Periodic Reporting for period 2 - QUABODYP (QUAntum Black hOle DYnamics and Phenomenology)
Berichtszeitraum: 2022-09-01 bis 2023-08-31
Questions related to the fate of singularities in black holes or in cosmological situations are a sign that our current theory of geometry breaks down in such extreme conditions and should be replaced by a more complete, fundamental theory. The problem of quantum gravity consists of constructing a theory of gravity formulated in the language of quantum mechanics and compatible with general relativity, remains unsolved as of today.
The overall objectives of this project are to tackle the implementation of dynamics in quantum gravity in order to address long-standing fundamental theoretical issues, and to study the possibility that related quantum effects could be observable by next-generation detectors. The research methodology is based on two approaches to be carried out in parallel since complementary. The first line of research is more closely related to the Loop Quantum Gravity framework and it relies on a novel approach to implement symmetry reduction at the quantum level. The second line is based on the investigation of the new physical degrees of freedom that arise in presence of a boundary and it is related to field theory techniques employed in the context of gauge/gravity duality. The project applies and combines these new ideas and methods to investigate the fate of classical black hole (BH) singularities, the symmetry algebra of boundary charges (both at finite and infinite distance) and to extract phenomenology through gravitational waves physics techniques.
Since the most energetic astrophysical events in the universe might carry the signature of quantum gravity effects, the potential theoretical and observational implications of the project outcomes will contribute to enhance EU scientific excellence in the field. The project requires a cross-fertilization of expertise from several areas of theoretical physics and will thereby expand the networks of collaborators between the host groups, as well as different European nodes the Researcher interacted with.
The overall objectives of this project are to tackle the implementation of dynamics in quantum gravity in order to address long-standing fundamental theoretical issues, and to study the possibility that related quantum effects could be observable by next-generation detectors. The research methodology is based on two approaches to be carried out in parallel since complementary. The first line of research is more closely related to the Loop Quantum Gravity framework and it relies on a novel approach to implement symmetry reduction at the quantum level. The second line is based on the investigation of the new physical degrees of freedom that arise in presence of a boundary and it is related to field theory techniques employed in the context of gauge/gravity duality. The project applies and combines these new ideas and methods to investigate the fate of classical black hole (BH) singularities, the symmetry algebra of boundary charges (both at finite and infinite distance) and to extract phenomenology through gravitational waves physics techniques.
Since the most energetic astrophysical events in the universe might carry the signature of quantum gravity effects, the potential theoretical and observational implications of the project outcomes will contribute to enhance EU scientific excellence in the field. The project requires a cross-fertilization of expertise from several areas of theoretical physics and will thereby expand the networks of collaborators between the host groups, as well as different European nodes the Researcher interacted with.
The work performed on WP1 and WP2 of the project relied on the construction of a kinematical Hilbert space describing the quantum geometry of a spherically symmetric BH, where the symmetry reduction is imposed at the quantum level. The main results of this investigation collected in one publication were first the derivation, from the full Loop Quantum Gravity theory, of an effective Hamiltonian that can be used to solve for quantum black hole geometries; second, quantum-corrected metrics for the interior BH geometry have been found, showing how the classical BH singularity is replaced by a homogeneous expanding Universe and an asymptotically de Sitter Universe appears in the post-bounce region. These results reveal how a positive cosmological constant can emerge from purely quantum gravitational effects and it opens the way to a “Black hole cosmology” scenario.
The WP3 and WP4 of the project developed an interesting new approach to the problem of dynamics in quantum gravity that is based on the idea that, in the presence of a boundary, the phase space of gauge and gravity theories needs to be extended by edge modes. In the first part of the period covered by the report this new treatment was applied in the context of gravity in a series of 3 publications, that studied in detail the algebra of the boundary symmetry generators for different formulations of gravity. This approach opened the way to a new local holographic description of quantum gravity dynamics in terms of charge conservation laws.
Moreover, this new line of investigation is also deeply connected with the revised understanding of the symmetry group of asymptotically flat spacetimes. Specifically, application of the covariant phase space formalism developed in the first 3 publications to the case of null infinity has led, in 2 following publications, to the proposal of a new extension of the BMS group and a new charge bracket allowing for leaky boundary conditions. Furthermore, transformations under this extended symmetry group of the gravitational phase space quantities have been exploited in another publication to recast the asymptotic Einstein’s equations in a compact and simple form. This new characterization of the phase space of null infinity revealed the existence of a spin-2 charge associated to a new kind of symmetry and whose conservation law has been shown to be equivalent to the sub-subleading soft graviton theorem in yet another publication. Pursuing this investigation further led in a following publication to the proposal of an infinite tower of higher spin charges encoded in the subleading terms of incoming radiation and forming a canonical representation of a w_{1+∞} loop algebra on the gravitational phase space.
The WP3 and WP4 of the project developed an interesting new approach to the problem of dynamics in quantum gravity that is based on the idea that, in the presence of a boundary, the phase space of gauge and gravity theories needs to be extended by edge modes. In the first part of the period covered by the report this new treatment was applied in the context of gravity in a series of 3 publications, that studied in detail the algebra of the boundary symmetry generators for different formulations of gravity. This approach opened the way to a new local holographic description of quantum gravity dynamics in terms of charge conservation laws.
Moreover, this new line of investigation is also deeply connected with the revised understanding of the symmetry group of asymptotically flat spacetimes. Specifically, application of the covariant phase space formalism developed in the first 3 publications to the case of null infinity has led, in 2 following publications, to the proposal of a new extension of the BMS group and a new charge bracket allowing for leaky boundary conditions. Furthermore, transformations under this extended symmetry group of the gravitational phase space quantities have been exploited in another publication to recast the asymptotic Einstein’s equations in a compact and simple form. This new characterization of the phase space of null infinity revealed the existence of a spin-2 charge associated to a new kind of symmetry and whose conservation law has been shown to be equivalent to the sub-subleading soft graviton theorem in yet another publication. Pursuing this investigation further led in a following publication to the proposal of an infinite tower of higher spin charges encoded in the subleading terms of incoming radiation and forming a canonical representation of a w_{1+∞} loop algebra on the gravitational phase space.
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.
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.