A single rotating black hole may be the inevitable fate of any universe that follows Einstein's laws of gravity. This project tests a mathematical prediction called the final state conjecture: that all vacuum spacetimes eventually settle into a Kerr black hole, defined by just two numbers—mass and spin. The key question is whether these black holes are stable. If a spacetime starts close to a Kerr solution, does it stay close, or do tiny ripples grow and tear the geometry apart? The answer sits at the intersection of physics, geometry, and analysis, and the researchers will use techniques from the last three decades to study the linearised Einstein equations, including the extreme case where spin equals mass. This is fundamental science with no immediate practical application. But understanding black hole stability is essential for interpreting gravitational wave signals and for knowing whether Einstein’s theory is mathematically consistent. Past work on similar geometric analysis has underpinned everything from GPS corrections to the mathematics behind medical imaging. A proof of stability would confirm that Kerr black holes are the natural endpoints of gravitational collapse—a deep result about the structure of spacetime itself.
View original technical description
In Newtonian physics, matter produces gravity. In General Relativity, gravity is replaced by curvature: Einstein’s equations tell us that matter on a spacetime causes it to curve. Surprisingly, they also tell us that gravitational energy itself can interact to form nontrivially curved geometries, even in the absence of any matter! One class of examples are black holes, strongly curved spacetimes characterized by having a region which is causally disconnected from its complement. The strong curvature, or “gravitational pull,” associated to black holes suggests that we are fated to end up in one. In mathematics, this expectation goes by the name of final state conjecture: slightly more precisely, it asserts that (the exterior regions of) vacuum stationary black holes are the endstate of a generic initial configuration for Einstein’s equations. All vacuum stationary black holes are conjecturally members of a single two-parameter family, the Kerr family (a,M) with |a|=M. Therefore, a basic test of the final state conjecture is to understand if it holds for initial configurations which are already close to Kerr values. In other words, are Kerr black holes stable? This question is fundamentally interdisciplinary in nature: it lies at the intersection of Physics (it concerns a physical theory), Geometry (the object of study is spacetime), and Analysis (stability is best understood in the language of differential equations). In this project, mainly relying on techniques from Geometry and Mathematical Analysis developed in the last 3 decades, we seek to understand the stability properties of Kerr black holes under the linearization of the Einstein vacuum equations, up to and including the extremal case |a|=M. In the subextremal case |a|
Plain English summaries and category classifications on this site are generated by AI and may not perfectly reflect the original research.
Is something wrong? Let us know