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Sub-area of scientific computing for solving General Relativity equations
Numerical relativity is one of the branches of general relativity that uses numerical methods and algorithms to solve and analyze problems. To this end
Numerical_relativity
Theory of gravitation as curved spacetime
General relativity, also known as the general theory of relativity, and as Einstein's theory of gravity, is the geometric theory of gravitation published
General_relativity
(Aichelburg–Sexl ultraboost, generalized symmetries), Miguel Alcubierre (numerical relativity, Alcubierre drives), Richard L. Arnowitt (ADM formalism), Abhay Ashtekar
List of contributors to general relativity
List_of_contributors_to_general_relativity
Two interrelated physics theories by Albert Einstein
The theory of relativity comprises two physics theories by Albert Einstein: special relativity and general relativity, proposed and published in 1905
Theory_of_relativity
Theory of gravity by Albert Einstein
General relativity is a theory of gravitation developed by Albert Einstein between 1907 and 1915. The theory of general relativity says that the observed
Introduction to general relativity
Introduction_to_general_relativity
Physics principle
of relativity is the idea that the laws of physics should remain consistent over time and from one place to another. Several principles of relativity have
Principle_of_relativity
Mexican theoretical physicist (born 1964)
University, receiving his PhD degree in 1994 through study of numerical general relativity. After 1996 he worked at the Max Planck Institute for Gravitational
Miguel_Alcubierre
Topics referred to by the same term
relativity in Wiktionary, the free dictionary. Relativity may refer to: Galilean relativity, Galileo's conception of relativity Numerical relativity,
Relativity
American physicist (1932–2023)
included general relativity and cosmology. His work has also provided early foundations for studies of quantum gravity and numerical relativity. Misner received
Charles_W._Misner
Low-velocity approximation of special relativity
Galilean invariance or Galilean relativity states that the laws of motion are the same in all inertial frames of reference. Galileo Galilei first described
Galilean_invariance
Field-equations in general relativity
relativity General relativity resources History of general relativity Hamilton–Jacobi–Einstein equation Mathematics of general relativity Numerical relativity
Einstein_field_equations
American physicist
physicist, working mostly in the field of general relativity and cosmology, including numerical relativity, kinetic theory, black hole physics, and gravitational
Richard_Matzner
Issue in science history
Albert Einstein presented the theories of special relativity and general relativity in publications that either contained no formal references to previous
Relativity_priority_dispute
and the precise numerical quantities obtained only depend on the coordinate system used. This suggested a way of formulating relativity using 'invariant
Mathematics of general relativity
Mathematics_of_general_relativity
Hamiltonian formulation of general relativity
Hamiltonian formulation of general relativity that plays an important role in canonical quantum gravity and numerical relativity. It was first published in 1959
ADM_formalism
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
1957 international physics conference
field equations. This line of research led to the development of numerical relativity. The relative state formulation, better known today as the many-worlds
Chapel_Hill_Conference
Numerical simulations of physical problems via computers
fires. Numerical relativity is a (relatively) new field interested in finding numerical solutions to the field equations of both special relativity and general
Computational_physics
Concept that simultaneity depends on choice of reference frame
In physics, the relativity of simultaneity is the concept that distant simultaneity – whether two spatially separated events occur at the same time – is
Relativity_of_simultaneity
Debate about credit for general relativity
Einstein's discovery of the gravitational field equations of general relativity and David Hilbert's almost simultaneous derivation of the theory using
General relativity priority dispute
General_relativity_priority_dispute
Textbooks on the theory of relativity have been published by several notable physicists and mathematicians: The primary sources section of the latter article
List of textbooks on relativity
List_of_textbooks_on_relativity
German-born theoretical physicist (1879–1955)
German-born theoretical physicist best known for developing the known theory of relativity. Einstein also made important contributions to quantum theory. His mass–energy
Albert_Einstein
Concept in physics and mathematics
Galilean group. The Galilean group is the group of motions of Galilean relativity acting on the four dimensions of space and time, forming the Galilean
Galilean_transformation
Description of gravity using discrete values
based on Albert Einstein's general theory of relativity, which incorporates his theory of special relativity and deeply modifies the understanding of concepts
Quantum_gravity
Abstract coordinate system
geometric points whose position is identified both mathematically (with numerical coordinate values) and physically (signaled by conventional markers).
