Search references for INITIAL VALUE-FORMULATION-GENERAL-RELATIVITY. Phrases containing INITIAL VALUE-FORMULATION-GENERAL-RELATIVITY
See searches and references containing INITIAL VALUE-FORMULATION-GENERAL-RELATIVITY!INITIAL VALUE-FORMULATION-GENERAL-RELATIVITY
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)
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
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
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
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)
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
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
invariance). In 1916, relativity would be extended to include the effects of gravity in the theory of general relativity. Relativity is a theory that accurately
Special_relativity
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
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
fields, transcended the limits of special relativity and resulted in the formulation of general relativity. Nearly simultaneously with Einstein, Minkowski
History_of_special_relativity
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
Quantum field theory of electromagnetism
experimental observation value. This is called the cosmological constant problem or vacuum catastrophe. The first formulation of a quantum theory describing
Quantum_electrodynamics
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
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
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
Speed of electromagnetic waves
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
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
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
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
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
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
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
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
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)
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
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
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
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
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
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
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
Italian mathematical physicist
propagation, Rational Extended Thermodynamics (RET), and hyperbolic formulations of general relativity. He graduated in Theoretical Physics cum laude from the University
Tommaso_Ruggeri
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
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
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
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
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
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
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
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
English mathematician, mathematical physicist (born 1931)
discovery that black hole formation is a robust prediction of the general theory of relativity". He proposed the Penrose triangle and corresponded with M. C
Roger_Penrose
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
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
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
Trace radiation from the early universe
Retrieved 2023-07-05. Hobson, M.P.; Efstathiou, G.; Lasenby, A.N. (2006). General Relativity: An Introduction for Physicists. Cambridge University Press. pp. 388
Cosmic_microwave_background
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
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
Hungarian-American mathematician (1893–1974)
to the Einstein field equations in vacuum with initial values and in algorithms of numerical relativity that simulate the spiral and merger of binary systems
Cornelius_Lanczos
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
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
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
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
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
Theory of the strong nuclear interactions
grows until a quark–antiquark pair is spontaneously produced, turning the initial hadron into a pair of hadrons instead of isolating a color charge. Although
Quantum_chromodynamics
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
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
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
Paths of particles in the Schwarzschild solution to Einstein's field equations
In general relativity, Schwarzschild geodesics describe the motion of test particles in the gravitational field of a central fixed mass M , {\textstyle
Schwarzschild_geodesics
Description of large objects' physics
approaching the speed of light, special relativity is needed. In cases where objects become extremely massive, general relativity becomes applicable. Classical
Classical_mechanics
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
Series of three books by E. T. Whittaker on the history of electromagnetic theory
never claimed credit for relativity and in fact referred to it as Einstein's relativity. He notes finally that Lorentz's formulation was valid only for small
A History of the Theories of Aether and Electricity
A_History_of_the_Theories_of_Aether_and_Electricity
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
Term in general relativity
In general relativity and quantum gravity, the Gibbons–Hawking–York boundary term is a term that needs to be added to the Einstein–Hilbert action when
Gibbons–Hawking–York boundary term
Gibbons–Hawking–York_boundary_term
Law of classical electromagnetism
infinitely-narrow wire. If the conductor has some thickness, the proper formulation of the Biot–Savart law (again in SI units) is: B ( r ) = μ 0 4 π ∭ V
Biot–Savart_law
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
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
Scientific biography of Albert Einstein by Abraham Pais
postulates of special relativity, writing that the book neglects evidence that Einstein had considered alternative formulations before adopting his second
Subtle_Is_the_Lord
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
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
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
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
Mathematical transformation in physics
physical laws (e.g. to a Hamiltonian or Lagrangian) rather than the initial conditions, values or magnitudes of the equations themselves and state that the laws
Time-translation_symmetry
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
travel, tourism, insurance
INITIAL VALUE-FORMULATION-GENERAL-RELATIVITY
INITIAL VALUE-FORMULATION-GENERAL-RELATIVITY
Boy/Male
Gujarati, Hindu, Indian
Value; Inside Trueness
Boy/Male
Hindu, Indian
Value
Girl/Female
American, British, English, Italian
Of High Value
Girl/Female
American, British, English
Of High Value
Boy/Male
Arabic, Muslim
Destiny; Dignity; Value
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
Value; Price
Girl/Female
Arabic, Indian, Muslim, Parsi, Sindhi
Value; Price; Worth
Boy/Male
Muslim
Value, Price
Girl/Female
Muslim/Islamic
Value Worth
Boy/Male
Indian
Value, Price
Boy/Male
Anglo, British, English, Finnish, Swedish
Valley; Usually with a Stream; From the Glen
Boy/Male
Australian, Finnish
Rule
Girl/Female
Indian
The initial reality
Female
Italian
Variant spelling of Italian Ginevra, probably GENEVRA means "race of women."
Girl/Female
Tamil
The initial reality
Female
Welsh
Medieval Welsh name, probably GENERYS means "white lady."Â
Girl/Female
Arabic, Muslim
Superiority; Attribute; Value
Female
English
Pet form of French Geneviève, probably GENEVA means "race of women."
Boy/Male
Arabic
Value
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
INITIAL VALUE-FORMULATION-GENERAL-RELATIVITY
INITIAL VALUE-FORMULATION-GENERAL-RELATIVITY
travel, tourism, insurance