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Diagram of different points in spacetime
In theoretical physics, a Penrose diagram (named after mathematical physicist Roger Penrose) is a two-dimensional diagram capturing the causal relations
Penrose_diagram
English mathematician, mathematical physicist (born 1931)
Sir Roger Penrose (born 8 August 1931) is an English mathematician, mathematical physicist, and philosopher of science. He is Emeritus Rouse Ball Professor
Roger_Penrose
Graphical notation for multilinear algebra calculations
In mathematics and physics, Penrose graphical notation or tensor diagram notation is a (usually handwritten) visual depiction of multilinear functions
Penrose_graphical_notation
Field-equations in general relativity
formulation Fundamental concepts Equivalence principle Riemannian geometry Penrose diagram Geodesics Mach's principle Formulation ADM formalism BSSN formalism
Einstein_field_equations
Geroch–Held–Penrose formalism Newman–Penrose formalism, a set of notation for general relativity Penrose diagram, a two-dimensional diagram capturing the
List of things named after Roger Penrose
List_of_things_named_after_Roger_Penrose
Set of spacetime events, light-connected to a given event
Structure". Stanford Encyclopedia of Philosophy. Retrieved 3 March 2020. Penrose, Roger (2005). The road to reality: a complete guide to the laws of the
Light_cone
British theoretical physicist (born 1929)
Oliver Penrose FRS FRSE (born 6 June 1929) is a British theoretical physicist and emeritus professor at Heriot-Watt University. His topics of interest
Oliver_Penrose
Graph of space and time in special relativity
at rest in the accelerated rocket. Physics portal Minkowski space Penrose diagram Rapidity "What are position vs. time graphs?". Khan Academy. Retrieved
Spacetime_diagram
Region in spacetime from which nothing can escape
example, this occurs with a uniformly accelerated particle. A spacetime diagram of this situation is shown in the figure to the right. As the particle
Event_horizon
Mathematical study of illumination of rooms with mirrored walls
The original problem was first solved in 1958 by Roger Penrose using ellipses to form the Penrose unilluminable room. He showed that there exists a room
Illumination_problem
Hypothetical topological feature of spacetime
travel. Wormholes can also be depicted in a Penrose diagram of a Schwarzschild black hole. In the Penrose diagram, an object traveling faster than light will
Wormhole
German-born theoretical physicist (1879–1955)
(2010). Einstein, Podolsky & Rosen (1935). Peres (2002). Mermin (1993). Penrose (2007). Bell (1966). Fine (2017). Einstein (1950). Goenner, Hubert F. M
Albert_Einstein
British geneticist
Shirley Victoria Penrose Hodgson (born 22 February 1945) is a British geneticist. Hodgson studied at Somerville College, Oxford. She worked as a GP, then
Shirley_Hodgson
Effect in special relativity
also sometimes referred to as the Penrose–Terrell effect, the Terrell–Penrose effect or the Lampa–Terrell–Penrose effect. In 1924, a paper by Anton Lampa
Terrell_rotation
Compact astronomical body
although they would later reverse their positions. However, in 1965, Roger Penrose proved that general relativity predicts that singularities appear in all
Black_hole
Physics principle that simultaneity depends on choice of reference frame
source located midway between the two observers along the x-axis. The diagram illustrates a coordinate system where ct constitutes the vertical axis
Relativity_of_simultaneity
Measured time difference as explained by relativity theory
mirror A. In the frame in which the clock is at rest (see left part of the diagram), the light pulse traces out a path of length 2L and the time period between
Time_dilation
Boundary region of asymptotically flat spacetimes in general relativity
conformal infinity are most often visualized on a Penrose diagram, where they make up the boundary of the diagram. There are two distinct regions of null infinity
Null_infinity
Path of an object through spacetime
often suppressed. An event is then represented by a point in a Minkowski diagram, which is a plane usually plotted with the time coordinate, say t {\displaystyle
World_line
Hypothetical FTL transportation by warping space
formulation Fundamental concepts Equivalence principle Riemannian geometry Penrose diagram Geodesics Mach's principle Formulation ADM formalism BSSN formalism
Alcubierre_drive
Condition in which spacetime itself breaks down
