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Wave in general relativity
A gravitational soliton is a soliton solution of the Einstein field equation. It can be separated into two kinds, a soliton of the vacuum Einstein field
Gravitational_soliton
Exact gravitational-wave solution to Einstein's field equations
Nathan Rosen describing cylindrical gravitational waves. Einstein first predicted the existence of gravitational waves in 1916. He returned to the problem
Einstein–Rosen_metric
Topologically stable solution of a partial differential equation
In mathematics and physics, solitons, topological solitons and topological defects are three closely related ideas, all of which signify structures in
Topological_defect
Mathematical transform to generate soliton solutions of Einstein's field equations
transform are called gravitational solitons (gravisolitons). Despite the term 'soliton' being used to describe gravitational solitons, their behavior is
Belinski–Zakharov_transform
Hypothetical compact star
Preon star Strange star Quark star Non-topological soliton § Soliton-stars Gravitational soliton Brecher, K. (1993-05-01). "Gray Holes". American Astronomical
Q_star
Russian theoretical physicist
transform in 1978 showing that black holes are a special example of gravitational solitons. Another his notable result (obtained in 1985—1987 together with
Vladimir_Belinski
Special class of solitons
In quantum field theory, a non-topological soliton (NTS) is a soliton field configuration possessing, contrary to a topological one, a conserved Noether
Non-topological_soliton
Solution to the Einstein field equations
applied. This implies that the Schwarzschild black hole is a form of gravitational soliton. The spatial curvature of the Schwarzschild solution for r > rs
Schwarzschild_metric
transform; the first gravitational solitons, 1979 – Dennis Walsh, Robert Carswell, and Ray Weymann discover the gravitationally lensed quasar Q0957+561
Timeline of gravitational physics and relativity
Timeline_of_gravitational_physics_and_relativity
Property of certain dynamical systems
general solutions are termed gravitational solitons, of which the Schwarzschild metric, the Kerr metric and some gravitational wave solutions are examples
Integrable_system
Exact solution for the Einstein field equations
applied. This implies that the Kerr black hole has the form of a gravitational soliton. If the complete rotational energy E r o t = c 2 ( M − M i r r
Kerr_metric
Verdaguer, E. (2001). Gravitational solitons. Cambridge University Press. ISBN 0-521-80586-4. A monograph on the use of soliton methods to produce stationary
Exact solutions in general relativity
Exact_solutions_in_general_relativity
Hypothetical elementary particle that mediates gravity
elementary particle that mediates the force of gravitational interaction. It is a quantum of gravitational wave energy. There is no complete quantum field
Graviton
Type of non-topological soliton
non-topological soliton. A soliton is a localized field configuration that is stable—it cannot spread out and dissipate. In the case of a non-topological soliton, the
Q-ball
Black holes are characterized only by mass, charge, and spin
holes may be considered to be bound states of hairless black holes and solitons.[by whom?] In 2004, the exact analytical solution of a (3+1)-dimensional
No-hair_theorem
Field theory in physics that aims to unify the fundamental forces and particles
relativity likewise describes gravitation as the result of the metric tensor field, which describes the shape of spacetime: Gravitational interaction: a long-range
Unified_field_theory
Theoretical attempts to unify the forces of nature
phenomenon. Einstein tried to form a generalized theory of gravitation that would unify the gravitational and electromagnetic forces (and perhaps others), guided
Classical unified field theories
Classical_unified_field_theories
PDE to describe nonlinear wave motion
perturbations of the KdV soliton using the inverse scattering transform. The transverse stability and dynamics of a single planar soliton with respect to perturbations
Kadomtsev–Petviashvili equation
Kadomtsev–Petviashvili_equation
Theoretical (d–1)-dimensional singularity
emit gravitational waves that would be detectable by LIGO and similar experiments. Topological defect Cosmic string Membrane (M-theory) Gravitational singularity
Domain_wall_(string_theory)
