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Reformulation of general relativity
The initial value formulation of general relativity is a reformulation of Albert Einstein's theory of general relativity that describes a universe evolving
Initial value formulation (general relativity)
Initial_value_formulation_(general_relativity)
Tests of general relativity serve to establish observational evidence for the theory of general relativity. The first three tests, proposed by Albert
Tests_of_general_relativity
Theory of gravitation as curved spacetime
quantization procedures of quantum theory. Using the initial-value-formulation of general relativity (cf. evolution equations above), the result is the
General_relativity
form in all reference frames. The term 'general covariance' was used in the early formulation of general relativity, but the principle is now often referred
Mathematics of general relativity
Mathematics_of_general_relativity
have made major contributions to the (mainstream) development of general relativity, as acknowledged by standard texts on the subject. Some related lists
List of contributors to general relativity
List_of_contributors_to_general_relativity
1984 graduate textbook by Robert M. Wald
further study. The essential mathematical methods for the formulation of general relativity are presented in Chapters 2 and 3 while more advanced techniques
General_Relativity_(book)
The two-body problem in general relativity (or relativistic two-body problem) is the determination of the motion and gravitational field of two bodies
Two-body problem in general relativity
Two-body_problem_in_general_relativity
Sub-area of scientific computing for solving General Relativity equations
problem may be divided into the initial value problem and the evolution, each requiring different methods. Numerical relativity is applied to many areas, such
Numerical_relativity
Facet of general relativity
mass was introduced (Arnowitt et al., 1960) from an initial-value formulation of general relativity. It was later reformulated in terms of the group of
Mass_in_general_relativity
Theory of interwoven space and time by Albert Einstein
In physics, the special theory of relativity, or simply special relativity, is a scientific theory of the relationship between space and time. In Albert
Special_relativity
Hypothetical FTL transportation by warping space
the ADM form, which is often used in discussing the initial-value formulation of general relativity. This might explain the widespread misconception that
Alcubierre_drive
In general relativity, an exact solution is a (typically closed form) solution of the Einstein field equations whose derivation does not invoke simplifying
Exact solutions in general relativity
Exact_solutions_in_general_relativity
Hamiltonian formulation of general relativity
is a Hamiltonian formulation of general relativity that plays an important role in canonical quantum gravity and numerical relativity. It was first published
ADM_formalism
fields, transcended the limits of special relativity and resulted in the formulation of general relativity. Nearly simultaneously with Einstein, Minkowski
History_of_special_relativity
Speed of electromagnetic waves in vacuum
calls "the explicit-constant formulation", where each "unit is defined indirectly by specifying explicitly an exact value for a well-recognized fundamental
Speed_of_light
Topics referred to by the same term
Major-General commanding the Household Division Maximal globally hyperbolic development, relevant in initial value formulation (general relativity) This
MGHD
Attraction of masses and energy
weaker as objects get farther away. Gravity is described by the general theory of relativity, proposed by Albert Einstein in 1915, which describes gravity
Gravity
Condition in which spacetime itself breaks down
no time can it be objectively said to have formed. General relativity also predicts that the initial state of the universe, at the beginning of the Big
Gravitational_singularity
German-born theoretical physicist (1879–1955)
his long journey from his special theory of relativity to a new idea of gravitation with the formulation of his equivalence principle, which asserts that
Albert_Einstein
Concept of absolute rotation
inspired by Mach's principle, Einstein's formulation of the principle is not a fundamental assumption of general relativity, although the principle of equivalence
Mach's_principle
Theory of gravity
between general relativity and quantum mechanics. Shape dynamics is dynamically equivalent to the canonical formulation of general relativity, known as
Shape_dynamics
Physics concept expressed as E = mc²
by an object. This observation is one of the pillars of the general theory of relativity. The prediction that all forms of energy interact gravitationally
Mass–energy_equivalence
Scientific subjects
abandoned. Quantum mechanics was combined with the theory of relativity in the formulation of Paul Dirac. Other developments include quantum statistics
Branches_of_physics
Equations in physical cosmology
homogeneous and isotropic models of the universe within the context of general relativity. They were first derived by Alexander Friedmann in 1922 from Einstein's
Friedmann_equations
Laws in physics about force and motion
(1968). Special Relativity. W. W. Norton and Company. p. 224. ISBN 0-393-09804-4. Havas, Peter (1 October 1964). "Four-Dimensional Formulations of Newtonian
Newton's_laws_of_motion
Description of physical properties at the atomic and subatomic scale
