12 problems

Let initial data be prescribed on a big bang singularity, and consider quiescent solutions to Einstein's equations, meaning, roughly, solutions whose leading-order asymptotics are…

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…

Let $u'$ be the derivative component of a vector field $u$ in the interval-arithmetic framework for recursively solving initial value problems. A value of $u'$ is non-maximal when…

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 $\mathcal C$ be an initial constant-time surface, let $\mathbf E^{\rm in}$ and $\mathbf B^{\rm in}$ be initial electric and magnetic fields on $\mathcal C$, and let…

Let $\mathcal C$ be an initial constant-time surface, let $(\chi_{\rm in},\dot\chi_{\rm in})$ be classical initial data on $\mathcal C$, and let $\omega_{\mathcal C}$ be a state on…

Let $\chi$ be the classical scalar field, let $\omega_{\mathcal C}$ be an initial state on an initial surface $\mathcal C$, and consider the three 3-smeared initial two-point funct…

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…

Rough-dependence conjecture. High-Reynolds-number violent turbulence is caused by rough dependence on initial data rather than by the sensitive dependence on initial data associate…