Particle Dynamics in Schwarzschild Spacetime  

Spinless Test Particles > s.a. classical particles; test-particle motion; schwarzschild geometry [line element, curvature].
* Idea: Structureless particles in general relativity move along timelike geodesics of the metric.
* Circular orbits: Test bodies can follow stable circular orbits at a radial distance r depending on their angular momentum, but always greater than 6R, where R is the Schwarzschild radius.
* Precession: Non-circular orbits in Schwarzschild spacetime do not close, and are only approximately ellipses; With a quadrupole moment, the main contributions are δquadr = 6π (GM)Qm3/L4, and δgr = 6π (GM)2m2/L2c2, both positive.
@ General references: in Weinberg 72; Wald 84, pp 140ff; Do-Nhat PLA(98); Dean AJP(99)jan [phase plane analysis]; Mitra gq/99 [radial]; Kerner et al CGQ(01)gq [nearly circular]; Ajith et al PRD(05)gq/04 [post-Newtonian approximants]; Boccaletti et al re GRG(05) [Beltrami's method]; Hall a0807 [exact results]; Brannen IJMPD(09) [Schwarzschild and Painlevé-Gullstrand coordinates]; Hioe & Kuebel a1008 (comment Han a1008), a1010 [parametrized space of orbits]; Bini et al CQG(11)-a1408 [non-geodesic orbits]; Tsupko PRD(14)-a1505 [unbound trajectories, strong deflection].
@ Null geodesics: Stuckey AJP(93)may; Čadež & Kostić PRD(05)gq/04; Belbruno & Pretorius CQG(11)-a1103 [dynamical-systems approach]; Muñoz AJP(14)jun [exact solutions]; Semerák ApJ(15)-a1412 [short formula]; > s.a. geodesics.
@ Other geodesics: Marck CQG(96)gq/95; Boccaletti et al GRG(05)gq; Leiva et al MPLA(09)-a0808 [in rainbow gravity]; Scharf JModP(11)-a1101 [in terms of elliptic functions]; Ohanian a1102 [reversed gravitational acceleration for free fall motion at high speeds]; Schmidt PRD(11)-a1104 [large eccentricity, perihelion advance]; Kostić GRG(12)-a1201 [timelike, classification]; Grib et al G&C(12)-a1203 [particle collisions]; Tejeda & Rosswog MNRAS(13)-a1303 [accurate Newtonian description].
@ And gravitational radiation: Cardoso & Lemos PLB(02)gq.
@ With radiation damping and radiation reaction: Burko PRD(03)gq/02; > s.a. orbits of gravitating bodies.
@ Scattering: Mendoza et al Ent(09)gq/07 [absorption and reflection]; Jia et al a1512 [bending].
@ Charged particles: Cardoso et al PRD(03)
> Related topics: see gravitational self-force; sources of gravitational waves; Twin Paradox.

OIther Types of Particles > s.a. chaotic motion in a curved spacetime; spinning particles.
@ Spinning particles: Rietdijk & van Holten CQG(93); White et al CQG(00) [radial infall]; Burko PRD(04)gq/03; Bini et al CQG(04)gq, CQG(05)gq [spin precession]; Plyatsko CQG(05)gq [ultrarelativistic, circular orbits]; Turakulov & Safonova MPLA(05) [s = 1, corrections to geodesics]; Dolan et al PRD(06)gq [massive spin-1/2, scattering]; Bini et al GRG(11)-a1408 [spin-geodesic deviations]; Plyatsko & Fenyk PRD(12)-a1111; Jefremov et al PRD-a1503 [ISCO].
@ Quadrupolar particles: Bini & Geralico PRD(13)-a1408.


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