to how accurately the value of a physical quantity can be predicted prior to its measurement, given a complete set of initial conditions (the uncertainty
Quantum_mechanics
holes have primarily been subjects of research since the advent of general relativity in the early 1900s, although similar concepts were discussed before
History_of_black_hole_physics
General relativity model near spacetime singularities
The Wikibook General relativity has a page on the topic of: BKL singularity A Belinski–Khalatnikov–Lifshitz (BKL) singularity is a model of the dynamic
BKL_singularity
Hypothesis that inertial and gravitational masses are equivalent
This form was a critical input for the development of the theory of general relativity. The strong form requires Einstein's form to work for stellar objects
Equivalence_principle
French mathematician, physicist and engineer (1854–1912)
all of Maxwell's equations, an important step in the formulation of the theory of special relativity, for which he is also credited with laying down the
Henri_Poincaré
Key results in general relativity on gravitational singularities
(after Roger Penrose and Stephen Hawking) are a set of results in general relativity that attempt to answer the question of when gravitation produces singularities
Penrose–Hawking singularity theorems
Penrose–Hawking_singularity_theorems
Albert Einstein's hypothetical situations to argue scientific points
of light. For special relativity, he employed moving trains and flashes of lightning to explain his theory. For general relativity, he considered a person
Einstein's thought experiments
Einstein's_thought_experiments
Belgian scientist and Catholic priest (1894–1966)
law with the solution to the Einstein field equations in the general theory of relativity for a homogenous and isotropic universe. That work led Lemaître
Georges_Lemaître
Conjecture in physics
about the structure of gravitational singularities in the context of general relativity. Singularities that arise in the solutions of Einstein's equations
Cosmic_censorship_hypothesis
Formulation of general relativity
canonical formulation of general relativity (or canonical gravity). It is a Hamiltonian formulation of Einstein's general theory of relativity. The basic
Canonical_quantum_gravity
Graph of space and time in special relativity
temporal and the horizontal axis to spatial coordinate values. Especially when used in special relativity (SR), the temporal axes of a spacetime diagram are
Spacetime_diagram
Physical theory of the cosmos
energy in its simplest formulation is modeled by a cosmological constant term in Einstein field equations of general relativity, but its composition and
Big_Bang
Mathematical structures that allow quantum mechanics to be explained
as eigenvalues; more precisely as spectral values of linear operators in Hilbert space. These formulations of quantum mechanics continue to be used today
Mathematical formulation of quantum mechanics
Mathematical_formulation_of_quantum_mechanics
Compact astronomical body
the value that the full theory of general relativity would predict. By 1915, Einstein refined these ideas into his general theory of relativity, which
Black_hole
Equations describing classical electromagnetism
the equations as a boundary value problem, analytical mechanics, or for use in quantum mechanics. The covariant formulation (on spacetime rather than space
Maxwell's_equations
Formulation of quantum mechanics
The path-integral formulation of quantum mechanics generalizes the action principle of classical mechanics. It replaces the classical notion of a single
Path-integral_formulation
Law of physics and chemistry
violated by general relativity on the cosmological scale. In quantum mechanics, Noether's theorem is known to apply to the expected value, making any
Conservation_of_energy
Relativistic quantum mechanical wave equation
relativistic formulation of quantum mechanics. One notable result by Heisenberg and Jordan was the introduction of two terms for spin and relativity into the
Dirac_equation
Thought experiment in special relativity
In physics, the twin paradox is a thought experiment in special relativity involving twins, one of whom takes a space voyage at relativistic speeds and
Twin_paradox
The following is a timeline of gravitational physics and general relativity. 3rd century B.C. – Aristarchus of Samos proposes the heliocentric model. 1543
Timeline of gravitational physics and relativity
Timeline_of_gravitational_physics_and_relativity
Light bending by mass between source and observer
amount of gravitational lensing is described by Albert Einstein's general theory of relativity. If light is treated as corpuscles travelling at the speed of
Gravitational_lens
Lowest possible energy of a quantum system or field
causes problems however, as in Einstein's theory of general relativity the absolute energy value of space is not an arbitrary constant and gives rise
Zero-point_energy
Aspect of relativity in physics
were first predicted by Albert Einstein as a consequence of his general theory of relativity, appearing as "ripples in spacetime curvature". Hundreds of these
Gravitational_wave
Theory of quantum gravity merging quantum mechanics and general relativity
theory of gravity based directly on Albert Einstein's geometric formulation, general relativity. As a theory, LQG postulates that the structure of space and
Loop_quantum_gravity
Mathematical formulation of special and general relativity
is Lagrangian mechanics applied in the context of special relativity and general relativity. The relativistic Lagrangian can be derived in relativistic
