231 problems

Let $(\mathcal{M},\mathbf{g})$ be the maximal development of generic asymptotically flat initial data for Einstein's vacuum field equations. Weak cosmic censorship conjecture. The…

Let the maximal globally hyperbolic development of generic initial data be given, and let a Cauchy horizon arise in its spacetime development. Christodoulou's strong cosmic censors…

Let $B$ be a spatial region and let $C$ denote its circumferential radius. Thorne's hoop conjecture. A horizon will be present within $B$ if the mass within $B$ exceeds the mass of…

Let $g_{a,M}$ denote a member of the two-parameter family of Kerr black-hole spacetimes, with zero cosmological constant and $a<M$. Kerr stability conjecture. Any slightly perturbe…

Let $(\boldsymbol{\rm X},\boldsymbol{\rm g})$ be an asymptotically flat, stationary vacuum Einstein spacetime. Black hole uniqueness conjecture. The spacetime is the Kerr spacetime…

Consider a thermal quantum system at temperature $T$, and let the out-of-time-order correlation (OTOC) quantify information scrambling. When the OTOC grows exponentially, write the…

The strong cosmic censorship conjecture concerns the interiors of generic black-hole spacetimes and the possibility of extending their spacetime metrics beyond the Cauchy horizon.…

Let $(\mathcal{M}_{AdS},g_{AdS})$ denote the trivial anti-de Sitter solution, let $\mathcal{I}$ be its conformal boundary, and consider arbitrarily small perturbations of its initi…

Hawking's chronology protection conjecture. The laws of physics prevent the formation of time machines or spacetime regions containing closed timelike curves.

Let $(M,g)$ be a non-flat $\operatorname{AF}_0$ gravitational instanton. Schwarzschild uniqueness conjecture. The metric $g$ is, up to isometry, the Schwarzschild metric. Evidence…

Black hole no-hair conjecture. Black holes in nature are conjectured to be described by these three quantities alone.

A space-periodic vacuum configuration is a regular static vacuum spacetime whose geometry repeats periodically along an axis, as in the Myers–Korotkin–Nicolai solutions. Myers's co…

Let $(\mathcal{M},\overline{g})$ be the maximal Cauchy development of complete, generic vacuum initial data lacking trapped or marginally trapped surfaces. Let $\mathcal{J}^+$ be i…

The Unruh state is a distinguished quantum state for a massless field on a black-hole spacetime, constructed here in the slowly rotating Kerr setting and shown in the source to hav…

Let $\mathcal{Q}^+$ be the quotient of the maximal future development, $J^-(\mathcal{I}^+)$ the causal past of future null infinity, $\mathcal{A}$ the apparent horizon, and…

Let $\mathcal{I}^+$ denote future null infinity, and consider the admissible data in the one-ended spherically symmetric Einstein–Maxwell–Klein–Gordon model. Weak Cosmic Censorship…

Consider a generic gravitational-collapse scenario in which a scalar field evolves in the spacetime generated by Cauchy initial data. Let the scalar field's decay along the event h…

Let an AdS Kerr black hole in $d$ dimensions be a higher-dimensional rotating black-hole solution with a negative cosmological constant, and let its Ricci-flat Kerr counterpart be…

Let $E$, $B$, $X$, and $Y$ satisfy the stated asymptotic, axis, and event-horizon boundary conditions for a stationary and axisymmetric black-hole solution. The parameters are angu…

Let $\mathcal{H}^+$ be the future event horizon and let … is satisfied on $\mathcal{H}^+$. This is stated as a stronger conjecture implying the absence of future Cauchy horizons; t…

Extension principle. An extension principle analogous to the one formulated by Mihalík should hold in the non-trapped region.

In Einstein–Yang–Mills theory, consider black hole solutions with non-trivial Yang–Mills fields and horizon charges encoding the relevant horizon data. Corichi–Nucamendi–Sudarsky c…

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…

Stationary-state conjecture. The time-asymptotic state is just the superposition of several known stationary solutions, including charged Kerr black holes and the static coupled so…

Let … . This would extend the previously discussed exclusion of Kasner-like and BKL-type behavior to black-hole interiors, but the claim remains conjectural because generic collaps…