General Relativity & Quantum Cosmology

The concept of symmetries is crucial in our comprehension of modern theoretical physics. The Corner Proposal introduces a novel framework where symmetries are reinstated as foundational principles in our understanding of gravity. This aims to describe gravity using a language that is more adapted to quantization. In this presentation, I will start by providing an overview of the essential results leading to the main ideas the proposal. This will then allow me to state the proposal in the general case to then specialize to 1+1 dimensional gravity.

Finally, I will present elements of our recent research applying the proposal to the case of 1+1 dimensional gravity. I will demonstrate the framework's promising potential by calculating the entanglement entropy between two spatial regions—a significant challenge in quantum gravity. The result is the 1+1 dimensional equivalent of the well-established Bekenstein-Hawking area law governing the entropy of gravitational systems with the expected behavior of the quantum corrections.

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Fueling and feedback couple supermassive black holes (SMBHs) to their host galaxies across many orders of magnitude in spatial and temporal scales, making this problem notoriously challenging to simulate. We use a multi-zone computational method based on the general relativistic magneto-hydrodynamic (GRMHD) code KHARMA that allows us to span 7 orders of magnitude in spatial scale, to simulate accretion onto a non-spinning SMBH from an external medium with Bondi radius ~ 2e5 G*M/c^2, where M is the SMBH mass. For the classic idealized Bondi problem, spherical gas accretion without magnetic fields, our simulation results agree very well with the general relativistic analytic solution. Meanwhile, when the accreting gas is magnetized, the SMBH magnetosphere becomes saturated with a strong magnetic field. The density profile varies as ~ r^(-1) rather than r^(-3/2) and the accretion rate is consequently suppressed by over 2 orders of magnitude below the Bondi rate. We find continuous energy feedback from the accretion flow to the external medium at a level of 1% of the accreted rest mass energy (~ 0.01 Mdot * c^2). Energy transport across these widely disparate scales occurs via turbulent convection triggered by magnetic field reconnection near the SMBH. Thus, strong magnetic fields that accumulate on horizon scales transform the flow dynamics far from the SMBH and naturally explain observed extremely low accretion rates compared to the Bondi rate, as well as at least part of the energy feedback.

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Correlation functions are ubiquitous in quantum field theory, but their use in quantum gravity beyond perturbative and asymptotically flat regimes has been limited, due to difficulties with diffeomorphism invariance and the dynamical nature of geometry. We address these challenges in the context of nonperturbative quantum gravity, motivated by the goal of computing geometric correlators from first principles, as a possible window to early-universe cosmology. I will report on recent work in 2D Lorentzian quantum gravity, formulated in terms of causal dynamical triangulations, which demonstrates the feasibility of constructing and measuring manifestly diffeomorphism-invariant curvature correlators. I will discuss some unusual features of the connected correlators and new results on their behaviour in two dimensions, obtained with the help of Monte Carlo simulations.

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