Relativistic Lagrangian mechanics
Relativistic_Lagrangian_mechanics
Obsolete postulated medium for the propagation of light
along with the elegant formulation given to it by Hermann Minkowski, contributed much to the rapid acceptance of special relativity among working scientists
Luminiferous_aether
Mathematical model combining space and time
manifolds of higher dimensions. It enabled the formulation of Einstein's general theory of relativity, made profound impact on group theory and representation
Spacetime
Spacetime manifold
well-posed initial value formulation for Einstein’s equations. This is considered a natural and essential condition in General Relativity: given arbitrary
Globally_hyperbolic_spacetime
Maximally symmetric Lorentzian manifold with a negative cosmological constant
plane is a surface of constant negative curvature. Einstein's general theory of relativity places space and time on equal footing, so that one considers
Anti-de_Sitter_space
Mathematical transformation in physics
the conservation of energy. In many nonlinear field theories like general relativity or Yang–Mills theories, the basic field equations are highly nonlinear
Time-translation_symmetry
Description of a quantum-mechanical system
equal footing. Paul Dirac incorporated special relativity and quantum mechanics into a single formulation that simplifies to the Schrödinger equation in
Schrödinger_equation
Interpretation of quantum mechanics
is compatible with relativity. Bell has shown that the nonlocality does not allow superluminal communication. Bohm's formulation of de Broglie–Bohm theory
De_Broglie–Bohm_theory
Fundamental principle of classical physics
reference frames. In general relativity, the concept of inertial motion got a broader meaning. Taking into account general relativity, inertial motion is
Inertia
French mathematical physicist (1923–2025)
the mathematics of general relativity. Her proof that the Einstein field equations can be expressed as a well-posed initial-value problem was listed by
Yvonne_Choquet-Bruhat
Physics problem related to laws of motion and gravity
The gravitational three-body problem has also been studied using general relativity. Physically, a relativistic treatment becomes necessary in systems
Three-body_problem
Mathematics of general relativity
relativistic classical field theories of gravitation, particularly general relativity, an energy condition is a generalization of the statement "the energy
Energy_condition
German–British physicist (1882–1970)
university's Philosophy Faculty Prize. In 1905, he began researching special relativity with Minkowski, and subsequently wrote his habilitation thesis on the
Max_Born
Change in wavelength of light
relation also evolved during the 1920s. The solution to the equations of general relativity described by de Sitter contained no matter, but in 1922 Alexander
Redshift
electromagnetic wave equation Initial mass function Initial singularity Initial stability Initial value formulation (general relativity) Injection kicker magnets
Index_of_physics_articles_(I)
Formulation of classical mechanics
In physics, Lagrangian mechanics is an alternate formulation of classical mechanics founded on the d'Alembert principle of virtual work. It was introduced
Lagrangian_mechanics
American gravitational physicist (b. 1947)
the University of Alabama on October 27, 2015, titled "The Formulation of General Relativity," celebrating the centennial of Einstein's theory. Wald is
Robert_Wald
Theory of subatomic structure
fundamental properties of Einstein's general theory of relativity is that it is background independent, meaning that the formulation of the theory does not in any
String_theory
or more parameter(s) family of similar structures, such that for an initial value of the parameter(s) one has the same structure (Lie algebra) one started
Deformation_quantization
Approximation or recovery of classical mechanics in certain theories
mechanics. Similarly for the deformation of Newtonian gravity into general relativity, with deformation parameter Schwarzschild-radius/characteristic-dimension
Classical_limit
Parameter describing the strength of a force
applies to some formulations of quantum field theory, in particular, canonical quantization in the interaction picture. In other formulations, the same event
Coupling_constant
Physical quantity of dimension energy × time
principle are used in Feynman's formulation of quantum mechanics and in general relativity. For systems with small values of action close to the Planck
Action_(physics)
Tensor field in Riemannian geometry
affine connection. It is a central mathematical tool in the theory of general relativity, the modern theory of gravity. The curvature of spacetime is in principle
Riemann_curvature_tensor
Method in physics used to deal with infinities
physics contains only renormalizable operators, but the interactions of general relativity become nonrenormalizable if one attempts to construct a field theory
Renormalization
Quantum field theory of electromagnetism
to experimental observation value. This is called cosmological constant problem or vacuum catastrophe. The first formulation of a quantum theory describing
Quantum_electrodynamics
m=E/c^{2}} . And finally in June and July 1905 he declared the relativity principle a general law of nature, including gravitation. He corrected some mistakes
History of electromagnetic theory
History_of_electromagnetic_theory
Continuous progression from past to future
inextricable from space within the concept of spacetime described by general relativity. Time can therefore be dilated by velocity and matter to pass faster
