. Seljak, U.; Zaldarriaga M. (March 17, 1997). "Signature of Gravity Waves in the Polarization of the Microwave Background". Phys. Rev. Lett
Cosmic_microwave_background
Solution of Einstein field equations
equations in a Kerr-Newman-de Sitter spacetime". Classical and Quantum Gravity. 40 (13). arXiv:2307.04073. doi:10.1088/1361-6382/accbfe. S2CID 258085066
Kerr–Newman–de–Sitter_metric
Solution of Einstein field equations
very close to those that would be felt from a point mass in Newtonian gravity. To study the tidal forces in more detail, the Bel decomposition of the
Gödel_metric
Hypothetical elementary particle that mediates gravity
In theories of quantum gravity, the graviton is the hypothetical elementary particle that mediates the force of gravitational interaction. It is a quantum
Graviton
Path of an object through spacetime
multiplying by a scalar. Therefore, all tangent vectors for a point p span a linear space, termed the tangent space at point p. For example, taking a 2-dimensional
World_line
Time scale
because it is outside all gravity wells, is not influenced by gravitational time dilation. The proper time of objects within a gravity well will pass more slowly
Coordinate_time
Formalism in general relativity
been adapted to study quantum gravity. Numerical relativity Quantum gravity Euclidean quantum gravity Piecewise linear manifold Euclidean simplex Path
Regge_calculus
lensing), Alejandro Corichi (fundamental contributions to quantum gravity and loop quantum gravity) Thibault Damour (effective one-body formalism), Georges Darmois
List of contributors to general relativity
List_of_contributors_to_general_relativity
Topics referred to by the same term
molecule Strain (general relativity), measure of spacetime stretching in linearized gravity Strain (injury), an injury to a muscle Strain (mechanics), a measure
Strain
Proposed theories of gravity
ideal theory of gravity. These attempts can be split into four broad categories based on their scope: Classical theories of gravity, which do not involve
Alternatives to general relativity
Alternatives_to_general_relativity
Theory of gravity by Albert Einstein
relativity also predicts novel effects of gravity, such as gravitational waves, gravitational lensing and an effect of gravity on time known as gravitational time
Introduction to general relativity
Introduction_to_general_relativity
American astrophysicist
laureates". nobel.se. 1993. Joseph Hooton Taylor Jr. on Nobelprize.org including the Nobel Lecture, 8 December 1993 Binary Pulsars and Relativistic Gravity
Joseph_Hooton_Taylor_Jr.
Physics principle
add two further axioms in order to build a consistent theory including gravity. These are the Equivalence Principle and locality. Locality means that
Principle_of_relativity
Exact solution to the Einstein field equations
year. In this paper, Oppenheimer and Snyder used Einstein's own theory of gravity to prove how black holes could develop for the first time in contemporary
Oppenheimer–Snyder_model
Physical theory with matter as quantum fields but gravity as a classical field
Semiclassical gravity is an approximation to the theory of quantum gravity in which one treats matter and energy fields as being quantum and the gravitational
Semiclassical_gravity
Statement of spherically symmetric spacetimes
and is called Israel's theorem. The converse is not true in Newtonian gravity. The theorem was first proven by Jørg Tofte Jebsen in 1921 and rediscovered
Birkhoff's theorem (relativity)
Birkhoff's_theorem_(relativity)
Exact gravitational-wave solution to Einstein's field equations
Minkowski spacetime Metric tensor Equations Formalisms Equations Linearized gravity Einstein field equations Friedmann Geodesics Mathisson–Papapetrou–Dixon
Einstein–Rosen_metric
Belgian scientist and Catholic priest (1894–1966)
Formulation ADM formalism BSSN formalism Einstein field equations Linearized gravity Post-Newtonian formalism Raychaudhuri equation Hamilton–Jacobi–Einstein
Georges_Lemaître
Proposed model of gravity
effects important in a seemingly linear regime, such as the Solar System. Because there is no four-dimensional, linearized effective theory that reproduces
DGP_model
Tensor quantum field of mixed symmetry
C.; Henneaux, M.; Hörtner, S. (2013). "Twisted self-duality for linearized gravity in D dimensions". Physical Review D. 88 (6) 064032. arXiv:1306.1092
Curtright_field
Concept in general relativity
by a certain axi-symmetric pp-wave. An example of pp-wave given when gravity is in presence of matter is the gravitational field surrounding a neutral
Pp-wave_spacetime
Equations describing classical electromagnetism
vacuum behaves like a perfect linear "material" without additional polarization and magnetization. More generally, for linear materials the constitutive
Maxwell's_equations
Theory of quantum gravity
Hořava–Lifshitz gravity (or Hořava gravity) is a theory of quantum gravity proposed by Petr Hořava in 2009. It solves the problem of different concepts
Hořava–Lifshitz_gravity
Method of approximation in general relativity
absolute values less than 1. For example, if one goes one step beyond linearized gravity to get the expansion to the second order in h: g μ ν ≈ η μ ν − η μ
Post-Newtonian_expansion
Generalization of straight line to a curved space time
falling particle always moves along a geodesic. In general relativity, gravity can be regarded as not a force but a consequence of a curved spacetime
Geodesics in general relativity
Geodesics_in_general_relativity
Idea in quantum gravity
Induced gravity (or emergent gravity) is an idea in quantum gravity that spacetime curvature and its dynamics emerge as a mean field approximation of
Induced_gravity
Einstein field equation solution
pointing in the z {\displaystyle z} -direction, held together by its own gravity. It was first obtained by William Bonnor in 1954, although it is named
Melvin_metric
Theory of gravity
(also called teleparallel gravity), was an attempt by Albert Einstein to base a unified theory of electromagnetism and gravity on the mathematical structure
Teleparallelism
Exact solution in general relativity
one recovers the Schwarzschild metric. The classical Newtonian theory of gravity may then be recovered in the limit as the ratio r s / r {\displaystyle
Reissner–Nordström_metric
Concept of absolute rotation
Einstein's gravitation theory Hoyle–Narlikar theory of gravity – Comformal theory of gravity Hughes–Drever experiment Luminiferous aether – Obsolete
Mach's_principle
Classical theory of gravitation
theory gravity Loop quantum gravity Cabral, Francisco; Lobo, Francisco S. N.; Rubiera-Garcia, Diego (December 2019). "Einstein–Cartan–Dirac gravity with
Einstein–Cartan_theory
German physicist (1873–1916)
Formulation ADM formalism BSSN formalism Einstein field equations Linearized gravity Post-Newtonian formalism Raychaudhuri equation Hamilton–Jacobi–Einstein
Karl_Schwarzschild
LINEARIZED GRAVITY
LINEARIZED GRAVITY
Boy/Male
Biblical
Hardness; his gravity; his offense.