string 2-dimensional singularity: domain wall Fuzzball (string theory) Penrose–Hawking singularity theorems White hole BKL singularity Initial singularity
Gravitational_singularity
Physics concept expressed as E = mc²
formulation Fundamental concepts Equivalence principle Riemannian geometry Penrose diagram Geodesics Mach's principle Formulation ADM formalism BSSN formalism
Mass–energy_equivalence
Two interrelated physics theories by Albert Einstein
formulation Fundamental concepts Equivalence principle Riemannian geometry Penrose diagram Geodesics Mach's principle Formulation ADM formalism BSSN formalism
Theory_of_relativity
Description of gravity using discrete values
called spin networks. Spin networks were initially introduced by Roger Penrose in abstract form, and later shown by Carlo Rovelli and Lee Smolin to derive
Quantum_gravity
Mathematical model combining space and time
dimension of time into a single four-dimensional continuum. Spacetime diagrams are useful in visualizing and understanding relativistic effects, such
Spacetime
Abstract coordinate system
formulation Fundamental concepts Equivalence principle Riemannian geometry Penrose diagram Geodesics Mach's principle Formulation ADM formalism BSSN formalism
Frame_of_reference
Equations describing classical electromagnetism
formulation Fundamental concepts Equivalence principle Riemannian geometry Penrose diagram Geodesics Mach's principle Formulation ADM formalism BSSN formalism
Maxwell's_equations
Exact solution in general relativity
158, 312–324. ISBN 978-0-226-87032-8. Spacetime diagrams including Finkelstein diagram and Penrose diagram, by Andrew J. S. Hamilton "Particle Moving Around
Reissner–Nordström_metric
Speed of electromagnetic waves
Standards 1977, 2nd ed.). Courier Dover. p. 280. ISBN 978-0-486-40913-9. Penrose, R (2004). The Road to Reality: A Complete Guide to the Laws of the Universe
Speed_of_light
Diagram used to represent quantum field theory calculations
local gauge transformations. A spin network, as described in Penrose (1971), is a kind of diagram in which each line segment represents the world line of a
Spin_network
Branch of differential geometry
formulation Fundamental concepts Equivalence principle Riemannian geometry Penrose diagram Geodesics Mach's principle Formulation ADM formalism BSSN formalism
Riemannian_geometry
Contraction of length in the direction of propagation in Minkowski space
1924, it was not widely read. Only in 1959 when James Terrell and Roger Penrose wrote about the visual effect now called Terrell rotation were the difficulties
Length_contraction
Trace radiation from the early universe
formulation Fundamental concepts Equivalence principle Riemannian geometry Penrose diagram Geodesics Mach's principle Formulation ADM formalism BSSN formalism
Cosmic_microwave_background
Theory of gravity by Albert Einstein
that is more informal than a textbook presentation, see chapter 14.4 of Penrose 2004. The geometrical meaning of Einstein's equations is explored in chapters
Introduction to general relativity
Introduction_to_general_relativity
Thought experiment in special relativity
(space–time) diagrams at right show the paths of light signals travelling between Earth and ship (1st diagram) and between ship and Earth (2nd diagram). These
Twin_paradox
Solution of Einstein field equations
110d3529G. doi:10.1103/PhysRevD.110.043529. Andrew Hamilton: Black hole Penrose diagrams (JILA Colorado) Figure 2 in Stuchlik; Kološ; Kovář; Slany (2020). "Influence
Kerr–Newman–de–Sitter_metric
German physicist (1873–1916)
formulation Fundamental concepts Equivalence principle Riemannian geometry Penrose diagram Geodesics Mach's principle Formulation ADM formalism BSSN formalism
Karl_Schwarzschild
Albert Einstein's hypothetical situations to argue scientific points
formulation Fundamental concepts Equivalence principle Riemannian geometry Penrose diagram Geodesics Mach's principle Formulation ADM formalism BSSN formalism
Einstein's thought experiments
Einstein's_thought_experiments
Physics principle
formulation Fundamental concepts Equivalence principle Riemannian geometry Penrose diagram Geodesics Mach's principle Formulation ADM formalism BSSN formalism
Principle_of_relativity
British astrophysicist (1882–1944)
formulation Fundamental concepts Equivalence principle Riemannian geometry Penrose diagram Geodesics Mach's principle Formulation ADM formalism BSSN formalism
Arthur_Eddington
Scientific phenomenon
Consider the spacetime diagram in Fig. 10. Worldlines for a tuning fork (the source) and a receiver are both illustrated on this diagram. The tuning fork and
