Klein-Gordon Fields in Curved Spacetimes and Other Backgrounds  

In General > s.a. causality violation; geometric phase; huygens' principle; klein-gordon fields [Hamiltonian]; quantum klein-gordon fields; Superradiance.
* Dynamics: The most common possible forms depend on a conformal parameter ξ, and are given by

gabab φ – (m2 + ξR) φ = 0 ,   from the Lagrangian density   \(\cal L\) = –\(1\over2\)|g|1/2 [gabaφ ∇bφ + (m2 + ξR) φ2] .

* Coupling to gravity: Minimal coupling corresponds to the value ξ = 0; A non-minimal coupling is often introduced from discussions of the conformal anomaly (it is required to make the trace of the stress-energy tensor vanish); When m = 0, setting ξ = (n–2)/4(n–1) (= 1/6 in 4D) with φ → Ω1–n/2φ under g → Ω2g makes the equation conformally invariant.
@ General references: Castagnino & Ferraro PRD(89) [modes diagonalizing H]; Longhi & Materassi IJMPA(99) [global variables]; Strohmaier LMP(00)mp [Cauchy problem]; Droz-Vincent CQG(01)gq/00 [mode solution]; Vaidya & Sparling mp/02 [singular potential]; Poisson PRD(02)gq [weak curvature, radiative falloff]; Dai & Stojković PRD(12)-a1209 [massless field, superluminal phase velocity].
@ Coupling to gravity: Sonego & Faraoni CQG(93) [from the equivalence principle]; Srivastava et al a1110 [from quantum fluctuations]; Hrycyna PLB(17)-a1511 [cosmological constraints].
@ Conformal transformations: Faraoni & Faraoni FP(02) [and potential-free form]; Kaiser PRD(10)-a1003 [with multiple scalar fields].
@ Non-globally-hyperbolic: Wald JMP(80) [static, recovery of deterministic dynamics]; Vickers & Wilson gq/01 [with hypersurface singularities]; Ishibashi & Wald CQG(03)gq; Stalker & Tahvildar-Zadeh CQG(04)gq [supercharged Reissner-Nordström]; Seggev CQG(04)gq/03 [stationary]; Bullock RVMP(12) [static].
@ Accelerated observer: Gerlach PRD(88); Tian et al gq/06 [Rindler spacetime].
@ Coupled to gravity: Clayton et al PLA(98)gq [stability]; Malik CQG(08)-a0712; Mendes et al PRD(14)-a1310 [quantum versus classical instability]; > s.a. solutions of general relativity and initial-value formulation.

Specific Types of Backgrounds > s.a. wave equations.
@ Spherically symmetric: Couch & Torrence GRG(86), GRG(88) [transparent]; Bizoń et al CQG(09) [late-time tails].
@ Schwarzschild: Couch JMP(81) [solutions, and higher spins]; Pravica PRS(99); Zecca NCB(00); Roszkowski CQG(01) [energy diffusion]; Koyama & Tomimatsu PRD(01)gq [tails]; Roszkowski CQG(01)ap; Weinstein NPPS(02)gq/01; Casadio & Luzzi PRD(06)ht [minimal coupling, method of comparison equations]; Dafermos & Rodnianski a0811-ln [and other black-hole backgrounds]; Thuestad et al a1705 [and Kerr, including the black-hole interior].
@ Reissner-Nordström: Ori PRD(98)gq/97 [massless]; Koyama & Tomimatsu PRD(01)gq/00 [tails]; Xue et al PRD(02)ht [numerical]; Crispino et al PRD(09)-a0904 [massless]; Bizoń & Friedrich CQG(13) [extreme, massless field].
@ Kerr: Couch JMP(85) [and higher spins]; Ori PRD(98) [massless]; Scheel et al PRD(04)gq/03 [tails, numerical]; Strafuss & Khanna PRD(05)gq/04 [massive, instability]; Finster et al CMP(05) [propagator], CMP(06)gq/05 [decay of solutions]; Beyer & Craciun CQG(08)gq/06 [new symmetry]; Gleiser et al CQG(08)-a0710 [late-time tails]; Burko & Khanna CQG(09)-a0711 [2+1, tails]; Finster et al CMP(08) [decay]; Beyer JMP(09); Andersson & Blue a0908; Beyer JMP(11)-a1105 [massive field, stability]; Rácz & Tóth CQG(11) [late-time tails, numerical]; Beyer et al GRG(13)-a1206 [stability of solutions of the Klein-Gordon equation]; Burko & Khanna PRD(14) [late-time tails, mode-coupling mechanism]; Yang et al PRD(14)-a1311 [Green function].
@ Kerr-Newman black holes: Furuhashi & Nambu PTP(04)gq [massive, instability]; Konoplya & Zhidenko PRD(13)-a1307 [massive, charged, quasinormal modes, tails and stability]; Bezerra et al CQG(14)-a1312.
@ (Anti)-de Sitter: Torrence & Couch CQG(85) [no-scattering conditions]; Yagdjian & Galstian CMP(09) [fundamental solutions]; Hrycyna APPB(17)-a1705-conf [higher-dimensional, non-conformal coupling]; > s.a. AdS spacetime [5D]; BRST quantization.
@ FLRW spacetime: Silbergleit ap/02 [equation of state]; Copeland et al PRD(09)-a0904.
@ Other cosmological backgrounds: Villalba & Isasi JMP(02)gq [with B field]; Alimohammadi & Vakili AP(04)gq/03 [constant curvature]; Kozlov & Volovich IJGMP(06)gq [finite-action]; Malik JCAP(07)ap/06 [perturbed FLRW models, up to second-order]; Maciejewski et al gq/06 [global dynamics and chaos]; Kim & Minamitsuji PRD(10)-a1002 [anisotropic spacetimes]; Holzegel & Warnick JFA(14)-a1209 [asymptotically anti-de Sitter black holes]; > s.a. bianchi IX models.
@ Lower-dimensional: Fewster CQG(99)gq/98, CQG(99)gq/98 [2D cylinder]; Harriott & Williams MPLA(01) [2+1, extended source]; McKeon & Patrushev EPJP(11)-a1009 [2D, canonical structure].
@ Other backgrounds: Friedman & Morris CMP(97)gq/94 [with closed timelike curves]; Fernandes et al gq/07 [vacuumless defects]; Radu & Visinescu MPLA(07)-a0706 [generalized Kaluza-Klein monopole background]; Arias et al PRD(11)-a1103 [in an inhomogeneous random medium].

Generalized Backgrounds > s.a. fractals in physics.
@ Discretizations: Dmitriev et al JPA(06) [non-linear, energy and linear momentum].
@ Other backgrounds: Freidel et al IJMPA(08)-a0706 [κ-Minkowski spacetime]; Bibikov & Prokhorov JPA(09) [Y-junction of three semi-infinite axes]; Krausshar a1103 [Möbius strip and Klein bottle ion higher dimensions].

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