Relativistic chaos

Phenomena

Spacetime
Kepler problem Gravitational lensing Gravitational redshift Gravitational time dilation Gravitational waves Frame-dragging Geodetic effect Event horizon Singularity Black hole
Spacetime diagrams Minkowski spacetime Metric tensor

Equations
Linearized gravity Einstein field equations Friedmann Geodesics Mathisson–Papapetrou–Dixon Hamilton–Jacobi–Einstein Raychaudhuri Teukolsky
Formalisms
ADM NP BSSN Post-Newtonian
Advanced theory
Kaluza–Klein theory Quantum gravity Quantum field theory in curved spacetime

In physics, relativistic chaos is the application of chaos theory to dynamical systems described primarily by general relativity, and also special relativity.

John D. Barrow showed in 1982 that the Einstein field equations exhibit chaotic behaviour and modelled the Mixmaster universe as a dynamical system.^[1] Later work showed that relativistic chaos is coordinate invariant.^[2]

References

X. Ni; et al. (2012). "Effect of chaos on relativistic quantum tunneling" (PDF). Europhysics Letters. 98 (5) 50007. Bibcode:2012EL.....9850007N. doi:10.1209/0295-5075/98/50007. S2CID 568332. Archived from the original on June 17, 2017.
P. Schewe; J. Riordon; B. Stein (2003). "Relativistic Chaos". Physical News Update (664). Archived from the original on 2011-08-05.

H.-W. Lee (1995). "Relativistic chaos in time-driven linear and nonlinear oscillators". In P. Garbaczewski; M. Wolf; A. Weron (eds.). Proceedings of the XXXIst Winter School of Theoretical Physics. Lecture Notes in Physics. Vol. 457. pp. 503–506. Bibcode:1995LNP...457..503L. doi:10.1007/3-540-60188-0_76. ISBN 3-540-60188-0.

Background	Principle of relativity (Galilean relativity Galilean transformation) Special relativity Doubly special relativity
Fundamental concepts	Frame of reference Speed of light Hyperbolic orthogonality Rapidity Maxwell's equations Proper length Proper time Proper acceleration Relativistic mass
Formulation	Lorentz transformation Textbooks
Phenomena	Time dilation Mass–energy equivalence (E=mc²) Length contraction Relativity of simultaneity Relativistic Doppler effect Thomas precession Ladder paradox Twin paradox Terrell rotation
Spacetime	Light cone World line Minkowski diagram Biquaternions Minkowski space

Background	Introduction Mathematical formulation
Fundamental concepts	Equivalence principle Riemannian geometry Penrose diagram Geodesics Mach's principle
Formulation	ADM formalism BSSN formalism Einstein field equations Linearized gravity Post-Newtonian formalism Raychaudhuri equation Hamilton–Jacobi–Einstein equation Ernst equation
Phenomena	Black hole Event horizon Singularity Two-body problem Gravitational waves: astronomy detectors (LIGO and collaboration Virgo LISA Pathfinder GEO) Hulse–Taylor binary Other tests: precession of Mercury lensing (together with Einstein cross and Einstein rings) redshift Shapiro delay frame-dragging / geodetic effect (Lense–Thirring precession) pulsar timing arrays
Advanced theories	Brans–Dicke theory Kaluza–Klein Quantum gravity
Solutions	Cosmological: Friedmann–Lemaître–Robertson–Walker (Friedmann equations) Lemaître–Tolman Kasner BKL singularity Gödel Milne Spherical: Schwarzschild (interior Tolman–Oppenheimer–Volkoff equation) Reissner–Nordström Axisymmetric: Kerr (Kerr–Newman) Weyl−Lewis−Papapetrou Taub–NUT van Stockum dust discs Melvin Others: pp-wave Ozsváth–Schücking Alcubierre Ellis In computational physics: Numerical relativity

Scientists