Most basic type of physical force
gravity, electromagnetism, weak interaction, and strong interaction. The gravitational and electromagnetic interactions produce long-range forces whose effects
Fundamental_interaction
French mathematician (born 1970)
Joachim; Raphaël, Pierre; Martel, Yvan (2009). "Two-soliton solutions to the three-dimensional gravitational Hartree equation". Communications on Pure and Applied
Yvan_Martel
Unified field theory
G} is the gravitational constant, and μ 0 {\displaystyle \mu _{0}} is the permeability of free space. In the Kaluza theory, the gravitational constant
Kaluza–Klein_theory
American physicist (1929-2016)
Finkelstein and Charles W. Misner found the gravitational kink, a topological defect in the gravitational metric, whose quantum theory could exhibit spin 1/2
David_Finkelstein
Particle whose invariant mass is zero
graviton is a hypothetical tensor boson proposed to be the carrier of gravitational force in some quantum theories of gravity, but no such theory has been
Massless_particle
Hypothetical FTL transportation by warping space
allow for backward time travel and thus make the Alcubierre drive invalid. Solitons offer a mathematical "loophole" in general relativity to theoretically
Alcubierre_drive
Process of calculating the causal factors that produced a set of observations
such system from geophysics is that of the Earth's gravitational field. The Earth's gravitational field is determined by the density distribution of the
Inverse_problem
British theoretical physicist
Project Gibbons, Gary William (1973). Some aspects of gravitational radiation and gravitational collapse. lib.cam.ac.uk (PhD thesis). University of Cambridge
Gary_Gibbons
Fringe theory of physics
goal is to describe how the combined structure and dynamics of all gravitational and Standard Model particle fields are part of the E8 Lie algebra. The
An Exceptionally Simple Theory of Everything
An_Exceptionally_Simple_Theory_of_Everything
Elementary particle with extremely low mass
(excluding massless particles). The weak force has a very short range, the gravitational interaction is extremely weak due to the very small mass of the neutrino
Neutrino
Chinese-American physicist (1926–2024)
physics, relativistic heavy ion (RHIC) physics, nontopological solitons, and soliton stars. He was a university professor emeritus at Columbia University
Tsung-Dao_Lee
List of particles in matter including fermions and bosons
indistinguishable from gravitation, because a massless spin-2 field would couple to the stress–energy tensor in the same way that gravitational interactions do
List_of_particles
Exotic particle made of an antiproton and positron
antimatter has negative gravitational mass, which is considered highly unlikely, though not yet empirically disproven (see gravitational interaction of antimatter)
Antihydrogen
Dynamic disturbance in a medium or field
viscosity. Gravitational waves also travel through space. The first observation of gravitational waves was announced on 11 February 2016. Gravitational waves
Wave
Partial differential equation with nonlinear terms
integrable models, when solutions are sometimes a sort of superposition of solitons; this happens e.g. for the Korteweg–de Vries equation. It is often possible
Nonlinear partial differential equation
Nonlinear_partial_differential_equation
Dynamical system governed by Hamilton's equations
American Mathematical Society, ISBN 978-0-8218-4413-7 Dickey, L. A. (2003). Soliton equations and Hamiltonian systems. Advanced series in mathematical physics
Hamiltonian_system
German physicist
noncommutative solitons, waves, vortices, baby Skyrmions, monopoles and instantons. In particular, the construction of multi-solitons in Ward's modified
Olaf_Lechtenfeld
Smoot, George F.; Tye, S.-H. Henry (2020-04-08). "Ghostly Galaxies as Solitons of Bose-Einstein Dark Matter". Physical Review D. 101 (8) 083012. arXiv:1902
Direct detection of dark matter
Direct_detection_of_dark_matter
Type of heat transfer within fluids
"Analytic self-similar solutions of the Oberbeck–Boussinesq equations". Chaos, Solitons and Fractals. 78: 249–255. arXiv:1502.05039. doi:10.1016/j.chaos.2015.08
Rayleigh–Bénard_convection
Incorrect but seminal physical theory
motivation and results, Tony Skyrme introduced solitons to build a model for nucleons. These solitons were topologically stable vortices of a 'pion fluid'
Vortex_theory_of_the_atom
