The results of WP1 and WP2 have allowed us to reduce the number of assumptions put in the derivation of an effective BH geometry extending spacetime beyond the classical singularity, by developing a framework that is closer to the full Loop Quantum Gravity techniques. Along this direction, there is already advanced work in progress towards the first construction of a shear operator, which is expected to be completed by the end of the year. Application of these new techniques to the near horizon BH geometry can then be used to predict Planckian corrections to the gravitational waveform of BH mergers. At least preliminary results on this topic of the proposal are expected by the end of the project.
The lines of research pertaining to WP3 and WP4 of the proposal are the ones that have been particularly successful, producing results that contributed to open a new conservation between different scientific communities. In particular, the new mathematical approach to the investigation of symmetries has revealed the existence of an infinite tower of new charges that clarified the connection of results previously obtained in the context of celestial holography to the phase space of gravity. Moreover, these new higher spin charges have attracted attention also from the gravitational wave community, as they have been connected to the multipole expansions of the gravitational radiation close to null infinity, as well as to the associated subleading gravitational memory effects.
Work in progress with the supervisor at the partner organization, as well as with some of the primary researchers in those communities based in Europe, are expected to generate important progress in the programme of reconstructing an asymptotically flat metric from holographic data. In particular, by the end of the project a more clear dictionary between the multipole moments and the complex charges forming the higher spin charge algebra is expected to be derived, thus bringing promising perspectives in the gauge invariant quantization of the gravitational field with asymptotically flat boundary conditions. Moreover, gravitational memory effects have been shown to have an observable effect from binary-black-hole mergers, which will also allow the subleading infrared properties of gravity to be studied observationally by future gravitational-wave detectors.
This way, the project has already contributed to improve the competitiveness of cutting-edge European research in the field, with the potential to influence the policy of large experimental scientific collaborations, and create a more competitive EU market, capable of attracting new scientists and further research funding at the international level.
