Project description
The Kerr metric describes the geometry of a rotating black hole and plays a central role in modern gravitational physics. Understanding gravitational perturbations on a Kerr background is essential for several key applications. In particular, black hole perturbation theory underlies the calculation of gravitational waves emitted in extreme mass-ratio inspirals, where a small black hole orbits a supermassive one, and it governs the quasi-normal mode spectrum that characterizes the gravitational wave signal following the merger of two black holes.
A major milestone in this field was Teukolsky’s 1973 discovery, using the Newman–Penrose formalism, of a single separable second-order equation governing perturbations of certain Weyl curvature scalars. Solutions to the Teukolsky equation encode the gravitational degrees of freedom, and the associated metric perturbations can be reconstructed by acting on these solutions with appropriate differential operators.
In parallel, there exists a powerful chiral formulation of General Relativity, originating in the work of Plebanski in the late 1970s. This formalism rewrites the Einstein equations in a self-dual language and can be viewed as taking a “square root’’ of the usual second-order field equations. As a result, it naturally introduces geometrically meaningful first-order differential operators.
The aim of this project is to apply the chiral formalism to the problem of perturbations around the Kerr black hole. The expectation is that the first-order structure inherent in the chiral approach may lead to simplifications, new insights, or alternative formulations of the standard Teukolsky framework. Ultimately, the project seeks to develop a chiral version of black hole perturbation theory and to explore its implications for gravitational wave physics.