Frame_of_reference
System consisting of two black holes in close orbit around each other
solving the full equations of general relativity. This can be done in numerical relativity simulations. Numerical relativity models space-time and simulates
Binary_black_hole
Aspect of relativity in physics
during the merger phase, which can be modeled with the techniques of numerical relativity. The first direct detection of gravitational waves, GW150914, came
Gravitational_wave
Canadian theoretical physicist
(born 1961) is a Canadian theoretical physicist specializing in numerical relativity. Choptuik graduated from University of British Columbia with a master's
Matthew_Choptuik
Condition in which spacetime itself breaks down
exist in the theory of general relativity, the best theory of gravity available. A singularity in general relativity can be defined by the scalar invariant
Gravitational_singularity
Swiss astrophysicist
at the Rochester Institute of Technology. Her research focuses on numerical relativity, gravitational-wave astrophysics, black-hole mergers, neutron-star
Manuela Campanelli (scientist)
Manuela_Campanelli_(scientist)
German physicist (1873–1916)
provided the first exact solution to the Einstein field equations of general relativity, for the limited case of a single spherical non-rotating mass, which he
Karl_Schwarzschild
Set of spacetime events, light-connected to a given event
In special and general relativity, a light cone (or null cone) is the path that a flash of light, emanating from a single event — localized to a single
Light_cone
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
Compact astronomical body
ISBN 978-94-017-0934-7. Berger, B. K. (2002). "Numerical Approaches to Spacetime Singularities". Living Reviews in Relativity. 5 (1) 1: 2002–1. arXiv:gr-qc/0201056
Black_hole
Aspect of general relativity
{\displaystyle g^{\mu \nu }\Gamma ^{\sigma }{}_{\mu \nu }=0\,.} In numerical relativity, the preferred gauge is the so-called "3+1 decomposition", based
Solutions of the Einstein field equations
Solutions_of_the_Einstein_field_equations
Concept of absolute rotation
was a guiding factor in Einstein's development of the general theory of relativity. Einstein realized that the overall distribution of matter would determine
Mach's_principle
American physicist, writer, and Nobel Laureate (born 1940)
waves". With John A. Wheeler and Charles Misner, he coauthored the general relativity textbook Gravitation in 1973. He has also written popular science, notably
Kip_Thorne
American theoretical physicist (b. 1943)
Gaurav (2026). "Binary black hole coalescence phenomenology from numerical relativity". Physical Review D. 113 (4). doi:10.1103/kk1h-rh4h. Gleiser, Reinaldo
Richard_H._Price
Generalization of straight line to a curved space time
In general relativity, a geodesic generalizes the notion of a "straight line" to curved spacetime. Importantly, the world line of a particle free from
Geodesics in general relativity
Geodesics_in_general_relativity
Astrophysicist
of numerical relativity: the subject that deals with equations involving general relativity using supercomputers. He is a coauthor of the Numerical Recipes
Saul_Teukolsky
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
Collapsed core of a massive star
gravitational waves from binary neutron star mergers are observed. Numerical relativity simulations of binary neutron star mergers have found relationships
Neutron_star
Equations describing classical electromagnetism
separately) makes the compatibility of Maxwell's equations with special relativity manifest. Maxwell's equations in curved spacetime, commonly used in high-energy
Maxwell's_equations
Methods and computing tools developed and used in astrophysics research
dynamics. A recently developed field with interesting results is numerical relativity. Many astrophysicists use computers in their work, and a growing
Computational_astrophysics
Branch of differential geometry
dimensions. It enabled the formulation of Einstein's general theory of relativity, made profound impact on group theory and representation theory, as well
Riemannian_geometry
Indian-American physicist (1910–1995)
equilibrium and the stability of ellipsoidal figures of equilibrium, general relativity, mathematical theory of black holes and theory of colliding gravitational
Subrahmanyan_Chandrasekhar
Hypothetical FTL transportation by warping space
