Peter Hintz
Pennsylvania State University, PA·Mathematics & Statistics
Black holes are regions of space where gravity is so strong that not even light can escape. Gravitational waves are ripples in space and time.
- Fields
Mathematics & Statistics
Physics
- Topics
general relativity
black holes
Kerr spacetime
- Grants
- 1 known grant, through May 2028
What they work on
- 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.
- Analyze the stability of several classes of spacetimes containing many black holes, using tools from hyperbolic partial differential equations, the mathematics of waves, together with spectral and scattering theory.
- Construct solutions of Einstein's field equations for large-mass-ratio black hole mergers and for black hole scattering, and give a precise description of their overall geometry using geometric singular analysis.
More about the research
Detectors have measured these waves coming from pairs of black holes that spiral together and merge. After a merger, the single black hole left behind quickly settles into a steady state, a process called ringdown. Einstein's equations of general relativity describe all of this, but they are hard nonlinear partial differential equations. Nonlinear means effects feed back on themselves; partial differential equations describe how quantities change across space and time. Computer simulations can solve these equations approximately, yet basic questions still need rigorous mathematical proof.
Why it matters
This is basic mathematical research. Proving that black hole models are stable would put the black hole descriptions used in astrophysics and gravitational-wave astronomy on firm theoretical ground. The new methods for wave equations may also be useful for other problems involving waves and hyperbolic equations.
Known grants
From NIH and NSF research grants. Labs often have other funding we can't see.
Closest labs
Sergiu Klainerman
Princeton University, NJ·Mathematics & Statistics
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.
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.
Xuwen Zhu
Northeastern University, MA·Mathematics & Statistics
Study how gravitational instantons, four-dimensional spaces that solve Einstein's equations, degenerate and how their moduli spaces are structured, using geometric microlocal analysis and PDE techniques.
The school
Pennsylvania State University: 60 labs on PI Pages, $1.3B a year on research, 743 research doctorates a year.
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