Relativistic_Doppler_effect
Belgian scientist and Catholic priest (1894–1966)
formulation Fundamental concepts Equivalence principle Riemannian geometry Penrose diagram Geodesics Mach's principle Formulation ADM formalism BSSN formalism
Georges_Lemaître
Theory of gravitation as curved spacetime
spacetime's causal structure. This structure can be displayed using Penrose–Carter diagrams in which infinitely large regions of space and infinite time intervals
General_relativity
Russian and Soviet physicist and mathematician (1888–1925)
formulation Fundamental concepts Equivalence principle Riemannian geometry Penrose diagram Geodesics Mach's principle Formulation ADM formalism BSSN formalism
Alexander_Friedmann
Exact solution for the Einstein field equations
Monographs on Physics. Vol. 69. p. 375. Andrew Hamilton: Black hole Penrose diagrams (JILA Colorado) Bueno, Pablo; Cano, Pablo A.; Goelen, Frederik; Hertog
Kerr_metric
1989 book by Roger Penrose
is a 1989 book by the mathematical physicist Roger Penrose that posits a quantum mind theory. Penrose argues that human consciousness is non-algorithmic
The_Emperor's_New_Mind
Solution of Einstein field equations
remain at constant values of x, y, and z. Their density in this coordinate diagram increases with x, but their density in their own frames of reference is
Gödel_metric
Smallest stable circular orbit of a particle
formulation Fundamental concepts Equivalence principle Riemannian geometry Penrose diagram Geodesics Mach's principle Formulation ADM formalism BSSN formalism
Innermost stable circular orbit
Innermost_stable_circular_orbit
Concept in physics and mathematics
formulation Fundamental concepts Equivalence principle Riemannian geometry Penrose diagram Geodesics Mach's principle Formulation ADM formalism BSSN formalism
Galilean_transformation
American physicist, writer, and Nobel Laureate (born 1940)
formulation Fundamental concepts Equivalence principle Riemannian geometry Penrose diagram Geodesics Mach's principle Formulation ADM formalism BSSN formalism
Kip_Thorne
Swiss astronomer (1898–1974)
formulation Fundamental concepts Equivalence principle Riemannian geometry Penrose diagram Geodesics Mach's principle Formulation ADM formalism BSSN formalism
Fritz_Zwicky
Puzzle of disappearance of information in a black hole
to Roger Penrose, loss of unitarity in quantum systems is not a problem: quantum measurements are by themselves already non-unitary. Penrose claims that
Black hole information paradox
Black_hole_information_paradox
Concept of absolute rotation
formulation Fundamental concepts Equivalence principle Riemannian geometry Penrose diagram Geodesics Mach's principle Formulation ADM formalism BSSN formalism
Mach's_principle
Hypothesis that inertial and gravitational masses are equivalent
formulation Fundamental concepts Equivalence principle Riemannian geometry Penrose diagram Geodesics Mach's principle Formulation ADM formalism BSSN formalism
Equivalence_principle
Indian-American physicist (1910–1995)
Symposium 2010 which was attended by leading astrophysicists such as Roger Penrose, Kip Thorne, Freeman Dyson, Jayant V. Narlikar, Rashid Sunyaev, G. Srinivasan
Subrahmanyan_Chandrasekhar
Light bending by mass between source and observer
formulation Fundamental concepts Equivalence principle Riemannian geometry Penrose diagram Geodesics Mach's principle Formulation ADM formalism BSSN formalism
Gravitational_lens
Equation explaining structure of a spherical body of isotropic material
formulation Fundamental concepts Equivalence principle Riemannian geometry Penrose diagram Geodesics Mach's principle Formulation ADM formalism BSSN formalism
Tolman–Oppenheimer–Volkoff equation
Tolman–Oppenheimer–Volkoff_equation
Measure of relativistic velocity
formulation Fundamental concepts Equivalence principle Riemannian geometry Penrose diagram Geodesics Mach's principle Formulation ADM formalism BSSN formalism
Rapidity
Low-velocity approximation of special relativity
formulation Fundamental concepts Equivalence principle Riemannian geometry Penrose diagram Geodesics Mach's principle Formulation ADM formalism BSSN formalism
Galilean_invariance
Mathematical transformation in physics
formulation Fundamental concepts Equivalence principle Riemannian geometry Penrose diagram Geodesics Mach's principle Formulation ADM formalism BSSN formalism
Time-translation_symmetry
Meanings of mass in special relativity