Boy/Male
Muslim/Islamic
Dignity Gravity
Boy/Male
Biblical
Hardness; his gravity; his offense.
Girl/Female
Indian
Gravity
Boy/Male
Muslim
Gravity
Boy/Male
Indian
Gravity
Biblical
Hardness, His gravity, His offense
Boy/Male
Arabic, Hindu, Indian, Muslim, Sindhi
Dignity; Gravity; From Muslim
LINEARIZED GRAVITY
LINEARIZED GRAVITY
Girl/Female
Indian, Telugu
God Gift
Boy/Male
Muslim/Islamic
A Prophet's Name
Girl/Female
Greek
A river of the under world.
Girl/Female
Arabic, Muslim
Good; Caring
Girl/Female
Tamil
Epshita | à®à®ªà¯à®·à¯€à®¤à®¾
Goddess Lakshmi, Desired
Girl/Female
Muslim
(Wife of the prophet Musa)
Boy/Male
Indian, Punjabi, Sikh
Firm Friend
Boy/Male
Assamese, Indian
Happy
Female
French
Variant spelling of French Giselle, GISSELLE means "pledge, hostage, noble offspring."
Boy/Male
Hindu, Indian, Marathi
Decorated
LINEARIZED GRAVITY
LINEARIZED GRAVITY
LINEARIZED GRAVITY
LINEARIZED GRAVITY
LINEARIZED GRAVITY
a.
Being in unison; having the same degree of gravity or acuteness; sounded alike in pitch.
n.
A rare element of the chromium group found in certain minerals, as wolfram and scheelite, and isolated as a heavy steel-gray metal which is very hard and infusible. It has both acid and basic properties. When alloyed in small quantities with steel, it greatly increases its hardness. Symbol W (Wolframium). Atomic weight, 183.6. Specific gravity, 18.
a.
The state of having weight; beaviness; as, the gravity of lead.
n.
The liquid remaining after solids suspended in the liquid have been sedimented by gravity or by centrifugation. Contrasted with the solid sediment, or (in centrifugation) the pellet.
n.
A rare element of the light platinum group, found associated with platinum ores, and isolated as a hard, brittle steel-gray metal which is very infusible. Symbol Ru. Atomic weight 103.5. Specific gravity 12.26. See Platinum metals, under Platinum.
n.
A nonmetallic element occurring naturally in large quantities, either combined as in the sulphides (as pyrites) and sulphates (as gypsum), or native in volcanic regions, in vast beds mixed with gypsum and various earthy materials, from which it is melted out. Symbol S. Atomic weight 32. The specific gravity of ordinary octohedral sulphur is 2.05; of prismatic sulphur, 1.96.
n.
An instrument for determining the specific gravity of liquid bodies, porous bodies, and powders, as well as solids.
n.
Seriousness; gravity; discretion.
adv.
Aloft; on high; in a direction contrary to that of gravity; toward or in a higher place or position; above; -- the opposite of down.
n.
A curved line, such that a heavy body, descending along it by the action of gravity, will always arrive at the lowest point in the same time, wherever in the curve it may begin to fall; as, an inverted cycloid with its base horizontal is a tautochrone.
n.
To act or talk without seriousness, gravity, weight, or dignity; to act or talk with levity; to indulge in light or trivial amusements.
n.
A small hydrometer for determining the specific gravity of urine.
n.
The estimation of the specific gravity of urine by the urinometer.
n.
Gravity or austerity; extreme strictness; rigor; harshness; as, the severity of a reprimand or a reproof; severity of discipline or government; severity of penalties.
n.
Tungstate of iron and manganese, generally of a brownish or grayish black color, submetallic luster, and high specific gravity. It occurs in cleavable masses, and also crystallized. Called also wolfram.
n.
a small wave on the surface of water or other liquids for which the driving force is not gravity, but surface tension.
n.
The quality or state of being sage; wisdom; sagacity; prudence; gravity.
v. i.
To be supported by water or other fluid; not to sink; to float; as, any substance will swim, whose specific gravity is less than that of the fluid in which it is immersed.
n.
A wise man; a man of gravity and wisdom; especially, a man venerable for years, and of sound judgment and prudence; a grave philosopher.
a.
Importance, significance, dignity, etc; hence, seriousness; enormity; as, the gravity of an offense.