Sergiu Klainerman
Princeton University, NJ·Mathematics & Statistics
Many of the key equations of physics are nonlinear: their solutions can interact with themselves in complicated ways, especially when fields are strong. Black holes, gravitational collapse, shock-like waves in gases and light moving through crystals are all governed by such equations.
- Fields
Mathematics & Statistics
Physics
Astronomy & Astrophysics
- Topics
general relativity
Kerr black holes
black hole stability
- Grants
- 1 known grant, through Jul 2027
What they work on
- Work toward proving the nonlinear stability of Kerr black holes with large angular momentum, removing the main obstacle to extending known results for slowly rotating black holes.
- Study gravitational collapse, the formation of trapped surfaces and cosmic censorship in general relativity using a new approach based on foliations of spacetime.
- Investigate whether multi-dimensional rarefaction waves in gas dynamics remain stable, extending the well-understood one-dimensional theory.
- Analyze wave propagation in non-isotropic media, such as in crystal optics, as a stability problem in electrodynamics.
More about the research
Proving what these equations do over long times, such as whether a solution stays stable or forms a singularity, is a central challenge in mathematics. It also tends to require new techniques that later prove useful elsewhere.
Why it matters
This is basic mathematical research. Proving that rotating black holes are stable would give firm mathematical support to a central picture in general relativity and astrophysics. The geometric methods developed may also clarify how nonlinear equations behave in gas dynamics and electrodynamics, and could inform other areas of mathematical physics.
Known grants
From NIH and NSF research grants. Labs often have other funding we can't see.
Closest labs
Peter Hintz
Pennsylvania State University, PA·Mathematics & Statistics
Prove nonlinear stability of Kerr black holes, the standard model of a rotating black hole, for all spins below the maximum, showing that small disturbances decay over time, using geometric and microlocal analysis of wave equations.
Sung-Jin Oh
University of California-Berkeley, CA·Mathematics & Statistics·Early-career
Prove a forward-in-time scattering criterion for initially outgoing solutions of the energy-critical wave maps and hyperbolic Yang-Mills equations, as a step toward the soliton resolution conjecture in the one-soliton regime.
Lee Lindblom
University of California-San Diego, CA·Physics
Develop a way to determine the neutron-star equation of state, the pressure–density relationship of matter inside neutron stars, from observations and strong-gravity theory, without assuming any particular microphysics of that matter.
The school
Princeton University: 26 labs on PI Pages, $559M a year on research, 403 research doctorates a year.
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