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Les Houches lectures on Spinfoam Path Integrals
Oleksandra Hrytseniak, Etera R. Livine, Valentine Maris
In these lecture notes for the Les Houches School on Loop Quantum Gravity 2025, which took place in September 2025, we give a pedagogical review of the basics of the spinfoam frame…
Symmetries of cosmological perturbations: The residual low-multipole ambiguity
Jibril Ben Achour, Etera Livine, Vincent Vennin
In cosmology, long-wavelength modes are related to large-gauge transformations (LGT), i.e. changes of coordinates that modify the physical geometry of the cosmological patch. These…
Elementary blocks of Loop Quantum Gravity
Mehdi Assanioussi, Etera R. Livine
We embark on the vast program of integrating the dynamics of Loop Quantum Gravity (LQG). Adopting the strategy of decomposing spin network states into small blocks of (quantum) geo…
Effective Dynamics of Spherically Symmetric Static Spacetime
Etera R. Livine, Yuki Yokokura
In general relativity, the Einstein equations provide spherically symmetric static spacetimes with dynamics defined as an evolution along the radial coordinate . The geometrical…
Test-Field vs Physical Quasi-Normal Modes in Scalar-Tensor Theories
Alexandre Arbey, Etera R. Livine, Clara Montagnon
In the context of the general effort to model black hole dynamics, and in particular their return-to-equilibrium through quasi-normal modes, it is crucial to understand how much te…
Scalar Quasi-Normal Modes of a Loop Quantum Black Hole
Etera R. Livine, Clara Montagnon, Naritaka Oshita +1
We compute the Quasi-Normal Mode (QNM) frequencies for scalar perturbations for modified Schwarzschild black holes in Loop Quantum Gravity. We study the singularity-free polymerize…
Spinfoam Models for Quantum Gravity: Overview
Etera R. Livine
In the quest of a physical theory of quantum gravity, spin foam models, or in short spinfoams, propose a well-defined path integral summing over quantized discrete space-time geome…
Regularized Black Holes from Doubled FLRW Cosmologies
Marc Geiller, Etera R. Livine, Francesco Sartini
Reduced general relativity for four-dimensional spherically-symmetric stationary space-times, more simply called the black hole mini-superspace, was shown in previous work to admit…
Loop Quantum Gravity and Quantum Information
Eugenio Bianchi, Etera R. Livine
We summarize recent developments at the interface of quantum gravity and quantum information, and discuss applications to the quantum geometry of space in loop quantum gravity. In…
Schrödinger symmetry of Schwarzschild-(A)dS black hole mechanics
Jibril Ben Achour, Etera R. Livine, Daniele Oriti
We show that the dynamics of Schwarzschild-(A)dS black holes admits a symmetry under the 2d Schrödinger group, whatever the sign or value of the cosmological constant. This is achi…
Schrödinger Symmetry in Gravitational Mini-Superspaces
Jibril Ben Achour, Etera R. Livine, Daniele Oriti +1
We prove that the simplest gravitational symmetry reduced models describing cosmology and black holes mechanics are invariant under the Schrödinger group. We consider the flat FRW…
Dynamical symmetries of homogeneous minisuperspace models
Marc Geiller, Etera R. Livine, Francesco Sartini
We investigate the phase space symmetries and conserved charges of homogeneous gravitational minisuperspaces. These (0+1)-dimensional reductions of general relativity are defined b…
Intertwiner Entanglement Excitation and Holonomy Operator
Qian Chen, Etera R. Livine
In the loop quantum gravity framework, spin network states carry entanglement between quantum excitations of the geometry at different space points. This intertwiner entanglement i…
Classical dynamics for Loop Gravity: The 2-vertex model
Eneko Aranguren, Iñaki Garay, Etera R. Livine
The study of toy models in loop quantum gravity (LQG), defined as truncations of the full theory, is relevant to both the development of the LQG phenomenology, in cosmology and ast…
Hidden symmetry of the static response of black holes: Applications to Love numbers
Jibril Ben Achour, Etera R. Livine, Shinji Mukohyama +1
We show that any static linear perturbations around Schwarzschild black holes enjoy a set of conserved charges which forms a centrally extended Schrödinger algebra sh(1) = sl$(2,\m…
Symmetries and conformal bridge in Schwarzschild-(A)dS black hole mechanics
Jibril Ben Achour, Etera R. Livine
We show that the Schwarzschild-(A)dS black hole mechanics possesses a hidden symmetry under the three-dimensional Poincaré group. This symmetry shows up after having gauge-fixed th…
BMS Mechanics and the Black Hole Interior
Marc Geiller, Etera R. Livine, Francesco Sartini
The spacetime in the interior of a black hole can be described by an homogeneous line element, for which the Einstein--Hilbert action reduces to a one-dimensional mechanical model.…
Hawking radiation by spherically-symmetric static black holes for all spins: II -- Numerical emission rates, analytical limits and new constraints
Alexandre Arbey, Jérémy Auffinger, Marc Geiller +2
In the companion paper [Phys. Rev. D 103 (2021) 10, [2101.02951]] we have derived the short-ranged potentials for the Teukolsky equations for massless spins in genera…
Loop Quantum Gravity's Boundary Maps
Qian Chen, Etera R. Livine
In canonical quantum gravity, the presence of spatial boundaries naturally leads to a boundary quantum states, representing quantum boundary conditions for the bulk fields. As a co…
Hawking radiation by spherically-symmetric static black holes for all spins: I -- Teukolsky equations and potentials
Alexandre Arbey, Jérémy Auffinger, Marc Geiller +2
In the context of the dynamics and stability of black holes in modified theories of gravity, we derive the Teukolsky equations for massless fields of all spins in general spherical…
Twisted Geometries Coherent States for Loop Quantum Gravity
Andrea Calcinari, Laurent Freidel, Etera Livine +1
We introduce a new family of coherent states for loop quantum gravity, inspired by the twisted geometry parametrization. We compute their peakedness properties and compare them wit…
Symmetries of the Black Hole Interior and Singularity Regularization
Marc Geiller, Etera R. Livine, Francesco Sartini
We reveal an Poincaré algebra of conserved charges associated with the dynamics of the interior of black holes. The action of these Noether charges integrates…
The Cosmological Spinor
Jibril Ben Achour, Etera R. Livine
We build upon previous investigation of the one-dimensional conformal symmetry of the Friedman-Lema\^ itre-Robertson-Walker (FLRW) cosmology of a free scalar field and make it expl…
The Cosmological Constant from Conformal Transformations: Möbius Invariance and Schwarzian Action
Jibril Ben Achour, Etera R. Livine
The homogeneous Friedman-Lema\^ıtre-Robertson-Walker (FLRW) cosmology of a free scalar field with vanishing cosmological constant was recently shown to be invariant under the one-d…