the Alcubierre metric is consistent with Einstein's equations, general relativity does not incorporate quantum mechanics. Some physicists have presented
Alcubierre_drive
Belgian scientist and Catholic priest (1894–1966)
the solution to the Einstein field equations in the general theory of relativity for a homogenous and isotropic universe. That work led Lemaître to propose
Georges_Lemaître
Relation of space and time in relativity theory
Hyperbolically orthogonal lines appear in special relativity as temporal and spatial directions that show the relativity of simultaneity. Keeping time and space
Hyperbolic_orthogonality
Concept in physics
Einstein derived the theory of special relativity in 1905, from principles now called the postulates of special relativity. Einstein's formulation only requires
Postulates of special relativity
Postulates_of_special_relativity
Diagram of different points in spacetime
(suitable for the curved spacetimes of e.g. general relativity) of the Minkowski diagram of special relativity where the vertical dimension represents time,
Penrose_diagram
English mathematician, mathematical physicist (born 1931)
black hole formation is a robust prediction of the general theory of relativity". He proposed the Penrose triangle and corresponded with M. C. Escher
Roger_Penrose
Measured time difference as explained by relativity theory
clocks, either because of a relative velocity, a consequence of special relativity, or a difference in gravitational potential between their locations due
Time_dilation
Speed of electromagnetic waves in vacuum
of relativity, and so showed that the parameter c had relevance outside of the context of light and electromagnetism. In the theory of relativity, c interrelates
Speed_of_light
Formalism of general relativity
gravity Hamiltonian mechanics Numerical relativity Baumgarte, Thomas W. and Shapiro, Stuart L. (1998). "On the Numerical Integration of Einstein's Field
BSSN_formalism
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
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
Meanings of mass in special relativity
The word "mass" has two meanings in special relativity: invariant mass (also called rest mass) is an invariant quantity which is the same for all observers
Mass_in_special_relativity
Region in spacetime from which nothing can escape
temporarily but will return. In 1958, David Finkelstein used general relativity to introduce a stricter definition of a local black hole event horizon
Event_horizon
Italian professor of relativistic astrophysics and numerical relativity
(born 1967) is an Italian professor of relativistic astrophysics and numerical relativity at the Goethe University Frankfurt. His main field of study is the
Luciano_Rezzolla
Path of an object through spacetime
is now used most often in the context of relativity theories (i.e., special relativity and general relativity). A world line of an object (generally approximated
World_line
American theoretical physicist (1923–2004)
mechanics. With his student Larry Smarr, he originated the field of numerical relativity. Bryce DeWitt, Dynamical theory of groups and fields, Gordon and
Bryce_DeWitt
Physical phenomenon in electromagnetic field theory
remain consistent when viewed from various moving observers led to special relativity, a geometric theory of 4-space where intermediation is by light and radiation
Relativistic_electromagnetism
Mathematical model combining space and time
transformation and special theory of relativity. In 1908, Hermann Minkowski presented a geometric interpretation of special relativity that fused time and the three
Spacetime
Scientific phenomenon
when taking into account effects described by the special theory of relativity. The relativistic Doppler effect is different from the non-relativistic
Relativistic_Doppler_effect
Physics concept expressed as E = mc²
term electromagnetic mass. Mass–energy equivalence arose from special relativity as a paradox described by the French polymath Henri Poincaré (1854–1912)
Mass–energy_equivalence
Hypothetical hybrid star type
initial data of numerical relativity". In Evans, Charles R.; Finn, Lee S.; Hobill, David W. (eds.). Frontiers in Numerical Relativity. Cambridge University
Thorne–Żytkow_object
Formalism in general relativity
a vacuum solution. This can be applied to difficult problems in numerical relativity such as simulating the collision of two black holes. The elegant
Regge_calculus
French mathematician, physicist and engineer (1854–1912)
