Relativistic Perturbations

Historically, hyperboloidal compactification has been mainly considered by mathematical relativists. After the explicit construction of hyperboloidal scri-fixing and the demonstration of its benefits for scalar and gravitational perturbations, the method has become a useful tool with applications to many areas of black-hole perturbation theory, including the self-force and effective-one-body approaches to the binary black-hole problem.

This project includes the following topics:

• Astroseismology: Extend the applications of hyperboloidal foliations to stellar oscillations.
• Cosmological perturbations: Investigate relativistic perturbations of asymptotically de Sitter spacetimes using hyperboloidal methods.
• Time-symmetric methods: Explore the application of unconditionally stable time-symmetric integrators to long-time evolution of black-hole perturbations.
• Massive fields at null infinity: Study the asymptotic behavior of massive scalar fields near null infinity by using hyperboloidal compactification.