Skip to main content
European Commission logo print header

Infinite-dimensional symmetries, black holes, and holography

Periodic Reporting for period 1 - HoloBH (Infinite-dimensional symmetries, black holes, and holography)

Período documentado: 2019-08-01 hasta 2021-07-31

Black holes are at the root of the most striking puzzles that arise when attempting to combine the principles of quantum mechanics and Einstein’s theory of gravitation; they are therefore thought to be key to a formulation of a theory of quantum gravity.

In recent years, progress in our understanding of the elusive quantum nature of black holes has been made thanks to the so-called holographic principle. The latter establishes that the behavior of gravity in a given region of space is actually entirely encoded in terms of a different system, which lives only along the edge of that region. As such, it provides physicists with a dictionary that translates complicated problems into accessible ones. However, the holographic principle has not been developed yet for realistic kinds of spacetimes, such as the ones describing the universe we live in. The first overall objective of this research project is to fill this gap by developing a holographic correspondence for spacetimes which are of relevance for most astrophysical purposes; those spacetimes are the so-called asymptotically flat spacetimes.

The second overall objective of this project is to address some of the unresolved key issues in black hole physics, especially the mysterious origin of their vast entropy. The approach taken in this project is based on a recently discovered intriguing set of infinite symmetries (called ‘soft hair’) that appear close to black hole horizons. These symmetries were previously overlooked, and were hence expected to give important novel insights into the physics of black holes as they strongly constraint physical processes that occur in their vicinity.

We live an exceptional period to study black holes: we now have access to astrophysical observations of a very high accuracy, while the Event Horizon Telescope is providing us with genuine black hole images, including the one in the center of nearby galaxies. The importance of this research project comes from the deep implications of its outcomes in our understanding of black hole physics, and the fact that the discoveries made about the holographic nature of asymptotically flat spacetimes unveil new connections between physical theories and shed new light on the fascinating universal features of gauge theories and gravity.

The conclusions of this Marie Sklodowska-Curie (MSC) action are: 1) infinite-dimensional symmetries give fundamental insights on the universal principles that organize the degrees of freedom in gravitational theories; 2) the interconnection between black hole and asymptotic symmetries is key in order to unveil the fundamental holographic nature of black holes.
In this project, we investigated the emergence of infinite-dimensional symmetries in the near-horizon region of black holes in novel set-ups. The work performed consisted in prescribing a good set of boundary conditions for the gravitational fields near black holes event horizon, which is in general a very delicate task. We managed to provide such near-horizon boundary conditions and showed that the symmetries preserving this mathematical structure were extremely rich, as they turn to be in an infinite amount. We know from Noether’s theorem that each symmetry is associated to a physical conserved quantity. In this context, we used advanced methods in General Relativity to construct the Noether charges associated to near-horizon symmetries. We showed that they are physical as they act in a non-trivial way on a given black hole configuration and endow the latter with an infinite amount of soft hair.

In the second part of this project, we considerably extended the holographic paradigm for asymptotically flat spacetimes by making important advances in the program of celestial holography. This program proposes to associate to each massless particle in the four-dimensional spacetime an operator of a two-dimensional conformal field theory that lives on the sphere at null infinity (called the celestial sphere). In order to make the conformal (and hence holographic) properties of scattering processes more manifest, we worked in the so-called conformal basis instead of the usual momentum space for plane waves. The wavefunctions that are obtained in this framework have the considerable advantage of transforming as conformal primaries on the celestial sphere. The main results of this part of the project was to provide a unified treatment of the holographic dual modes that are associated to important factorization theorems in gauge theory and gravity.

An important open question in the field is to understand how the celestial sphere symmetries are related to the near-horizon symmetries when considering black hole spacetimes that are asymptotically flat. One of the main results of this project was to show that it is possible to map horizon symmetries with the symmetries appearing at the asymptotic boundary of conformally flat spacetimes by using conformal maps. By doing so, we encountered a new type of infinite-dimensional symmetry that we called 'superdilations' that gives rise to new features and had not been evidenced so far.

All results obtained were disseminated in scientific publications in the best peer-reviewed journal of the field, as well as in form of pre-prints in the open access The results were also disseminated via a great number of seminars at research institutions and several presentations at international workshops and conferences.
While the holographic principle is expected to be a fundamental principle of quantum gravity, its best developed implementation requires spacetimes with negative cosmological constant, in the framework of the so-called Anti-de Sitter/CFT correspondence. A fully-fledged holographic description of realistic kinds of spacetimes is still missing. This research project made important progress towards filling this gap, by developing a holographic correspondence for spacetimes which look flat from a far distance, which is of relevance for most astrophysical purposes.

In this MSC action, we also made important new advances in theoretical aspects of black holes by investigate further the origin of their thermodynamical properties. The approach we took was based on recently discovered intriguing set of infinite symmetries that appear close to black hole horizons. These symmetries were previously overlooked in the literature, and the fact that we showed that they emerge in a systematic way in different contexts gives important novel insights into the rich spacetime structure of black hole geometries.

Because almost the entirety of this action is based on symmetries and algebraic ideas, it guarantees that the outcomes of the work performed will be of interest beyond the time-frame of the project and that they will be applicable to an even wider range of scientific questions. Indeed, results based on symmetry principles are guaranteed to remain of particular importance in theoretical and mathematical physics and to be later adapted to other contexts. With this work, we have gained new insights on the universal principles that organize the symmetries in gravity, and thus made a big step forward in our understanding of the mysterious nature of the microscopic degrees of freedom in quantum gravity.
Conformal maps relating the black hole horizon with infinity