Particle Dynamics in Schwarzschild Spacetime| 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];
Eufrasio et al GRG(18)-a1812;
Ribeiro & Lima a1910 [timelike, exact solution].
@ 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];
Liu et al CQG(16)-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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