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The AdS/CFT correspondence often motivates research on questions ingravitational physics whose relevance might not be immediately clear from apurely GR-perspective, but which are nevertheless interesting. In theseproceedings, we summarise two such results recently obtained by the author. Oneconcerns, broadly speaking, the possible isometry-groups of a spacetime sourcedby physical matter. The other one provides a possible argument against therecently proposed complexity=action conjecture.

Discrete scale invariance in holography and an argument against the complexity=action proposal