equations, an important step in the formulation of the theory of special relativity, for which he is also credited with laying down the foundations, further
Henri_Poincaré
Reformulation of general relativity
brief account of the Cauchy problem in General Relativity". Lehner, Luis (2001). "Numerical Relativity: A review". Class. Quantum Grav. 18 (17): R25–R86
Initial value formulation (general relativity)
Initial_value_formulation_(general_relativity)
Proposed theory of gravitation
Jordan–Brans–Dicke theory) is a competitor to Einstein's general theory of relativity. It is an example of a scalar–tensor theory, a gravitational theory in
Brans–Dicke_theory
British astrophysicist (1882–1944)
of articles that announced and explained Einstein's theory of general relativity to the English-speaking world. World War I had severed many lines of scientific
Arthur_Eddington
Mathematical theory of the geometry of space and time
in anything other than weak field cases. Numerical relativity is a branch of general relativity using numerical methods to solve and analyze problems, often
Curved_spacetime
Trace radiation from the early universe
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
Dutch physicist (1853–1928)
effect. He derived the Lorentz transformation of the special theory of relativity, as well as the Lorentz force, which describes the force acting on a charged
Hendrik_Lorentz
test of the predictions of general relativity in the regime of strong gravity; a regime in which general relativity is completely untested. In particular
Extreme_mass_ratio_inspiral
German physicist
1966) is a German physicist specializing in the numerical simulation of compact objects in general relativity. Baumgarte completed his BSc in 1992 at LMU
Thomas_W._Baumgarte
Mathematical description of spacetime used in relativity
theories of special relativity and general relativity and is the most common mathematical structure by which special relativity is formalized. While
Minkowski_spacetime
New Zealand mathematician
geometry, an exact solution to the Einstein field equation of general relativity. His solution models the gravitational field outside an uncharged rotating
Roy_Kerr
Formula in general relativity
In general relativity, the quadrupole formula describes the gravitational waves that are emitted from a system of masses in terms of the (mass) quadrupole
Quadrupole_formula
Thought experiment in special relativity
ladder paradox (or barn-pole paradox) is a thought experiment in special relativity. It involves a ladder, parallel to the ground, travelling horizontally
Ladder_paradox
American anthropologist
He is recognized for his interdisciplinary work on linguistic relativity, numerical cognition, and the interplay between language, culture, and cognition
Caleb_Everett
Family of linear transformations
is now called special relativity, by deriving the Lorentz transformation under the assumptions of the principle of relativity and the constancy of the
Lorentz_transformation
Hypothesis that inertial and gravitational masses are equivalent
identical times. The extended form by Albert Einstein requires special relativity to also hold in free fall and requires the weak equivalence to be valid
Equivalence_principle
Russian and Soviet physicist and mathematician (1888–1925)
analysis.[citation needed] This dynamic cosmological model of general relativity would come to form the standard for both the Big Bang and Steady State
Alexander_Friedmann
Physics Institute in Potsdam and Hanover
Earth and in space solving the two-body problem in general relativity analytical and numerical solutions of Einstein's equations development and implementation
Max Planck Institute for Gravitational Physics
Max_Planck_Institute_for_Gravitational_Physics
Measure of relativistic velocity
In special relativity, the classical concept of velocity is converted to rapidity to accommodate the limit determined by the speed of light. Velocities
Rapidity
German mathematician (1885–1955)
mathematics. He was one of the first to conceive of combining general relativity with the laws of electromagnetism. Freeman Dyson wrote that Weyl alone
Hermann_Weyl
Light bending by mass between source and observer
gravitational lensing is described by Albert Einstein's general theory of relativity. If light is treated as corpuscles travelling at the speed of light, Newtonian
Gravitational_lens
Mathematical transformation in physics