Supergravity in eleven dimensions
meaning that both the extreme M2-branes and the M5-branes can be seen as solitons interpolating between two maximally supersymmetric Minkowski vacua at infinity
Eleven-dimensional supergravity
Eleven-dimensional_supergravity
Physics term for multiple concepts
of the universe Dark matter – Hypothetical invisible cosmic material Gravitational interaction of antimatter – Theory of gravity on antimatter Mirror matter –
Exotic_matter
Non-linear equation in fluid dynamics
dynamics for stratified media. It describes the motion of internal waves as solitons. The equation was first proposed by Marie-Louise Dubreil-Jacotin in 1932
Dubreil-Jacotin–Long_equation
Hypothetical horizonless compact object in general relativity
In physics, a topological star (also called a topological soliton in this context) is a smooth, horizonless solution of the five-dimensional Einstein–Maxwell
Topological_star
Approximation valid for weakly non-linear and fairly long waves
Scott Russell of the wave of translation (also known as solitary wave or soliton). The 1872 paper by Boussinesq introduces the equations now known as the
Boussinesq approximation (water waves)
Boussinesq_approximation_(water_waves)
German astronomer and mathematician (1571–1630)
Tirapegui, Enrique (2022). "Kepler in search of the 'Anaclastic'". Chaos, Solitons & Fractals. 164 112695. Bibcode:2022CSF...16412695C. doi:10.1016/j.chaos
Johannes_Kepler
Hypothetical particle in gravity theories
particle which emerges as an excitation of the metric tensor (i.e. gravitational field) in spacetime dimensions higher than four, as described in Kaluza–Klein
Graviphoton
Theory proposed by Roger Penrose
Press. ISBN 978-0-19-853498-3. OCLC 34545252. Dunajski, Maciej (2010). Solitons, instantons, and twistors. Oxford: Oxford University Press. ISBN 978-0-19-857062-2
Twistor_theory
universe Geons, electromagnetic or gravitational waves which are held together in a confined region by the gravitational attraction of their own field of
List of hypothetical particles
List_of_hypothetical_particles
Class of subatomic particle
Parastatistics – Notion in statistical mechanics Despite being the carrier of the gravitational force which interacts with mass, most attempts at quantum gravity have
Boson
Solitons in Euclidean spacetime
motion with Euclidean time and finite Euclidean action. In the context of soliton theory the corresponding solution is known as a kink. In view of their
Instanton
Solution to field equations in Standard Model particle physics
Chiral anomaly – Non-conservation of chiral current in physics Instanton – Solitons in Euclidean spacetime Theta vacuum – Yang–Mills theory vacuum state Periodic
Sphaleron
Application of Lagrangian mechanics to field theories
(\mathbf {x} ,t)} where Φ is the gravitational potential, ρ is the mass density, and G in m3·kg−1·s−2 is the gravitational constant. The density L {\displaystyle
Lagrangian_(field_theory)
Theory of forces and subatomic particles
situations. These include low-energy quantum chromodynamics, bound states, and solitons. The interactions between all the particles described by the Standard Model
Standard_Model
Subatomic particle with positive charge
conceptual approaches to the structure of protons are: the topological soliton approach originally due to Tony Skyrme and the more accurate AdS/QCD approach
Proton
Type of quark
with spin 1/2, and experiences all four fundamental interactions: gravitation, electromagnetism, weak interactions, and strong interactions. The antiparticle
Up_quark
Lower energy limit in string theory
monopole is bounded by its magnetic charge. Solitons and D-branes: In string theory, BPS states include solitons like D-branes. The mass of a D-brane is determined
Bogomol'nyi–Prasad–Sommerfield bound
Bogomol'nyi–Prasad–Sommerfield_bound
Hypothetical particle
between these two particles. Finally, since this theory can combine gravitational, electromagnetic, and quantum effects, their coupling could potentially
Dilaton
Subatomic particle having no substructure
Standard Model, such as the graviton, the particle that would carry the gravitational force, and sparticles, supersymmetric partners of the ordinary particles
Elementary_particle
Elementary particle or quantum of light
by warped spacetime, as in gravitational lensing, and their frequencies may be lowered by moving to a higher gravitational potential, as in the Pound–Rebka