Time
Theoretical framework in physics
(QFT) is a theoretical framework that combines field theory, special relativity and quantum mechanics. QFT is used in particle physics to construct physical
Quantum_field_theory
Change in the position of an object
geometry to describe a curved universe with gravity; the study is called general relativity. Quantum mechanics is a set of principles describing physical reality
Motion
Hypothetical object of spacetime
In general relativity, a white hole is a hypothetical region of spacetime and singularity that cannot be entered from the outside, although energy, matter
White_hole
Equations that describe the behavior of a physical system
solution can be obtained by setting the initial values, which fixes the values of the constants. Stated formally, in general, an equation of motion M is a function
Equations_of_motion
Puzzle of disappearance of information in a black hole
the predictions of quantum mechanics and general relativity are combined. The theory of general relativity predicts the existence of black holes that
Black hole information paradox
Black_hole_information_paradox
Result in general relativity
In general relativity, the Raychaudhuri equation, or Landau–Raychaudhuri equation, is a fundamental result describing the motion of nearby bits of matter
Raychaudhuri_equation
Field of classical mechanics concerned with the motion of spacecraft
mission planners to predict the results of propulsive maneuvers. General relativity is a more exact theory than Newton's laws for calculating orbits,
Orbital_mechanics
Problem in physics and celestial mechanics
particular cases. In general, the problem is chaotic and can only be solved numerically. The n-body problem in general relativity is considerably more
N-body_problem
Straight path on a curved surface or a Riemannian manifold
discusses the more general case of a pseudo-Riemannian manifold and geodesic (general relativity) discusses the special case of general relativity in greater
Geodesic
Unified field theory
dimension of space beyond the conventional four-dimensional spacetime of general relativity. According to this proposal, there are three dimensions of space and
Kaluza–Klein_theory
Principle suggesting that time travel paradoxes are inherently impossible
travel, which is theoretically permitted in certain solutions of general relativity that contain what are known as closed timelike curves. The principle
Novikov self-consistency principle
Novikov_self-consistency_principle
Pictorial representation of the behavior of subatomic particles
integral formulation of quantum field theory represents the transition amplitude as a weighted sum of all possible histories of the system from the initial to
Feynman_diagram
Symmetry breaking through the vacuum state
group. The displacement and the orientation are the order parameters. General relativity has a Lorentz symmetry, but in FRW cosmological models, the mean 4-velocity
Spontaneous_symmetry_breaking
Physical law for entropy and heat
only within the constraints as defined explicitly within General Relativity (or Special Relativity, depending on the local spacetime conditions). Good examples
Second_law_of_thermodynamics
Relativistic correction
kinematic effect in the flat spacetime of special relativity. In the curved spacetime of general relativity, Thomas precession combines with a geometric effect
Thomas_precession
Philosophical argument against general covariance
in the original coordinate system. So the initial value problem has no unique solution in general relativity. This is also true in electrodynamics—since
Hole_argument
Chinese-American mathematician (born 1949)
the boundary-value problem for the Monge-Ampère equation, the positive mass theorem in the mathematical analysis of general relativity (achieved with
Shing-Tung_Yau
requirements of special relativity, and the rules of quantum mechanics. The Dirac equation took into account the spin-1/2 value of the electron and its
History of quantum field theory
History_of_quantum_field_theory
Formulation of general relativity
Lagrangian formulation of the theory by considering the self-dual formulation of the Tetradic Palatini action principle of general relativity. These proofs
Self-dual_Palatini_action
Theory of gravity
metric tensor as a byproduct. New teleparallel gravity theory (or new general relativity) is a theory of gravitation on Weitzenböck spacetime, and attributes
Teleparallelism
Rate of change of velocity
mechanical accelerometer. In general relativity, gravity and inertial acceleration may be locally indistinguishable (see General relativity). In classical mechanics
Acceleration
Partial differential equation describing the evolution of temperature in a region
}{4kt}}\right).} The general solution of the heat equation on Rn is then obtained by a convolution, so that to solve the initial value problem with u(x,
Heat_equation
British theoretical physicist and mathematician (1923–2020)
in quantum field theory, astrophysics, random matrices, mathematical formulation of quantum mechanics, condensed matter physics, nuclear physics, and
Freeman_Dyson
Swiss astronomer (1898–1974)
attempt be made to put this effect on a sound theoretical footing with general relativity. He also considered and rejected explanations involving interactions
Fritz_Zwicky
INITIAL VALUE-FORMULATION-GENERAL-RELATIVITY
INITIAL VALUE-FORMULATION-GENERAL-RELATIVITY
Girl/Female
Muslim/Islamic
Value Worth
Female
English
Pet form of French Geneviève, probably GENEVA means "race of women."
