Gustavo Joaquin Turiaci

A bstract: The Euclidean Nariai geometry has long been proposed as the instanton describing the nucleation of maximal-mass black holes in de Sitter space. We place this interpretation on firmer footing by showing that, once an observer is included, the gravitational path integral produces the imaginary phase required for a transition rate. As a warmup, we revisit the Hawking-Moss instanton and, as a byproduct, find that scalar fields can enhance black-hole nucleation, suggesting a quantum-gravity bound on scalar potentials with de Sitter solutions. We then study the subsequent semiclassical evolution of the nucleated black hole. We show that the previously claimed “anti-evaporation” channel is unphysical, arising from a quantum state with singular horizons. In a smooth state, the black hole instead undergoes standard thermal Hawking evaporation. We verify explicit agreement with the no-boundary state and argue that this evaporation is not subject to large quantum-gravity corrections. The nucleated black hole thus evaporates completely back to the maximally-entropic empty de Sitter vacuum, making the full process a Boltzmann fluctuation.

Lecture notes prepared for the Les Houches school ‘‘Quantum Geometry: Mathematical Methods for Gravity, Gauge Theories and Non-Perturbative Physics’’ that took place during the summer 2024. We cover the techniques to perform the exact gravitational path integral of two-dimensional dilaton-gravity, and supergravity, over spacetimes with arbitrary topology, with an application to black holes. We discuss the connection with random matrix models and moduli spaces of hyperbolic surfaces briefly, since those concepts were covered in other lectures of the school.

A bstract: The dynamics of near-BPS black holes are governed by the breaking of the conformal symmetry that emerges near their horizons. Using the classification of superconformal symmetries, we systematically classify and quantize all effective theories that can arise in the near-BPS limit of black holes. Using these results, we argue — under certain physical assumptions — that BPS black holes cannot preserve more than four supercharges. This conclusion is consistent with existing constructions in string theory.

A bstract: We study quantum gravity corrections to the no-boundary wavefunction describing a universe with spatial topology S ¹ × S ² . It has been suggested that quantum effects become increasingly important when the size of the circle is large relative to the sphere. In this paper, we confirm this claim by an explicit four-dimensional one-loop calculation of the gravitational path integral preparing such a state. In the process, we clarify some aspects of the gravitational path integral on complex spacetimes. These quantum corrections play a crucial role in ensuring that the norm of the wavefunction is naturally expressed in terms of a path integral over S ² × S ² at the classical level. We extend some of the analysis to more general spatial topologies, as well as to the inclusion of fermions.

A bstract: The gravitational path integral on S ² × S ² can be interpreted either as evaluating a contribution to the norm of the Hartle-Hawking wavefunction conditional on spatial S ¹ × S ² topology, or the pair creation rate of black holes in de Sitter. Both interpretations are distinguished at the quantum level. The former requires the path integral to be real and the latter to be imaginary. We develop a formalism to efficiently compute the phase of the gravitational path integral on Einstein spaces. We apply it to a broad class of spacetimes and in particular S ² × S ^{D− 2} , finding it to be real and positive. We generalize some of the analysis to cases with charge and rotation.

A bstract: Logarithmic corrections to the entropy of extremal black holes have been successfully used to accurately match degeneracies from microscopic constructions to calculations of the gravitational path integral. In this paper, we revisit the problem of deriving such corrections for the case of extremal black holes, either non-supersymmetric or supersymmetric, and for near-extremal black holes. The zero-modes that are present at extremality are crucial, since their path integral cannot be treated quadratically and needs to be regulated. We show how the regulated result can be obtained by taking the zero-temperature limit of either the 4 d Einstein-Maxwell or 4 d supergravity path integral to find the Schwarzian or super-Schwarzian theories. This leads to drastically different estimates for the degeneracy of extremal black hole: it vanishes when the extremal limit does not preserve supersymmetry, while it reproduces Bekenstein-Hawking in the BPS case. In a companion paper, we discuss how such zero-modes affect the calculation of BPS black holes degeneracies, using supersymmetric localization for an exact computation of the gravitational path integral.