Higher order perturbations of Anti-de Sitter space and time-periodic solutions of vacuum Einstein equations

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Written by Andrzej Rostworowski

Motivated by the problem of stability of Anti-de Sitter (AdS) spacetime, we will discuss nonlinear grav-
itational perturbations of maximally symmetric solutions of vacuum Einstein equations in general
and the case of AdS in particular. We will present the evidence that, similarly to the self-gravitating
scalar field at spherical symmetry, the negative cosmological constant allows for the existence of
globally regular, asymptotically AdS, time-periodic solutions of vacuum Einstein equations that bi-
furcate from linear eigenfrequencies of AdS. Interestingly, preliminary results indicate that the
number of time-periodic solutions bifurcating from a given eigenfrequency equals the multiplicity of
this eigenfrequency.