Girl/Female
Tamil
The initial reality
Female
Welsh
Medieval Welsh name, probably GENERYS means "white lady."Â
Surname or Lastname
English
English : topographic name for someone who lived in a valley, Middle English vale (Old French val, from Latin vallis). The surname is now also common in Ireland, where it has been Gaelicized as de Bhál.Galician and Aragonese : topographic name from val ‘valley’, or habitational name from any of the places named with this word.
Girl/Female
Arabic, Indian, Muslim, Parsi, Sindhi
Value; Price; Worth
Girl/Female
American, British, English, Italian
Of High Value
Girl/Female
Arabic, Muslim
Superiority; Attribute; Value
Boy/Male
Arabic, Muslim
Destiny; Dignity; Value
Boy/Male
Anglo, British, English, Finnish, Swedish
Valley; Usually with a Stream; From the Glen
Boy/Male
Indian
Value, Price
Girl/Female
Arabic
Value; Price
Girl/Female
American, British, English
Of High Value
Boy/Male
Muslim
Value, Price
Female
Italian
Variant spelling of Italian Ginevra, probably GENEVRA means "race of women."
Boy/Male
Australian, Finnish
Rule
Boy/Male
Gujarati, Hindu, Indian
Value; Inside Trueness
Boy/Male
Arabic
Value
Girl/Female
Indian
The initial reality
Boy/Male
Hindu, Indian
Value
INITIAL VALUE-FORMULATION-GENERAL-RELATIVITY
INITIAL VALUE-FORMULATION-GENERAL-RELATIVITY
Boy/Male
Bengali, Indian
To do with the Sun
Surname or Lastname
English (East Anglia)
English (East Anglia) : nickname for a lusty man, from Middle English craske ‘fat’, ‘lusty’ (see Crass).
Girl/Female
Biblical
Descendant of Heber.
Boy/Male
Hindu, Indian, Marathi, Punjabi, Sikh
Protector of Warmth
Surname or Lastname
English
English : nickname from Middle English paramour ‘lover’ (Old French par amour ‘with love’).
Girl/Female
Tamil
Aditri | அதிதà¯à®°à¯€
Highest honor, Goddess Lakshmi
Boy/Male
Hindu, Indian, Marathi
King of Poetry
Female
Egyptian
, Egyptian unisex name.
Boy/Male
Hindu, Indian, Marathi
Wise; Intelligent; Good Hearted
Girl/Female
Spanish
Sweet.
INITIAL VALUE-FORMULATION-GENERAL-RELATIVITY
INITIAL VALUE-FORMULATION-GENERAL-RELATIVITY
INITIAL VALUE-FORMULATION-GENERAL-RELATIVITY
INITIAL VALUE-FORMULATION-GENERAL-RELATIVITY
INITIAL VALUE-FORMULATION-GENERAL-RELATIVITY
adv.
In an initial or incipient manner or degree; at the beginning.
n.
The act, process, or result of formulating or reducing to a formula.
a.
Common to many, or the greatest number; widely spread; prevalent; extensive, though not universal; as, a general opinion; a general custom.
n.
Current value; general estimation; the rate at which anything is generally valued.
n.
Value.
v. t.
To put an initial to; to mark with an initial of initials.
a.
Not restrained or limited to a precise import; not specific; vague; indefinite; lax in signification; as, a loose and general expression.
a.
Highly regarded; esteemed; prized; as, a valued contributor; a valued friend.
a.
Usual; common, on most occasions; as, his general habit or method.
n.
Precise signification; import; as, the value of a word; the value of a legal instrument
n.
One who values; an appraiser.
v. t.
To be worth; to be equal to in value.
v. i.
Unsettled; unfixed; undetermined; indefinite; ambiguous; as, a vague idea; a vague proposition.
n. pl.
Generalities; general terms.
imp. & p. p.
of Value
a.
Placed at the beginning; standing at the head, as of a list or series; as, the initial letters of a name.
a.
Of or pertaining to the beginning; marking the commencement; incipient; commencing; as, the initial symptoms of a disease.
v. t.
To raise to estimation; to cause to have value, either real or apparent; to enhance in value.
n.
Mineral deposits and rock masses designated with reference to their origin; as, the siliceous formation about geysers; alluvial formations; marine formations.
imp. & p. p.
of Initial