Tidal deformation of dynamical horizons in binary black hole mergers and its imprint on gravitational radiation

In this work, I study the tidal deformation of black holes in binary mergers in the strong field regime. A different approach to the problem of tidal deformability of black holes is taken using the source multipole moments of their dynamical horizons and numerical relativity, instead of the field multipole moments of the gravitational field at infinity. I compute these source multipole moments in the inspiral phase of binary black hole mergers, uncover several interesting new features in the evolution of the deformations of the dynamical horizon geometry, and characterize how nonspinning black holes deform. Owing to the mutual tidal interactions, I describe how the dynamical horizons of the two black holes deform and steadily acquire various multipole moments that would otherwise vanish when the horizons are isolated. Out of these, the dominant deformation is shown to be quadrupolar. I further show that their evolution has a familiar chirplike behavior. I also find that these deformations encode detailed information about the dynamics of the binary black hole system. Particularly, the dominant quadrupolar deformation is shown to be strongly correlated with the gravitational field of the system at future null infinity. Therefore, the gravitational waves carried away from the system contain imprints of the geometrical structure of the dynamical horizons in the strong-field regime. Thus, although causally disconnected from observers, these correlations may present us with a novel way to probe the strong field structure of gravitational fields in astrophysical scenarios. The results here may be important in the strong field tests of black holes and general relativity, for the no-hair conjecture in the strong field, dynamical regimes, and in astrophysical contexts especially when the black holes are close to the merger.