### Abstract

We find vacuum solutions such that massive gravitons are confined in a local spacetime region by their gravitational energy in asymptotically flat spacetimes in the context of the bigravity theory. We call such self-gravitating objects massive graviton geons. The basic equations can be reduced to the Schrödinger-Poisson equations with the tensor "wave function" in the Newtonian limit. We obtain a nonspherically symmetric solution with j=2, =0 as well as a spherically symmetric solution with j=0, =2 in this system where j is the total angular momentum quantum number and is the orbital angular momentum quantum number, respectively. The energy eigenvalue of the Schrödinger equation in the nonspherical solution is smaller than that in the spherical solution. We then study the perturbative stability of the spherical solution and find that there is an unstable mode in the quadrupole mode perturbations which may be interpreted as the transition mode to the nonspherical solution. The results suggest that the nonspherically symmetric solution is the ground state of the massive graviton geon. The massive graviton geons may decay in time due to emissions of gravitational waves but this timescale can be quite long when the massive gravitons are nonrelativistic and then the geons can be long-lived. We also argue possible prospects of the massive graviton geons: applications to the ultralight dark matter scenario, nonlinear (in)stability of the Minkowski spacetime, and a quantum transition of the spacetime.

Original language | English |
---|---|

Article number | 044005 |

Journal | Physical Review D |

Volume | 97 |

Issue number | 4 |

DOIs | |

Publication status | Published - 2018 Feb 5 |

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### ASJC Scopus subject areas

- Physics and Astronomy (miscellaneous)

### Cite this

*Physical Review D*,

*97*(4), [044005]. https://doi.org/10.1103/PhysRevD.97.044005

**Massive graviton geons.** / Aoki, Katsuki; Maeda, Keiichi; Misonoh, Yosuke; Okawa, Hirotada.

Research output: Contribution to journal › Article

*Physical Review D*, vol. 97, no. 4, 044005. https://doi.org/10.1103/PhysRevD.97.044005

}

TY - JOUR

T1 - Massive graviton geons

AU - Aoki, Katsuki

AU - Maeda, Keiichi

AU - Misonoh, Yosuke

AU - Okawa, Hirotada

PY - 2018/2/5

Y1 - 2018/2/5

N2 - We find vacuum solutions such that massive gravitons are confined in a local spacetime region by their gravitational energy in asymptotically flat spacetimes in the context of the bigravity theory. We call such self-gravitating objects massive graviton geons. The basic equations can be reduced to the Schrödinger-Poisson equations with the tensor "wave function" in the Newtonian limit. We obtain a nonspherically symmetric solution with j=2, =0 as well as a spherically symmetric solution with j=0, =2 in this system where j is the total angular momentum quantum number and is the orbital angular momentum quantum number, respectively. The energy eigenvalue of the Schrödinger equation in the nonspherical solution is smaller than that in the spherical solution. We then study the perturbative stability of the spherical solution and find that there is an unstable mode in the quadrupole mode perturbations which may be interpreted as the transition mode to the nonspherical solution. The results suggest that the nonspherically symmetric solution is the ground state of the massive graviton geon. The massive graviton geons may decay in time due to emissions of gravitational waves but this timescale can be quite long when the massive gravitons are nonrelativistic and then the geons can be long-lived. We also argue possible prospects of the massive graviton geons: applications to the ultralight dark matter scenario, nonlinear (in)stability of the Minkowski spacetime, and a quantum transition of the spacetime.

AB - We find vacuum solutions such that massive gravitons are confined in a local spacetime region by their gravitational energy in asymptotically flat spacetimes in the context of the bigravity theory. We call such self-gravitating objects massive graviton geons. The basic equations can be reduced to the Schrödinger-Poisson equations with the tensor "wave function" in the Newtonian limit. We obtain a nonspherically symmetric solution with j=2, =0 as well as a spherically symmetric solution with j=0, =2 in this system where j is the total angular momentum quantum number and is the orbital angular momentum quantum number, respectively. The energy eigenvalue of the Schrödinger equation in the nonspherical solution is smaller than that in the spherical solution. We then study the perturbative stability of the spherical solution and find that there is an unstable mode in the quadrupole mode perturbations which may be interpreted as the transition mode to the nonspherical solution. The results suggest that the nonspherically symmetric solution is the ground state of the massive graviton geon. The massive graviton geons may decay in time due to emissions of gravitational waves but this timescale can be quite long when the massive gravitons are nonrelativistic and then the geons can be long-lived. We also argue possible prospects of the massive graviton geons: applications to the ultralight dark matter scenario, nonlinear (in)stability of the Minkowski spacetime, and a quantum transition of the spacetime.

UR - http://www.scopus.com/inward/record.url?scp=85043707342&partnerID=8YFLogxK

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U2 - 10.1103/PhysRevD.97.044005

DO - 10.1103/PhysRevD.97.044005

M3 - Article

AN - SCOPUS:85043707342

VL - 97

JO - Physical Review D

JF - Physical Review D

SN - 2470-0010

IS - 4

M1 - 044005

ER -