formulation Fundamental concepts Equivalence principle Riemannian geometry Penrose diagram Geodesics Mach's principle Formulation ADM formalism BSSN formalism
Mass_in_special_relativity
Effect of general relativity
rotating black holes combined with the energy extraction mechanism by Penrose have been used to explain the observed properties of relativistic jets
Frame-dragging
Result in general relativity
bits of matter. The equation is important as a fundamental lemma for the Penrose–Hawking singularity theorems and for the study of exact solutions in general
Raychaudhuri_equation
Debate about credit for general relativity
formulation Fundamental concepts Equivalence principle Riemannian geometry Penrose diagram Geodesics Mach's principle Formulation ADM formalism BSSN formalism
General relativity priority dispute
General_relativity_priority_dispute
Solution of Einstein field equations
for example the rotational energy of a black hole is extracted via the Penrose processes, the remaining mass–energy will always stay greater than or equal
Kerr–Newman_metric
Formula in general relativity
formulation Fundamental concepts Equivalence principle Riemannian geometry Penrose diagram Geodesics Mach's principle Formulation ADM formalism BSSN formalism
Quadrupole_formula
American theoretical physicist (1911–2008)
Feynman incorporated the notion of the reversibility of time in his Feynman diagrams. Soon after the Japanese bombing of Pearl Harbor brought the U.S. into
John_Archibald_Wheeler
Equations in physical cosmology
formulation Fundamental concepts Equivalence principle Riemannian geometry Penrose diagram Geodesics Mach's principle Formulation ADM formalism BSSN formalism
Friedmann_equations
Metric based on the exact solution of Einstein's field equations of general relativity
formulation Fundamental concepts Equivalence principle Riemannian geometry Penrose diagram Geodesics Mach's principle Formulation ADM formalism BSSN formalism
Friedmann–Lemaître–Robertson–Walker metric
Friedmann–Lemaître–Robertson–Walker_metric
Philosophical argument based on the theory of relativity
Putnam (1967). It is sometimes called the Rietdijk–Putnam–Penrose argument. Roger Penrose advanced a form of this argument that has been called the Andromeda
Rietdijk–Putnam_argument
Solution to the Einstein field equations
1–32. doi:10.1007/BF01448427. S2CID 179177367. Earman, J. (1999). "The Penrose–Hawking singularity theorems: History and Implications". In Goenner, H
Schwarzschild_metric
Aspect of relativity in physics
Commonwealth Fund Book Program. New York London: Norton. ISBN 978-0-393-31276-8. Penrose, Roger (1965-01-18). "Gravitational Collapse and Space-Time Singularities"
Gravitational_wave
American astrophysicist
formulation Fundamental concepts Equivalence principle Riemannian geometry Penrose diagram Geodesics Mach's principle Formulation ADM formalism BSSN formalism
Joseph_Hooton_Taylor_Jr.
Thought experiment in special relativity
garage. The situation can be further illustrated by the Minkowski diagram below. The diagram is in the rest frame of the garage. The vertical light-blue band
Ladder_paradox
Physical phenomenon in electromagnetic field theory
formulation Fundamental concepts Equivalence principle Riemannian geometry Penrose diagram Geodesics Mach's principle Formulation ADM formalism BSSN formalism
Relativistic_electromagnetism
French mathematician, physicist and engineer (1854–1912)
formulation Fundamental concepts Equivalence principle Riemannian geometry Penrose diagram Geodesics Mach's principle Formulation ADM formalism BSSN formalism
Henri_Poincaré
American physicist (1939–2022)
formulation Fundamental concepts Equivalence principle Riemannian geometry Penrose diagram Geodesics Mach's principle Formulation ADM formalism BSSN formalism
James_M._Bardeen
Dutch physicist (1853–1928)
formulation Fundamental concepts Equivalence principle Riemannian geometry Penrose diagram Geodesics Mach's principle Formulation ADM formalism BSSN formalism
Hendrik_Lorentz
Theory of interwoven space and time by Albert Einstein
would be observed as length contracted. In 1959, James Terrell and Roger Penrose independently pointed out that differential time lag effects in signals
Special_relativity
German mathematician (1885–1955)
Hermann Weyl, 1885–1985, Centenary lectures delivered by C. N. Yang, R. Penrose, A. Borel, at the ETH Zürich Springer-Verlag, Berlin, Heidelberg, New York
Hermann_Weyl
American mathematician (1911–1999)
formulation Fundamental concepts Equivalence principle Riemannian geometry Penrose diagram Geodesics Mach's principle Formulation ADM formalism BSSN formalism
