Abstract:
Three simple idealised models are studied in order to develop some intuition about the leading order
effect of non-sphericity on the maximum turnaround size RTA,max of large scale bound cosmic structures. Two of them describe intrinsically axisymmetric static mass distributions whereas the other is
the Kerr-de Sitter metric where the axisymmetry is generated due to the rotation of the structure. In
all the cases the fractional change δRTA,max(θ)/R(0)
TA,max of RTA,max of a given structure, compared
to a spherical one with the same mass M, depends on the polar angle θ and is proportional to the
product of the relevant eccentricity parameter, times the square of a small quantity. This quantity
in the static examples is the ratio of two characteristic length scales, while in the spinning case it is
the ratio vout/c of the azimuthal speed of the outmost members of the structure, over the speed of
light. Furthermore, the angular average hδRTA,max(θ)/R(0)
TA,maxi is zero in the two static cases, while
it is negative and proportional to O(v
2
out/c2
) for the Kerr-de Sitter. Thus, δRTA,max(θ)/R(0)
TA,max for
an axisymmetric structure is very small for practically any value of the eccentricity parameter. We
speculate about some possible further implications of our result on the maximum turn around radius
of realistic cosmic structures.
