28 problems

Weyl-law conjecture. A version of Weyl’s law should also apply to non-selfadjoint black-hole operators.

Let $A$ be the area of a black hole's event horizon, let $l_P$ be the Planck length, and let $\kappa$ be a dimensionless constant of order unity. Bekenstein's event-horizon area qu…

Let $X$ be a Calabi–Yau threefold, and consider type IIA string theory compactified on $X$. Fix the magnetic D6- and D4-brane charges $P_{6}$ and $P_{4}$, and sum over electric D2-…

A black hole is characterized by a horizon whose quantum properties are encoded in the horizon itself. 't Hooft's horizon conjecture. The horizon itself should encode the quantum p…

Consider a massless minimally coupled scalar field in the in-vacuum state of a collapsing null-shell spacetime, and compare its renormalized stress-energy tensor with the correspon…

Let $t_s$ denote late Schwarzschild time, and consider gravitational perturbations of the collapsing null-shell spacetime with lowest angular multipole $\ell_{\min}=2$. Gravitation…

Let $\widehat{\mathfrak M}$ be a moduli space of Cauchy data on $\mathbb R^3$ for a matter-model and symmetry-class combination in which an exact extremal Kerr--Newman event horizo…

Let $\mathcal C=C_\mathrm{out}\cup \underline C{}_\mathrm{in}$ be a bifurcate null hypersurface, and let $\mathfrak M=\mathfrak M(\mathcal C)$ be the corresponding moduli space for…

Let the moduli space of solutions of the Einstein equations contain asymptotically extremal Reissner--Nordström black holes, and let the black hole formation threshold be the bound…

The examples under consideration are fine-tuned one-parameter families of smooth, spherically symmetric solutions exhibiting extremal critical collapse, meaning critical collapse i…

Let $M_{irr}=\sqrt{A/(16\pi)}$ be the irreducible mass, let $J$ be angular momentum, let $Q$ be electric charge, and let $E_{EM}$ denote the electromagnetic contribution. Kerr–Newm…

Stretched-horizon conjecture. Strings can spread over the horizon, forming a membrane-like structure known as the stretched horizon. The black-hole horizon may be governed by an op…

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 sourced wave equation … where $H$ is the Heaviside function, $\omega=0.5-0.1i$, and $\ell$ denotes the angular mode number. Suppose the source produces a late-time tai…

The charges of a single-centered $\frac{1}{4}$-BPS black hole are encoded by integers $(m,n,\ell)$, and let $d_*(m,n,\ell)$ denote the immortal dyon index, namely the indexed degen…

Charged-black-hole stability conjecture. Charged black holes remain stable against charged massive boson perturbations.

Black hole radiation behaves as black-body radiation with finite temperature and resembles a thermodynamic system characterised by entropy and other thermodynamic quantities. Maxim…

Gnat description conjecture. The interior of black holes should have a consistent description entirely in terms of gnats; consequently, when a black hole evaporates, it should do s…

Near a black-hole horizon, consider a particle–antiparticle pair produced in the Hawking-radiation process, with $l_p$ denoting the Planck length. Planck-scale separation conjectur…

Let $M$ be the black-hole mass, $\omega$ the frequency, and $f(z)=1-1/z$. For the radial Teukolsky equation and the alternative equation … with … where $c=a\omega$, the rotation pa…

A stationary event horizon is a null boundary with associated symmetries and charges. Stationary-horizon information conjecture. The symmetries and charges at stationary event hori…

Let $(\phi,F)$ be a solution of the Maxwell-Charged-Scalar field system with no particular symmetry assumption on a Reissner--Nordström space-time. Define the Maxwell charge $Q$ by…

Let $\Phi_\ell$ be the scalar field mode of angular momentum $\ell$, let $D^{(\ell)}_{i_1,i_2,\cdots,i_\ell}$ be the differential operator appearing in the ladder-operator construc…

A black hole horizon with its probes can be regarded as a closed quantum system, whose entropy is $S$ and inverse temperature is $\beta$. The fast-scrambler conjecture. Black hole…

Refined OSV conjecture. The refined black hole partition function has a large $N$ dual captured by refined topological string amplitudes.