Transcending the Boundaries of Holography

In this project, I will develop new and timely methods for studying gravity in asymptotically flat spacetime and in the region near black hole singularities, along with their possible holographic interpretations. The thermodynamics associated to black hole event horizons suggests a holographic description in terms of a quantum theory without gravity in fewer dimensions. From string theory, such holographic dualities have been constructed and were tested to amazing precision, but all currently-known examples rely crucially on a negative cosmological constant, which prevents us from using them to make predictions for black holes in our universe. On the other hand, approximating gravity near spacelike singularities has long been known to lead to rich and chaotic dynamics, which therefore appears to be a fundamental property of black holes. However, its relation to known holographic descriptions of black holes is still mysterious.Very recently, I established a new and systematic method of approximating gravity near singularities using dynamical Carroll geometry. By implementing the ultra-local limit of such approximations off shell, my method leads to tractable models in settings previously only accessible with supercomputer simulations, including spatial inhomogeneity and subleading corrections. It is also connected to several recent developments identifying near-singularity chaotic dynamics in AdS/CFT holography. Additionally, using related techniques, I will work towards more realistic holographic models with zero cosmological constant. Here, I will address key roadblocks by establishing how asymptotically flat spacetime metrics are determined by a general null boundary metric, energy-momentum tensor and radiation, which will also allow me to derive consistent ways of quantizing dual Carroll field theories. Through this project I will therefore make key advances in our understanding of black holes and their singularities in gravity and holography.