Gravitational collapse and oddparity black hole perturbations in minimal theory of bigravity
Abstract
We investigate dynamical properties of static and spherically symmetric systems in the selfaccelerating branch of the minimal theory of bigravity (MTBG). In the former part, we study the gravitational collapse of pressureless dust and find special solutions, where, in both the physical and fiducial sectors, the exterior and interior spacetime geometries are given by the Schwarzschild spacetimes and the FriedmannLemaîtreRobertsonWalker universes dominated by pressureless dust, respectively, with specific time slicings. In the case where the Lagrange multipliers are trivial and have no jump across the matter interfaces in both the physical and fiducial sectors, the junction conditions across them remain the same as those in general relativity (GR). For simplicity, we foliate the interior geometry by homogeneous and isotropic spacetimes. For a spatially flat interior universe, we foliate the exterior geometry by a timeindependent flat space, while for a spatially curved interior universe, we foliate the exterior geometry by a timeindependent space with deficit solid angle. Despite the rather restrictive choice of foliations, we find interesting classes of exact solutions that represent gravitational collapse in MTBG. In the spatially flat case, under a certain tuning of the initial condition, we find exact solutions of matter collapse in which the two sectors evolve independently. In the spatially closed case, once the matter energy densities and the Schwarzschild radii are tuned between the two sectors, we find exact solutions that correspond to the OppenheimerSnyder model in GR. In the latter part, we study oddparity perturbations of the Schwarzschildde Sitter solutions written in the spatially flat coordinates. For the highermultipole modes ℓ≥2 , we find that, in general, the system reduces to that of four physical modes, where two of them are dynamical and the remaining two are shadowy, i.e., satisfying only elliptic equations. In the case where the ratio of the lapse functions between the physical and fiducial sectors are equal to a constant determined by the parameters of the theory, the two dynamical modes are decoupled from each other, but sourced by one of the shadowy modes. Otherwise, the two dynamical modes are coupled to each other and sourced by the two shadowy modes. At least for the cases of collapse described in this paper, we find that the ratio of the lapse functions is determined by the properties of the collapse itself. On giving appropriate boundary conditions to the shadowy modes so as to not strongly backreact/influence the dynamics of the master variables, in the high frequency and short wavelength limits, we show that the two dynamical modes do not suffer from ghost or gradient instabilities. For the dipolar mode ℓ=1 , the two copies of the slowrotation limit of the Kerrde Sitter metrics cannot be a solution in the selfaccelerating branch, unless the mass and spin of black holes and effective cosmological constants are tuned to be the same. Therefore, deviation from GR is expected for rotating black holes in the selfaccelerating branch of MTBG.
 Publication:

Physical Review D
 Pub Date:
 March 2023
 DOI:
 10.1103/PhysRevD.107.064070
 arXiv:
 arXiv:2301.00498
 Bibcode:
 2023PhRvD.107f4070M
 Keywords:

 General Relativity and Quantum Cosmology;
 Astrophysics  Cosmology and Nongalactic Astrophysics;
 High Energy Physics  Theory
 EPrint:
 28 pages, published version