Photon
Elementary particle involved with rest mass
unchanged, whatever the location in time and space, and whatever the local gravitational field. In these theories, the gauge is a quantity that can be changed
Higgs_boson
Theory of fractal structure in the universe
universe Dickau, Jonathan J. (2009-08-30). "Fractal cosmology". Chaos, Solitons & Fractals. 41 (4): 2103–2105. Bibcode:2009CSF....41.2103D. doi:10.1016/j
Fractal_cosmology
operator with the D'Alembertian, similarly to the Klein–Gordon equation. Soliton-like solutions known as Gaussons figure prominently as analytical solutions
Logarithmic Schrödinger equation
Logarithmic_Schrödinger_equation
Something that has mass and volume
radiation to be observed directly, but whose presence can be inferred from gravitational effects on visible matter. Observational evidence of the early universe
Matter
Hypothetical superpartner to the graviton
observed dark matter density. However, since they decay only through gravitational interactions, their lifetime would be very long, of the order of M 2
Gravitino
Russian mathematician and physicist (1934–2017)
to the development of mathematics, quantum mechanics, string theory and solitons") and the State Prize of the Russian Federation (1995, 2004). He was president
Ludvig_Faddeev
Type of quark
with spin 1/2, and experiences all four fundamental interactions: gravitation, electromagnetism, weak interactions, and strong interactions. The antiparticle
Down_quark
Elementary particle, fundamental constituent of matter
fundamental interactions, also known as fundamental forces (electromagnetism, gravitation, strong interaction, and weak interaction), as well as the only known
Quark
Subatomic particle
fermionic Family hadron Interactions strong, weak, electromagnetic, gravitational Symbol n Antiparticle neutron Discovered Bruce Cork (1956) Mass 939
Antineutron
Elementary particle with negative charge
can undergo gravitational collapse to form a black hole. According to classical physics, these massive stellar objects exert a gravitational attraction
Electron
Dynamical instability of thin or elongated galaxies
Gravitating Systems. II — Nonlinear collective processes: Nonlinear waves, solitons, collisionless shocks, turbulence. Astrophysical applications, Berlin:
Firehose_instability
Subatomic particle
phenomena Annihilation Baryogenesis Baryon asymmetry Comet CP violation Gravitational interaction Positron emission Devices Cloud chamber Particle accelerator
Antiproton
Historical development of physics
and the prediction of such phenomena as gravitational lensing and the distortion of time in gravitational fields. Although relativity resolved the electromagnetic
History_of_physics
Meson that oscillates between matter and antimatter
Composition bs Statistics Bosonic Family Mesons Interactions Strong, Weak, Gravitational, Electromagnetic Antiparticle B s (bs) Mass 5366.3±0.6 MeV/c2 Mean lifetime
Strange_B_meson
Branch of applied mathematics
Newton's vector of hypothetical gravitational force—an instant action at a distance—with a gravitational field. The gravitational field is Minkowski spacetime
Mathematical_physics
421–427 (1982). Sawada, K.; T. Kotera (1974). "A method for finding N-soliton solutions of the KdV equation and KdV-like equation". Prog. Theor. Phys
List of scientific equations named after people
List_of_scientific_equations_named_after_people
Framework of superstring theory
1016/0370-2693(94)90763-3. S2CID 17534677. Strominger, Andrew (1990). "Heterotic solitons". Nuclear Physics B. 343 (1): 167–184. Bibcode:1990NuPhB.343..167S. doi:10
M-theory
Functional relationship between two quantities
"Financial power laws: Empirical evidence, models, and mechanisms". Chaos, Solitons & Fractals. 88: 3–18. Bibcode:2016CSF....88....3L. doi:10.1016/j.chaos
Power_law
Antiparticle of the electron
"Description and first application of a new technique to measure the gravitational mass of antihydrogen". Nature Communications. 4 (1) 1785: 1785–. Bibcode:2013NatCo
Positron
of atoms Gravity laser, a hypothetical concept of producing coherent gravitation waves Weber, Marvin J. (1999). Handbook of laser wavelengths. CRC Press
List_of_laser_types
Atoms composed of exotic particles
lepton. Since leptons are only sensitive to weak, electromagnetic and gravitational forces, muonic atoms are governed to very high precision by the electromagnetic
