Klein-Gordon Fields in Curved Spacetimes and Other Backgrounds| 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
gab ∇a∇b φ − (m2 + ξR) φ = 0 , from the Lagrangian density \(\cal L\) = −\(1\over2\)|g|1/2 [gab ∇aφ ∇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];
Dereziński & Siemssen PAA(19)-a1709 [evolution equation approach].
@ 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. conformal invariance; 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 PRD(17)-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;
Besset & Häfner a2004 [KN-de Sitter].
@ (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];
Kamiński a1904
[background with non-essentially self-adjoint Klein-Gordon operator].
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 [\(\kappa\)-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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