12 problems

Let $j$ denote the spin of the perturbation, $k\in\mathbb{Z}$, and let $T_{\text{Hawking}}$ be the Hawking temperature. For even integer spins, the Schwarzschild asymptotic frequen…

Shallow-QNM convergence conjecture. As $r{rm C} earrow r{rm e}$, the set

Damped-QNM persistence conjecture. Damped QNMs on extremal RNdS give rise to nearby damped QNMs of subextremal RNdS.

Let a black-hole background have a one-loop determinant associated with its quantum effective action, and let its (anti)quasinormal modes be the relevant solutions of the separated…

Consider the connection formula relating the solutions at $z=t$ and $z=1$, and assume that all $\Gamma$-function factors appearing in it are non-zero. Gamma-pole conjecture. The mi…

The effective potential of a black hole may admit two competing purely imaginary quasinormal modes, with one mode spectrally stable and dominant and the remaining modes appearing a…

Consider the equation with an inverse square potential and let $\theta$ be a co-mode for this equation. In the preceding model without the inverse square potential, the correspondi…

Let $(\mathcal{M},g)_\kappa$ be a family of spacetimes with non-degenerate Killing horizons whose surface gravity satisfies $0<\kappa\leq\kappa_0$, and suppose the relevant notion…

First-order QNM conjecture. To first order in $\mathfrak{m}$, QNMs of massless scalar fields for Schwarzschild–de Sitter spacetime with small black hole mass are the same as those…

Let $\alpha$ denote the relevant decay-rate or spectral-gap parameter for quasinormal modes of a Reissner–Nordström–de Sitter black hole, and let $\kappa_+$ and $\kappa_c$ be the s…

Let an asymptotically anti-de Sitter (aAdS) black hole be a black-hole spacetime with asymptotically anti-de Sitter geometry, and let its quasinormal frequencies (QNFs) be the comp…

Let $Z$ be the full quantum gravity partition function, and let $z_*$ denote a quasinormal mode (QNM) of the spacetime. Quasinormal-mode zero-pole conjecture. The QNMs are zeros or…