Exotic_atom
ellipsoid). In 1834, John Russell observed a nondecaying solitary water wave (soliton) in the Union Canal near Edinburgh and used a water tank to study the dependence
19th_century_in_science
Topological quantum field theory
of the Chern–Simons term to various theories gives rise to vortex- or soliton-type solutions Ten- and eleven-dimensional generalizations of Chern–Simons
Chern–Simons_theory
Theorem in classical statistical mechanics
Another way ergodicity can be broken is by the existence of nonlinear soliton symmetries. In 1953, Fermi, Pasta, Ulam and Tsingou conducted computer
Equipartition_theorem
Class of elementary particles
interaction, but they are subject to the other three fundamental interactions: gravitation, the weak interaction, and to electromagnetism, of which the latter is
Lepton
Quasiparticle of mechanical vibrations
all of which are ultimately due to the electric force. Magnetic and gravitational forces are generally negligible. The forces between each pair of atoms
Phonon
Plane curve: conic section
solution to the Korteweg–de Vries equation which describes the motion of a soliton wave in a canal. As shown first by Apollonius of Perga, a hyperbola can
Hyperbola
Particle with opposite charges
Commons has media related to Antiparticles. List of particles Antimatter Gravitational interaction of antimatter Parity, charge conjugation, and time reversal
Antiparticle
Spanish physicist (1939–2022)
Llorente, Fernando Rodriguez; —— (1994). "Chaotic magnetic fields". Chaos, Solitons & Fractals. 4 (10): 1943–1959. Bibcode:1994CSF.....4.1943Z. doi:10
Antonio_Fernández_Rañada
Transient quantum fluctuation (physics)
strong and weak forces, and their associated field bosons. For the gravitational and electromagnetic forces, the zero rest-mass of the associated boson
Virtual_particle
Predicted exotic atom
phenomena Annihilation Baryogenesis Baryon asymmetry Comet CP violation Gravitational interaction Positron emission Devices Cloud chamber Particle accelerator
True_muonium
Type of topological order in condensed matter physics
Theory of Large-Spin Heisenberg Antiferromagnets: Semiclassically Quantized Solitons of the One-Dimensional Easy-Axis Néel State". Physical Review Letters.
Symmetry-protected topological order
Symmetry-protected_topological_order
Russian physicist and mathematician
calculation of the mass spectrum and the scattering matrix. He studied solitons in the sine-Gordon model. He determined their mass and scattering matrix
Vladimir_Korepin
Subatomic particle
Statistics bosonic Family mesons Interactions strong, weak, electromagnetic, gravitational Symbol B+ , B− , B0 , B0 , B0 s, B0 s, B+ c, B− c Antiparticle B+ :
B_meson
Prize awarded by the Japan Academy
Observations of Water-Vapor Maser Emission Akira Hasegawa - "Discovery of Optical Soliton Properties in Fibers and of Self-organization of Plasma Turbulence" Kanji
Japan Academy Prize (academics)
Japan_Academy_Prize_(academics)
Hypothetical form of quarkonium
meson Composition tt Statistics bosonic Interactions strong, weak, gravitational, electromagnetic Status hypothetical Antiparticle self Electric charge
Theta_meson
Hypothetical subatomic particle
have not been entirely solved. In particular, no successful theory of gravitation based on a particle theory has yet been proposed. Although the Model
Preon
chip capable of 100 simultaneous wavelength-based operations, using a soliton microcomb and Mach–Zehnder interferometer mesh, marking a major step toward
2025_in_science
German-American mathematician and physicist (1908–1989)
but no non-trivial scattering, which play a basic role in the theory of Solitons, and the holomorphic representation in the Segal–Bargmann space (1961)
Valentine_Bargmann
Optica prize for quantum electronics
μm wavelength regime, demonstrating optical soliton propagation in fibers, and developing innovative soliton systems that have set records for high-capacity
Charles_Hard_Townes_Award
Nonlinear and exact periodic wave solution of the Korteweg–de Vries equation
height is twice the amplitude, H = 2a, in the infinitesimal wave limit. Soliton Waves and shallow water Nezlin, M.V. (1993), Physics of intense beams in
Cnoidal_wave
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GRAVITATIONAL SOLITON
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GRAVITATIONAL SOLITON
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