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
American theoretical physicist (1911–2008)
physicist. He was largely responsible for reviving interest in general relativity in the United States after World War II. Wheeler also worked with Niels
John_Archibald_Wheeler
British astrophysicist and computational cosmologist
astrophysicist and computational cosmologist. Her research uses numerical relativity to simulate the formation and development of the large-scale structures
Katy_Clough
black hole. Numerical solution for binary black hole (1960s–2005): The numerical solution of the two body problem in general relativity was achieved
List of unsolved problems in physics
List_of_unsolved_problems_in_physics
2012 special relativity demonstration game
relativity in an easy-to-understand fashion. The game is meant to be used as an interactive learning tool for those interested in physics. Numerical relativity
A_Slower_Speed_of_Light
Effect in special relativity
passing object would appear to undergo, according to the special theory of relativity, if it were travelling at a significant fraction of the speed of light
Terrell_rotation
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
American physicist (1932–2025)
explain it to them, as it seemed to contradict his understanding of general relativity. In 1967, to illustrate the principle of gravitational wave detection
Rainer_Weiss
Time delay caused by space-time distortion near massive objects
delay effect, is one of the four classic Solar System tests of general relativity. Radar signals passing near a massive object take slightly longer to travel
Shapiro_time_delay
Solution to the Einstein field equations
In Einstein's theory of general relativity, the Schwarzschild metric (also known as the Schwarzschild solution) is an exact solution to the Einstein field
Schwarzschild_metric
American physicist (1939–2022)
1939 – June 20, 2022) was an American physicist. He worked on general relativity, particularly in formulating the laws of black hole mechanics. He also
James_M._Bardeen
NUMERICAL RELATIVITY
NUMERICAL RELATIVITY
NUMERICAL RELATIVITY
Boy/Male
Tamil
Insight, Experience
Boy/Male
African, Arabic, Christian, German, Gujarati, Hindu, Indian, Kannada, Muslim, Swahili, Telugu
Angel; Messenger; Messenger Origin Islamic; Another Name for Prophet Muhammad
Boy/Male
Arabic
War Champion; Hero; Conqueror
Boy/Male
Muslim
Satisfied, Contented, Pleased, Chosen
Boy/Male
Assamese, Bengali, Christian, Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Sindhi, Telugu
Joyful
Boy/Male
Indian, Punjabi, Sikh
Full of Glories
Boy/Male
Arabic
Arabic Form of Paul
Girl/Female
Indian
Highborn, Respected, Noble
Girl/Female
Hindu
Remembered
Boy/Male
American, British, English
Lives at the Birch Tree Meadow
NUMERICAL RELATIVITY
NUMERICAL RELATIVITY
NUMERICAL RELATIVITY
NUMERICAL RELATIVITY
NUMERICAL RELATIVITY
adv.
In a numerical manner; in numbers; with respect to number, or sameness in number; as, a thing is numerically the same, or numerically different.
n.
Of or pertaining to number; consisting of number or numerals.
n.
A distributive adjective or pronoun; also, a distributive numeral.
adv.
According to number; in number; numerically.
n.
The same in number; hence, identically the same; identical; as, the same numerical body.
n.
A word expressing a number.
superl.
Numerically small; as, a low number.
n.
Any number, proper or improper fraction, or incommensurable ratio. The term also includes any imaginary expression like m + nÃ-1, where m and n are real numerics.
n.
A numerical coefficient in any particular case of the binomial theorem.
n.
The art or process of calculating the atomic proportions, combining weights, and other numerical relations of chemical elements and their compounds.
n.
A figure or character used to express a number; as, the Arabic numerals, 1, 2, 3, etc.; the Roman numerals, I, V, X, L, etc.
n.
Alt. of Numerical
n.
Numerical loss caused by death, wounds, discharge, or desertion.
n.
Expressing number; representing number; as, numeral letters or characters, as X or 10 for ten.
a.
Having an assignable arithmetical or numerical value or meaning; not imaginary.
a.
Resembling a worm; as, the lumbrical muscles of the hands of the hands and feet.
n.
Belonging to number; denoting number; consisting in numbers; expressed by numbers, and not letters; as, numerical characters; a numerical equation; a numerical statement.
n.
A lumbrical muscle.