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Gravitational collapse and odd-parity black hole perturbations in Minimal Theory of Bigravity | | Masato Minamitsuji
; Antonio De Felice
; Shinji Mukohyama
; Michele Oliosi
; | | Date: |
2 Jan 2023 | | Abstract: | We investigate dynamical properties of static and spherically symmetric
systems in the self-accelerating branch of the Minimal Theory of Bigravity
(MTBG). In the former part, we study the gravitational collapse of
pressure-less 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 Friedmann-Lemaître-Robertson-Walker
universes dominated by pressure-less dust, respectively, with specific time
slicings. 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 Oppenheimer-Snyder model in GR. In
the latter part, we study odd-parity perturbations of the Schwarzschild-de
Sitter solutions written in the spatially-flat coordinates. For the
higher-multipole modes $ellgeq2$, 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
that 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. On giving appropriate boundary conditions to the
shadowy modes as to not strongly back-react/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. | | Source: | arXiv, 2301.00498 | | Services: | Forum | Review | PDF | Favorites | |
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