Kerr Problems — Recent Updates https://kerrproblems.com Open problems in Kerr black hole physics K-001 — Full nonlinear stability of subextremal Kerr https://kerrproblems.com/problems/K-001 Prove that asymptotically flat vacuum initial data sufficiently close to a Kerr slice with |a|<M evolve to a spacetime with complete future null infinity, a regular event horizon, and quantitative con... Sun, 05 Apr 2026 00:00:00 GMT https://kerrproblems.com/problems/K-001 K-002 — Uniform nonlinear stability as a→M− https://kerrproblems.com/problems/K-002 Prove a version of Kerr stability whose constants and decay estimates remain uniform, or quantitatively controlled, as the spin approaches extremality.... Sun, 05 Apr 2026 00:00:00 GMT https://kerrproblems.com/problems/K-002 K-003 — Nonlinear asymptotic completeness near Kerr https://kerrproblems.com/problems/K-003 Construct a nonlinear scattering map between near-Kerr initial data and asymptotic radiation data at null infinity plus final Kerr parameters.... Sun, 05 Apr 2026 00:00:00 GMT https://kerrproblems.com/problems/K-003 K-004 — Peeling and polyhomogeneous null infinity for near-Kerr https://kerrproblems.com/problems/K-004 Prove a sharp asymptotic expansion for curvature and connection coefficients at future null infinity for nonlinear near-Kerr evolutions.... Sun, 05 Apr 2026 00:00:00 GMT https://kerrproblems.com/problems/K-004 K-005 — Sharp nonlinear Price law for curvature https://kerrproblems.com/problems/K-005 Prove optimal late-time inverse-power decay for gauge-invariant curvature quantities and relevant metric coefficients in nonlinear near-Kerr evolution.... Sun, 05 Apr 2026 00:00:00 GMT https://kerrproblems.com/problems/K-005 K-006 — Kerr stability with BMS charges and nonlinear memory https://kerrproblems.com/problems/K-006 Build a Kerr stability theorem that simultaneously controls Bondi mass/angular momentum aspects, BMS ambiguities, and nonlinear memory observables.... Sun, 05 Apr 2026 00:00:00 GMT https://kerrproblems.com/problems/K-006 K-007 — Einstein–Maxwell stability near Kerr https://kerrproblems.com/problems/K-007 Prove asymptotic stability for coupled gravitational and electromagnetic perturbations near a rotating black-hole endstate.... Sun, 05 Apr 2026 00:00:00 GMT https://kerrproblems.com/problems/K-007 K-008 — Full stability of asymptotically flat Kerr–Newman https://kerrproblems.com/problems/K-008 Prove linear and then nonlinear stability of the full subextremal Kerr–Newman family without small-charge or slow-rotation assumptions.... Sun, 05 Apr 2026 00:00:00 GMT https://kerrproblems.com/problems/K-008 K-009 — Einstein–massive Klein–Gordon near Kerr endstates https://kerrproblems.com/problems/K-009 Classify whether small Einstein–massive KG perturbations near Kerr disperse to Kerr, form long-lived clouds, or trigger nonlinear superradiant phenomena.... Sun, 05 Apr 2026 00:00:00 GMT https://kerrproblems.com/problems/K-009 K-010 — Nonlinear superradiant endstates in Kerr–AdS https://kerrproblems.com/problems/K-010 Determine the theorem-level nonlinear endstate for small perturbations of Kerr–AdS in the presence of reflecting infinity and superradiance.... Sun, 05 Apr 2026 00:00:00 GMT https://kerrproblems.com/problems/K-010 K-011 — Spin fields on dynamical near-Kerr backgrounds https://kerrproblems.com/problems/K-011 Prove robust decay and Morawetz estimates for spin 1 and spin 2 fields on time-dependent metrics that stay close to Kerr within a nonlinear bootstrap regime.... Sun, 05 Apr 2026 00:00:00 GMT https://kerrproblems.com/problems/K-011 K-012 — Low-regularity Kerr stability threshold https://kerrproblems.com/problems/K-012 Find the minimal differentiability and asymptotic-flatness assumptions under which a Kerr stability theorem can hold.... Sun, 05 Apr 2026 00:00:00 GMT https://kerrproblems.com/problems/K-012 K-013 — Formation plus relaxation to Kerr https://kerrproblems.com/problems/K-013 Prove a global theorem in which generic asymptotically flat vacuum data form a black hole and the exterior subsequently relaxes to Kerr with quantitative radiation control.... Sun, 05 Apr 2026 00:00:00 GMT https://kerrproblems.com/problems/K-013 K-014 — Nonlinear decay versus resonance expansions https://kerrproblems.com/problems/K-014 Relate late-time nonlinear Einstein dynamics near Kerr to a rigorous resonance/QNM plus tail expansion.... Sun, 05 Apr 2026 00:00:00 GMT https://kerrproblems.com/problems/K-014 K-101 — Strong Cosmic Censorship threshold for Kerr interiors https://kerrproblems.com/problems/K-101 Determine the strongest regularity class in which the maximal globally hyperbolic development of generic near-Kerr vacuum data is inextendible across the Cauchy horizon.... Sun, 05 Apr 2026 00:00:00 GMT https://kerrproblems.com/problems/K-101 K-102 — Derive the interior theorem directly from exterior data https://kerrproblems.com/problems/K-102 Remove interior auxiliary assumptions by proving the Kerr interior Cauchy-horizon picture directly from asymptotically flat exterior Cauchy data and exterior decay.... Sun, 05 Apr 2026 00:00:00 GMT https://kerrproblems.com/problems/K-102 K-103 — Vacuum curvature blow-up rates on the Kerr Cauchy horizon https://kerrproblems.com/problems/K-103 Prove sharp quantitative blow-up rates for curvature or gauge-invariant gravitational quantities along the Kerr Cauchy horizon for generic perturbations.... Sun, 05 Apr 2026 00:00:00 GMT https://kerrproblems.com/problems/K-103 K-104 — Generic C²- or Lipschitz-inextendibility of near-Kerr MGHDs https://kerrproblems.com/problems/K-104 Show that although C^0 extensions can exist, generic near-Kerr vacuum developments admit no extension with enough regularity to preserve a meaningful Einstein evolution across the Cauchy horizon.... Sun, 05 Apr 2026 00:00:00 GMT https://kerrproblems.com/problems/K-104 K-105 — Critical horizon-decay exponent controlling extendibility https://kerrproblems.com/problems/K-105 Identify the exact exterior decay rate along the event horizon that separates weaker extendibility from stronger blow-up at the Cauchy horizon.... Sun, 05 Apr 2026 00:00:00 GMT https://kerrproblems.com/problems/K-105 K-106 — Genericity of lower bounds for linearized-gravity interior instability https://kerrproblems.com/problems/K-106 Prove that the nontrivial lower-bound assumptions appearing in linearized-gravity blue-shift instability results are generic for exterior initial data.... Sun, 05 Apr 2026 00:00:00 GMT https://kerrproblems.com/problems/K-106