BEGIN:VCALENDAR VERSION:2.0 PRODID:-//linuxsoftware.nz//NONSGML Joyous v1.4//EN BEGIN:VEVENT SUMMARY:General relativistic solutions in minimal theory of bigravity DTSTART:20231012T143000Z DTEND:20231012T160000Z DTSTAMP:20260914T001603Z UID:ce46128b-f82b-442c-b69e-2d2b6fb9f6f5 SEQUENCE:1 CREATED:20231006T081455Z DESCRIPTION: Abstract: We investigate dynamical properties of static and s pherically symmetric systems in the self-accelerating branch of the Minima l Theory of Bigravity (MTBG).  In the former part\, we study the gravitat ional collapse of pressure-less dust and find special solutions\, where\, in both the physical and fiducial sectors\, the exterior and interior spac etime geometries are given by the Schwarzschild spacetimes and the Friedma nn-Lemaitre-Robertson-Walker universes dominated by pressure-less dust\, r espectively\, with specific time slicings. In the case that the Lagrange m ultipliers are trivial and have no jump across the matter interfaces in bo th 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. We find interesting classes of exact solutions that represent gravitational c ollapse in MTBG. In the spatially-flat case\, under a certain tuning of th e 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 Oppenheim er-Snyder model in GR. In the latter part\, we study odd-parity perturbati ons of the Schwarzschild-de Sitter solutions written in the spatially-flat coordinates. For the higher-multipole modes $\\ell\\geq2$\, we find that in general the system reduces to that of four physical modes\, where two o f them are dynamical and the remaining two are shadowy\, i.e.\, satisfying only elliptic equations. In the case that the ratio of the lapse function s between the physical and fiducial sectors are equal to a constant determ ined by the parameters of the theory\, the two dynamical modes are decoupl ed 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 shad owy 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 propertie s of the collapse itself. 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 in stabilities. LAST-MODIFIED:20231006T081455Z LOCATION:Sala de Seminários do DF\, Pavilhão de Física\, 2º piso URL:http://df.vps.tecnico.ulisboa.pt/pt/eventos/general-relativistic-solut ions-in-minimal-theory-of-bigravity/ X-ALT-DESC;FMTTYPE=text/html:

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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 gr avitational collapse of pressure-less dust and find special solutions\, wh ere\, in both the physical and fiducial sectors\, the exterior and interio r spacetime geometries are given by the Schwarzschild spacetimes and the F riedmann-Lemaitre-Robertson-Walker universes dominated by pressure-less du st\, respectively\, with specific time slicings.

In the case tha t the Lagrange multipliers are trivial and have no jump across the matter interfaces in both the physical and fiducial sectors\, the junction condit ions across them remain the same as those in general relativity (GR). For simplicity\, we foliate the interior geometry by homogeneous and isotropic spacetimes. We find interesting classes of exact solutions that represent gravitational collapse in MTBG.

In the spatially-flat case\, un der a certain tuning of the initial condition\, we find exact solutions of matter collapse in which the two sectors evolve independently. In the spa tially-closed case\, once the matter energy densities and the Schwarzschil d radii are tuned between the two sectors\, we find exact solutions that c orrespond to the Oppenheimer-Snyder model in GR. In the latter part\, we s tudy odd-parity perturbations of the Schwarzschild-de Sitter solutions wri tten in the spatially-flat coordinates.

For the higher-multipole modes $\\ell\\geq2$\, 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 se ctors 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 cou pled 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 as to not str ongly back-react/influence the dynamics of the master variables\, in the h igh frequency and short wavelength limits\, we show that the two dynamical modes do not suffer from ghost or gradient instabilities.

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