Seminars

In 2024, Hollands, Wald, and Zhang proposed a dynamical black hole entropy that can be defined even on non-stationary horizon cross-sections, up to first-order perturbations from a stationary background spacetime. Visser and Yan demonstrated that this entropy satisfies the first and second laws of equilibrium thermodynamics up to first-order perturbations, even when perturbations are also applied to the surface gravity, i.e., the temperature of black holes. In this seminar, we will discuss the first and second laws of thermodynamics that the dynamical black hole entropy obeys when considering second-order perturbations to the field and surface gravity, and examine its non-equilibrium effects.

A fundamental question in modern cosmology is how the universe emerged. One hypothesis is that quantum gravitational effects triggered the birth of the universe from nothing. This idea often called the quantum creation of the universe has been the subject of extensive investigation. Two leading scenarios are the no-boundary proposal and the tunneling proposal.

In this talk, we will revisit these proposals using the recently developed Lorentzian path integral formalism in quantum gravity. To evaluate this path integral, we apply mathematical theories such as resurgence theory and the Picard–Lefschetz theory. Within the framework of general relativity, we demonstrate that only the tunneling proposal yields a consistent and physically meaningful wave function for the universe. In contrast, the no-boundary proposal fails to contribute to a simple model of quantum cosmology. We also analyse linear perturbations and show that neither wave function sufficiently suppresses primordial perturbations, even when considering Trans-Plankian physics.

We adopt an effective action inspired by asymptotically safe gravity, in which the effective gravitational constant is parameterized as $G(\epsilon) = G_{N} /[1 + \tilde{\omega} (G_{N}^{2} \epsilon)^{\alpha}]$, where $G_{N}$ and $\epsilon$ denote Newton's gravitational constant and the energy density of the matter field, respectively, with two dimensionless model parameters, $\tilde{\omega}$ and $\alpha$. Within this framework, we investigate the complete gravitational collapse of a homogeneous ball of perfect fluid and find that singularity is completely resolved for $\alpha > 1$ but not for $1/2 \le \alpha \le 1$. Furthermore, we successfully construct a static exterior metric which, together with the interior solution, describes the dynamical formation of regular black holes in an asymptotically flat spacetime. The resulting regular black hole, obtained as the final static state, contains a de Sitter core and admits a static metric fully expressible in terms of the Lerch transcendent for general cases and in elementary functions for certain values of $\alpha$, including $\alpha = 2$.