9 problems

Self-consistent initial-data conjecture. Self-consistent initial data for the fourth-order time derivatives of the metric can be obtained from these classical initial data by solvi…

In semiclassical gravity, consider gravitational and quantum initial data on an initial surface, and let their Cauchy development be the resulting spacetime and quantum field confi…

Let $g_{ij}$ be a continuous induced metric on a collapse surface, and decompose the extrinsic curvature as … where $C_i$ is divergence-free and $L_{ij}$ is transverse-traceless. P…

Let $\mathcal C$ be a 3-manifold with $\hbar$-dependent initial metric $g^{\rm in}_{ij}$ and extrinsic curvature $K^{\rm in}_{ij}$, and let $\omega_{\mathcal C}$ be an $\hbar$-depe…

Let $\mathcal C$ be a 3-manifold with classical initial data $(g^{\rm in}_{ij},\dot g^{\rm in}_{ij},g^{(2)\,\rm in}_{ij},g^{(3)\,\rm in}_{ij})$, or…

Let $\mathcal C$ be an initial surface, let $\omega_{\mathcal C}$ be an initial state, and let $g^{(r)}$ denote the $r$th time derivative of the metric on $\mathcal C$. Semiclassic…

Let $g_{ij}$ be the induced metric and let $K_{ij}=\frac{1}{2}\dot g_{ij}$ be the extrinsic curvature on an initial surface. A physical solution is a solution smooth in $\hbar$ at…

Graham–Olum conjecture. The AANEC holds for any self-consistent solution in semiclassical gravity.

Universality conjecture. For macroscopic black holes formed by smooth infalling matter profiles of compact support, these universalities will continue to hold soon after the GDH tu…