TY - JOUR

T1 - 3D simulation of spindle gravitational collapse of a collisionless particle system

AU - Yoo, Chul Moon

AU - Harada, Tomohiro

AU - Okawa, Hirotada

N1 - Publisher Copyright:
© 2017 IOP Publishing Ltd.

PY - 2017/4/24

Y1 - 2017/4/24

N2 - We simulate the spindle gravitational collapse of a collisionless particle system in a 3D numerical relativity code and compare the qualitative results with the old work done by Shapiro and Teukolsky (ST) (1991 Phys. Rev. Lett. 66 994). The simulation starts from the prolate-shaped distribution of particles and a spindle collapse is observed. The peak value and its spatial position of curvature invariants are monitored during the time evolution. We find that the peak value of the Kretschmann invariant takes a maximum at some moment, when there is no apparent horizon, and its value is greater for a finer resolution, which is consistent with what is reported in ST. We also find a similar tendency for the Weyl curvature invariant. Therefore, our results lend support to the formation of a naked singularity as a result of the axially symmetric spindle collapse of a collisionless particle system in the limit of infinite resolution. However, unlike in ST, our code does not break down then but goes well beyond. We find that the peak values of the curvature invariants start to gradually decrease with time for a certain period of time. Another notable difference from ST is that, in our case, the peak position of the Kretschmann curvature invariant is always inside the matter distribution.

AB - We simulate the spindle gravitational collapse of a collisionless particle system in a 3D numerical relativity code and compare the qualitative results with the old work done by Shapiro and Teukolsky (ST) (1991 Phys. Rev. Lett. 66 994). The simulation starts from the prolate-shaped distribution of particles and a spindle collapse is observed. The peak value and its spatial position of curvature invariants are monitored during the time evolution. We find that the peak value of the Kretschmann invariant takes a maximum at some moment, when there is no apparent horizon, and its value is greater for a finer resolution, which is consistent with what is reported in ST. We also find a similar tendency for the Weyl curvature invariant. Therefore, our results lend support to the formation of a naked singularity as a result of the axially symmetric spindle collapse of a collisionless particle system in the limit of infinite resolution. However, unlike in ST, our code does not break down then but goes well beyond. We find that the peak values of the curvature invariants start to gradually decrease with time for a certain period of time. Another notable difference from ST is that, in our case, the peak position of the Kretschmann curvature invariant is always inside the matter distribution.

KW - gravitational collapse

KW - naked singularity

KW - numerical relativity

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U2 - 10.1088/1361-6382/aa6ad5

DO - 10.1088/1361-6382/aa6ad5

M3 - Article

AN - SCOPUS:85018970689

SN - 0264-9381

VL - 34

JO - Classical and Quantum Gravity

JF - Classical and Quantum Gravity

IS - 10

M1 - 105010

ER -