6 problems

A black string in $4+1$ or higher spacetime dimensions is subject to the Gregory–Laflamme instability, in which perturbations breaking translation symmetry along the string lead to…

A discretely self-similar (DSS) solution is a solution invariant under a discrete scale transformation. An unstable mode is a perturbation mode that grows away from the solution, a…

Let $A$ be a $(d-2)$-dimensional surface enclosing a $(d-1)$-dimensional volume in a $d$-dimensional spacetime, and let $S_A$ denote the entropy in the enclosed region. Higher-dime…

A stationary vacuum black hole is determined by its mass and angular momenta, and stability is understood in the sense relevant to the discussion of stationary vacuum black holes.…

Near-extremal instability conjecture. There exists a neighborhood of the black hole parameters near extremality for which the corresponding regular, non-extremal black holes are li…

Consider five-dimensional pure Einstein-Maxwell theory and seek an exact rotating, charged generalization of the Kerr-Newman black hole. The relevant fields must satisfy the Einste…