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Massive graviton geons

Katsuki Aoki1,*, Kei-ichi Maeda1,†, Yosuke Misonoh1,‡, and Hirotada Okawa2,1,§

  • 1Department of Physics, Waseda University, Shinjuku, Tokyo 169-8555, Japan
  • 2Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto 606-8502, Japan

  • *katsuki-a12@gravity.phys.waseda.ac.jp
  • †maeda@waseda.ac.jp
  • ‡misonoh@aoni.waseda.jp
  • §okawa@heap.phys.waseda.ac.jp
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Phys. Rev. D 97, 044005 – Published 5 February, 2018

DOI: https://doi.org/10.1103/PhysRevD.97.044005

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, ℓ=0 as well as a spherically symmetric solution with j=0, ℓ=2 in this system where j is the total angular momentum quantum number and ℓ 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.

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Phys. Rev. D 97, 044005– Published 5 February, 2018
  • Received 24 October 2017
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

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