TY - JOUR
T1 - Spinning massive test particles in cosmological and general static spherically symmetric spacetimes
AU - Zalaquett, Nicolas
AU - Hojman, Sergio A.
AU - Asenjo, Felipe A.
PY - 2014/4/21
Y1 - 2014/4/21
N2 - A Lagrangian formalism is used to study the motion of a spinning massive particle in Friedmann-Robertson-Walker and Gödel spacetimes, as well as in a general Schwarzschild-like spacetime and in static spherically symmetric conformally flat spacetimes. Exact solutions for the motion of the particle and general exact expressions for the momenta and velocities are displayed for different cases. In particular, the solution for the motion in spherically symmetric metrics is presented in the equatorial plane. The exact solutions are found using constants of motion of the particle, namely its mass, its spin, its angular momentum, and a fourth constant, which is its energy when the metric is time-independent, and a different constant otherwise. These constants are associated to Killing vectors. In the case of the motion on the Friedmann-Robertson-Walker metric, a new constant of motion is found. This is the fourth constant which generalizes previously known results obtained for spinless particles. In the case of general Schwarzschild-like spacetimes, our results allow for the exploration of the case of the Reissner-Nordstrom-(Anti)de Sitter metric. Finally, for the case of the conformally flat spacetimes, the solution is explicitly evaluated for different metric tensors associated to a universe filled with static perfect fluids and electromagnetic radiation. For some combination of the values of the constants of motion the particle trajectories may exhibit spacelike velocity vectors in portions of the trajectories.
AB - A Lagrangian formalism is used to study the motion of a spinning massive particle in Friedmann-Robertson-Walker and Gödel spacetimes, as well as in a general Schwarzschild-like spacetime and in static spherically symmetric conformally flat spacetimes. Exact solutions for the motion of the particle and general exact expressions for the momenta and velocities are displayed for different cases. In particular, the solution for the motion in spherically symmetric metrics is presented in the equatorial plane. The exact solutions are found using constants of motion of the particle, namely its mass, its spin, its angular momentum, and a fourth constant, which is its energy when the metric is time-independent, and a different constant otherwise. These constants are associated to Killing vectors. In the case of the motion on the Friedmann-Robertson-Walker metric, a new constant of motion is found. This is the fourth constant which generalizes previously known results obtained for spinless particles. In the case of general Schwarzschild-like spacetimes, our results allow for the exploration of the case of the Reissner-Nordstrom-(Anti)de Sitter metric. Finally, for the case of the conformally flat spacetimes, the solution is explicitly evaluated for different metric tensors associated to a universe filled with static perfect fluids and electromagnetic radiation. For some combination of the values of the constants of motion the particle trajectories may exhibit spacelike velocity vectors in portions of the trajectories.
KW - conformally flat spacetimes
KW - cosmological spacetimes
KW - exact solution
KW - spinning massive particle
UR - http://www.scopus.com/inward/record.url?scp=84898017019&partnerID=8YFLogxK
U2 - 10.1088/0264-9381/31/8/085011
DO - 10.1088/0264-9381/31/8/085011
M3 - Article
AN - SCOPUS:84898017019
SN - 0264-9381
VL - 31
JO - Classical and Quantum Gravity
JF - Classical and Quantum Gravity
IS - 8
M1 - 085011
ER -