Born-Infeld Theory  

In General > s.a. clifford algebra; modified electromagnetism.
* Idea: A non-linear form of electrodynamics; It predicts a maximum value for the electric field, preventing the occurrence of classical singularities; The Lagrangian density is

\(\cal L\)BI = β 2 [det(δμν + β−2 F μν)]1/2 ,

where β plays the role of the maximum value of the electric field; This is currently the most widely known type of non-linear electrodynamics.
@ General references: Mie AdP(13), AdP(13) [precursor]; Born & Infeld PRS(34); Dirac PRS(60) [reformulation]; Białynicki-Birula in(83) [rev]; Chruściński JPA(98) [Hamiltonian form]; Kerner NCB(04); Kogut & Sinclair PRD(06)hl [lattice, and quantization]; Smirnov tr-a1708.
@ Solutions: Yang PRS(00) [localized, magnetic strings]; Brihaye & Mercier PRD(01) [+ abelian Higgs]; Ferraro PLA(04) [2D, electrostatic]; Aiello et al PLA(07)ht/06 [electromagnetic waves and background fields]; Ferraro JHEP(10)-a1007 [2D electrostatic, complex method]; Kiessling PLA(11)-a1107 [uniqueness results for Maxwell-Born-Infeld theory]; Ferraro JHEP(13)-a1304 [2D]; Ferraro & Nigro JHEP(16)-a1508 [complex method].
@ Related topics: Schwarz ht/01-conf [and string theory]; Fortunato et al JMP(02) [second-order approximation, finite-energy solutions]; Cirilo-Lombardo JMP(07) [hidden symmetries]; Kenoufi & Gondran a0708 [complex Faraday tensor]; Kiessling a1107-proc [laws of motion for point charges in Maxwell-Born-Infeld theory]; > s.a. wave phenomena [2D, superluminal propagation].
> Online resources: see Wikipedia page.

Modifications > s.a. Eddington(-inspired)-Born-Infeld Gravity.
@ In curved spacetime: Gibbons & Hashimoto JHEP(00).
@ Non-abelian: Serié et al PRD(03); Cirilo-Lombardo CQG(05)ht/06; Obregón MPLA(06) [without sqrt].
@ Born-Infeld-Einstein theory: Pellicer & Torrence JMP(69); Deser & Gibbons CQG(98)ht [actions]; Vollick PRD(04)gq/03 [Palatini form]; Nieto PRD(04)ht [in any dimension, self-dual in D = 4]; Vollick PRD(05)gq [+ matter]; > s.a. black holes in modified theories.
@ For Einstein-Yang-Mills theory: Palatnik gq/04; Dyadichev et al PRD(05)ht/04 [non-abelian, Bianchi I, chaos].
@ Supersymmetric: Ketov MPLA(99); Ivanov RPJ(02)ht; Nishino et al CQG(05)ht/04 [N = 1 Dirac-Born-Infeld]; Hariton JPA(06).
@ Other: Tripathy & Khare PLB(01)ht/00 [topologically massive]; Hu et al IJTP(04) [discrete, non-commutative space]; Aiello et al PRD(04)gq [coupled to Lovelock gravity, black hole solutions]; Novello et al PRD(05)ap [extension for a scalar field, and cosmology]; Comelli IJMPA(05), PRD(05)gq; Kruglov JPA(10)-a0909 [with two parameters]; Chemissany et al PRD(12) [with higher derivatives]; Güllü et al PRD(15)-a1410 [4D, with a massless graviton]; Bufalo PLB(15)-a1505 [in very special relativity]; Ferrara et al NPB(16)-a1602 [two-field].

Gravitational Analog
@ General references: Wohlfarth CQG(04); Zinoviev ht/05; Lubo a0804 [and galaxy rotation curves]; Güllü et al CQG(10)-a1003 [3D, and new massive gravity]; Alishahiha et al PRD(10) [3D]; Güllü et al PRD(10)-a1004 [Born-Infeld-Hořava gravity]; Escobar a1209 [and scalar-tensor theory]; Odintsov et al PRD(14)-a1406; Beltrán et al a1704/PRP [rev]; Beltrán Jiménez et al a2104 [constraints and effective field theory].
@ Solutions: da Rocha et al a0907 [cosmic strings in NDL theory]; Chern & Yang JMP(14) [cosmic string model]; Bazeia et al CQG(17)-a1609 [BTZ-type]; Ozen et al PRD(17)-a1710 [black holes, entropy].
@ Born-Infeld-like f(R) gravity theories: Fabris et al PRD(12)-a1205; Kruglov IJTP(13), ApSS(16)-a1403; Makarenko et al PRD(14)-a1403.

Phenomenology > s.a. BIon; dark energy; cosmological models in general relativity; FLRW quantum cosmology; lensing.
* Cosmology: In theories with \(\cal L\)em = −\(1\over4\)F2 + α F4, without electric field, the F4 term produces a bounce that avoids the initial singularity.
@ General references: Boillat & Strumia JMP(99) [electron, spin effects]; Gibbons G&C(02) [pulse propagation]; Schuller AP(02) [and maximal acceleration]; Carley & Kiessling PRL(06)mp/05, Mazharimousavi & Halilsoy FP(12)-a0810 [H atom]; Ferraro PRL(07) [waveguide test]; Addazi et al PLB(16)-a1607 [condensate as a possible origin of neutrino masses and dark energy]; Jana et al PRD(18)-a1711 [speed of gravitational waves].
@ Cosmology: García-Salcedo & Bretón IJMPA(00); Vargas Moniz PRD(02) [quintessence]; Lu et al ht/05 [Einstein-BI, classical and quantum]; Vollick PRD(08)-a0807 [homogeneous, isotropic]; Copeland et al PRD(10) [Dirac-BI with perfect fluid]; Fiorini PRL(13) [absence of singularity].
@ Isolated objects: Pellicer & Torrence JMP(69) [Reissner-Nordström-like]; Bretón PRD(03) [black hole and isolated horizon]; Bilić et al JCAP(06)ap/05 [BI phantom gravastars]; Cirilo-Lombardo JMP(05)gq/06, gq/05-conf [Einstein-BI, static spherical]; Franklin & Garon PLA(11) [relativistic hydrogen spectrum]; Jana et al PRD(18)-a1808 [overcharging black holes, cosmic censorship]; Böhmer & Fiorini CQG(19)-a1901 [regular black holes]; > s.a. black holes; reissner-nordström spacetime.
@ Solutions as particle models: Mazharimousavi & Halilsoy PLB(09)-a0812 [black holes]; Chernitskii in(10)-a0911 [axisymmetric static solutions with ring singularity]; > s.a. geons.

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