Abraham_H._Taub
Mathematical description of spacetime used in relativity
representation of coordinates and velocities. He introduced the Minkowski diagram and used it to define concepts and demonstrate properties of Lorentz transformations
Minkowski_spacetime
Hamiltonian formulation of general relativity
formulation Fundamental concepts Equivalence principle Riemannian geometry Penrose diagram Geodesics Mach's principle Formulation ADM formalism BSSN formalism
ADM_formalism
Exact solution to Einstein's field equations
formulation Fundamental concepts Equivalence principle Riemannian geometry Penrose diagram Geodesics Mach's principle Formulation ADM formalism BSSN formalism
Weyl–Lewis–Papapetrou coordinates
Weyl–Lewis–Papapetrou_coordinates
American physicist
formulation Fundamental concepts Equivalence principle Riemannian geometry Penrose diagram Geodesics Mach's principle Formulation ADM formalism BSSN formalism
Russell_Alan_Hulse
Claim that human mathematicians are not describable as formal proof systems
The Penrose–Lucas argument is a logical argument partially based on Kurt Gödel's first incompleteness theorem. In 1931, Gödel proved that every effectively
Penrose–Lucas_argument
Generalization of straight line to a curved space time
formulation Fundamental concepts Equivalence principle Riemannian geometry Penrose diagram Geodesics Mach's principle Formulation ADM formalism BSSN formalism
Geodesics in general relativity
Geodesics_in_general_relativity
This second kind of symmetry approach has often been used with the Newman–Penrose formalism, which uses spinorial quantities for more efficient bookkeeping
Exact solutions in general relativity
Exact_solutions_in_general_relativity
American physicist (1929–2021)
Wright-Patterson Air Force Base. In 1962, together with Roger Penrose, he introduced the powerful Newman–Penrose formalism for working with spinorial quantities in
Ezra_T._Newman
Solution of Einstein field equations
formulation Fundamental concepts Equivalence principle Riemannian geometry Penrose diagram Geodesics Mach's principle Formulation ADM formalism BSSN formalism
Kasner_metric
Astronomical observation
FBOTs compared with other astronomical transients Star formation rate diagram for FBOTs. Multi-wavelength composite (X-ray, ultraviolet, optical, and
Fast_blue_optical_transient
Roger Penrose (Hawking–Penrose singularity theorems, Penrose diagrams, techniques from algebraic geometry and differential topology, Penrose limits,
List of contributors to general relativity
List_of_contributors_to_general_relativity
Dutch mathematician, physicist, and astronomer (1872–1934)
formulation Fundamental concepts Equivalence principle Riemannian geometry Penrose diagram Geodesics Mach's principle Formulation ADM formalism BSSN formalism
Willem_de_Sitter
Issue in science history
formulation Fundamental concepts Equivalence principle Riemannian geometry Penrose diagram Geodesics Mach's principle Formulation ADM formalism BSSN formalism
Relativity_priority_dispute
Maximally symmetric Lorentzian manifold with a positive cosmological constant
extension of de Sitter space, and can therefore be used to find its Penrose diagram. Let x 0 = α sin ( 1 α χ ) sinh ( 1 α t ) cosh ξ , x 1 = α cos
De_Sitter_space
Formalism of general relativity
formulation Fundamental concepts Equivalence principle Riemannian geometry Penrose diagram Geodesics Mach's principle Formulation ADM formalism BSSN formalism
BSSN_formalism
Family of linear transformations
mechanical Minkowski diagram Interactive graph on Desmos (graphing) showing Lorentz transformations with a virtual Minkowski diagram Interactive graph on
Lorentz_transformation
New Zealand mathematician
formulation Fundamental concepts Equivalence principle Riemannian geometry Penrose diagram Geodesics Mach's principle Formulation ADM formalism BSSN formalism
Roy_Kerr
Dutch mathematician (1910–1944)
formulation Fundamental concepts Equivalence principle Riemannian geometry Penrose diagram Geodesics Mach's principle Formulation ADM formalism BSSN formalism
Willem_Jacob_van_Stockum
Relativistic correction
formulation Fundamental concepts Equivalence principle Riemannian geometry Penrose diagram Geodesics Mach's principle Formulation ADM formalism BSSN formalism
Thomas_precession
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PENROSE DIAGRAM
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PENROSE DIAGRAM
PENROSE DIAGRAM
PENROSE DIAGRAM
PENROSE DIAGRAM
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