61 problems

In the exterior region of a black hole, the bulk entropy $S_{bulk}(\rho)$ is regulated by a bulk UV cutoff, while the area term in the quantum extremal surface formula depends on N…

Let a gravitational-collapse spacetime arise from one-ended initial data on a hypersurface $\Sigma$. For a point $p$ on a spacelike singularity $\mathcal{S}$, say that its causal p…

Consider smooth developments of the Einstein–Maxwell–Klein–Gordon system as in Theorem 1.1, with coupling parameter $\mathfrak{e}\neq 0$. Let $\mathcal{Q}^+$ be the quotient spacet…

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…

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…

Consider generic initial data giving rise to a perturbation of a Kerr black hole governed by the Einstein vacuum equations, and let the perturbed spacetime have a Cauchy horizon. I…

Let $\mathcal{H}$ and $\mathcal{I}$ denote the horizon and null infinity, respectively. Consider smooth scattering data settling down to a possibly extremal Kerr solution on…

Let $(\mathbf{E}_1,\mathbf{P}_1,\mathbf{J}_1)$ and $(\mathbf{E}_2,\mathbf{P}_2,\mathbf{J}_2)$ lie in $\mathbb{R}_+\times\mathbb{R}^3\times\mathbb{R}^3$, with…

Let the initial data contain $n$ disjoint outermost marginally outer trapped surfaces (MOTS) $\{\Sigma_i\}_{i=1}^n$, with areas $A_i$ and angular momenta $J_i$. Multi-horizon exten…

Let $(\mathcal{M},\mathbf{g})$ be a regular, stationary (appropriately defined), four-dimensional vacuum black hole solution of the Einstein vacuum equations with positive cosmolog…

Black hole settling-down conjecture. At $\Sigma_{t'}$, with $t'\gg t$, the spacetime will be described by a stationary metric. This is a dynamical black-hole statement: after black…

A strongly asymptotically predictable spacetime $(M,g_{\mu\nu})$ has black hole region … where $J^-(\mathscr{I}^+)$ is the causal past of future null infinity and $\psi$ is the ass…

Let $\boldsymbol\gamma=(\gamma_1,\ldots,\gamma_n)$ be an ordered collection of charges, let $\hat{\boldsymbol\gamma}$ denote the corresponding hatted charge data, and let…

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

Extreme black hole uniqueness conjecture. At least one tangent map parameter must be nonzero:

Consider very slowly rotating extremal Kerr–Newman black holes, with parameters satisfying $M^2=e^2+a^2$ and $|a|\ll M$, in the setting without spherical symmetry. Let the regulari…

Let $\mathfrak M$ be a Banach-space moduli space of initial data, and for $\mathfrak r\in[0,1]$ let $\mathfrak M^\mathfrak r_\mathrm{stab}\subset\mathfrak M$ consist of initial dat…

Let Kerr-AdS be a rotating asymptotically anti-de Sitter black-hole solution of the Einstein vacuum equations, and impose Dirichlet boundary conditions. A generic perturbation of i…

Rational-coefficient representation conjecture. The coefficients $e_{\mathcal{T}}$ are rational numbers depending only on the topology of $\mathcal{T}$. This proposed representatio…

An asymptotically flat solution of the vacuum Einstein equations is said to approximate $n$ outgoing black holes in a neighbourhood of future timelike infinity $i_+$. Outgoing blac…

Consider vacuum gravitational collapse, governed by … The rotating extremal Kerr solution plays the role of extremal Reissner–Nordström. Vacuum extremal-collapse conjecture. Extrem…

Consider ${\rm S}^{1}$-symmetric black holes whose fixed-point set, called the axis, is compact, and suppose the black hole has ends at which its charge is nonzero. Compact-axis bl…

Let $V\subset M$ be a precompact open set. For sufficiently small $\epsilon>0$, let $g_\epsilon$ be the formal solution on $M_\epsilon$ obtained by gluing small Kerr black holes al…

Let $g$ be a spacetime metric satisfying the vacuum Einstein equations … A Cauchy datum is regular and one-ended when it is regular and has one asymptotically flat end, and gravita…

Let $(\hat\gamma,\hat k)$ denote boosted subextremal Kerr black hole initial data with parameters $\hat{\mathfrak{m}}$ (mass) and $\hat{\mathfrak{a}}$ (specific angular momentum).…