Massive Graviton Geons

TL;DR

This paper introduces the concept of massive graviton geons, self-gravitating bound states of massive gravitons in bigravity theory, analyzing their solutions, stability, and potential implications for dark matter and spacetime stability.

Contribution

It presents the first vacuum solutions for massive graviton geons, including non-spherical configurations, and investigates their stability and possible physical relevance.

Findings

Existence of non-spherical and spherical graviton geon solutions.

The non-spherical solution has lower energy eigenvalue, indicating it as the ground state.

The spherical solution exhibits an unstable quadrupole mode, suggesting a transition to the non-spherical state.

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 Schr\"odinger-Poisson equations with the tensor "wavefunction" in the Newtonian limit. We obtain a non-spherically symmetric solution with $j=2,\ell=0$ as well as a spherically symmetric solution with $j=0,\ell=2$ in this system where $j$ is the total angular momentum quantum number and $\ell$ is the orbital angular momentum quantum number, respectively. The energy eigenvalue of the Schr\"odinger equation in the non-spherical 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 non-spherical solution. The results suggest that the non-spherically 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 non-relativistic 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.