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A New Strategy for Gravity and Black Holes

Periodic Reporting for period 4 - GravBHs (A New Strategy for Gravity and Black Holes)

Reporting period: 2021-04-01 to 2021-09-30

Black holes play a central role in the investigation of the Universe. We are fortunate to live in an era when this has become a widely appreciated truism, both in the observational front ---with the recent historic breakthroughs from the LIGO-Virgo collaboration, and the images from the Event Horizon Telescope--- and in the theoretical front, where the study of black holes provides a unique entry into the problem of uniting the physics of the very small ---quantum physics--- and the physics of the very large ---gravitational physics. Black holes naturally excite the imagination of scientists and laypeople alike. Their mystery and fascination makes them the perfect vehicle to convey why fundamental research on the Universe, even in its apparently remotest confines, is an intensely human endeavour which, even if not of immediate practical applicability, is of paramount interest to the society at large.

Unraveling the dynamics of black holes is an extremely intricate problem, due to the complexity of solving Einstein's equations of General Relativity in the fully non-linear regime where black holes become most interesting. Big efforts have been made to tackle this problem with the help of supercomputers ---certainly an invaluable tool, but also one that has serious shortcomings: the big expense required, in time and resources, and perhaps more importantly, the 'black box' opaqueness of its outcomes, which often yield relatively little physical insight. Novel, fresh approaches to gravitational dynamics can have a substantial impact, both in terms of practical improvement and as conceptual clarification.

At the core of this proposal lies a radically new idea that has already shown its potential for simplifying several of the thorniest problems in black hole physics, while still retaining their most interesting aspects. We use the number of spacetime dimensions, D, as an adjustable parameter in the theory. Then, by considering the limit in which D goes to infinity, we find that, in many instances, the equations of the problem simplify to the extent that they can often be solved in a closed, exact form. Subsequently, corrections in powers of 1/D can be computed, which improve the quantitative accuracy of the results.

This approach not only has practical use as an efficient calculational tool. It also sheds new light on dynamical features of black holes. For instance, it has revealed that the fluctuations of the black hole horizon can naturally be separated into two classes, one of which retains the peculiar features of a black hole, while the other class is common and universal to most types of black holes. This discovery has led to the development of simple, effective theories of black hole fluctuations that have been efficiently applied to a variety of problems, including applications to the 'holographic AdS/CFT' correspondence. We expect that further new insights can be obtained in other pressing problems in gravitational physics, in particular on the appearance and significance of 'naked' spacetime singularities, and on the quantum theory of black holes.

Given the current high level of public interest in all aspects of black holes, our team has engaged in a serious effort to reach out to wide audiences, enhancing the visibility of scientists as citizens in the midst of modern society, eager to share and return to the community the fruits of their research.
Our team focused its efforts on developing the effective theory of black holes in the limit of large D, and applying it to solve and illuminate a variety of problems in black hole physics. We have discovered a new and surprisingly efficient way to capture the most interesting dynamics of black holes, based on regarding them as 'blobs' on a black membrane. These blobs not only share all the properties of stationary black holes. They also move and oscillate in a manner that reproduces, easily and accurately, the characteristic vibrational modes of black holes. But this effective theory also allows us to address problems that, with conventional techniques, are extremely hard to solve. For instance, we are able to compute and follow the evolution of a black hole instability deep into the non-linear regime; and we can also perform calculations of black hole collisions using very basic, no-frills resources ---laptop computers, running for a few minutes using commercial software programs--- which conventionally would require complicated codes running for weeks in a supercomputer.

With this method, we have been able to identify a new class of higher-dimensional black hole and investigate the appearance of a naked singularity in the collision of two black holes: a violation of the cosmic censorship conjecture.

We have also given a new formulation of the weak cosmic censorship conjecture that accounts for the currently known violations, while also preserving the main physical content of the original conjecture. On the other hand, we have ruled out the last extant counterexample to strong cosmic censorship after quantum effects are properly accounted for.

Our group has also employed the techniques of braneworld holography to describe in an exact manner the effects of quantum fields on the geometry of a black hole. We have also teamed up with the UCSB group in order to study the currently fast-moving subject of traversable wormholes and their connections with holographic quantum information.

Besides publications in top journals (mostly in Phys. Rev. Lett, JHEP, and Phys.Rev.D) the PI of the project has been invited to write a major review (in collaboration with Prof. Herzog from King's College London) on the large-D limit of Einstein's equations, which has been published in Reviews of Modern Physics -- the most, prestigious, authoritative journal in the field of physics, with an impact factor (in 2019) of 45.037 .We have received invitations to deliver plenary talks and invited colloquia at prestigious conferences and research centers.
We regard our new approach to the dynamics of black holes as 'blobs on a brane' as a significant breakthrough. We have been able to chart out new territory in the phase space of black holes, by identifying new solutions, but more remarkably, by also solving their stability and successfully following their non-linear evolution. The discovery of an unexpected connection between gravitational dynamics and Ricci flows (a connection that requires the consideration of the large D limit) holds great promise.

We already foresee some of the main outcomes of this project. We will have in our hands a new powerful tool to solve problems of black hole dynamics, and also potentially other types of gravitational physics. These techniques are made available to the community in a manageable form explained in our major review article. We will have furthered the understanding of naked spacetime singularities: their appearance, their significance in a physics framework, and the direction to move forward in trying to prove a new form of weak cosmic censorship. On the hother hand, we will have provided the final clinch on the question of strong cosmic censorship once quantum effects are incorporated. Finally, we also will be able to further understand the effect of quantum fields on black holes beyond perturbation theory, on the possibilities of wormhole geometries, and on the physical mechanisms that enforce chronology protection in our universe.
Numerical Evolution of two colliding black holes in 7D with violation of cosmic censorship
Effective-theory evolution of two colliding black holes with violation of cosmic censorship