Colloquiums 

In the work PRD111.106009, we used the specific model of inflation and stochastic formalism to show the equivalence between the e-folding bound, that e-folding number is bounded by the Gibbons-Hawking entropy, and entropy bound, that entanglement entropy (approximately equal to Shannon entropy in our setup) is bounded by the Gibbons-Hawking entropy. These bounds show the eternal inflation is prohibited. However, the e-folding number is a locally defined quantity, but the eternal inflation is the scenario for the global spacetime. The Shannon entropy is also not enough globally defined because the global expansion effect is not under consideration. Then we used the volume-weighted probability distribution to consider the state including global statistics. Moreover, we obtain the result that eternal inflation is not prohibited from the aspect of entropy bound for the volume-weighted probability distribution. We will talk about the interpretation of the result and discuss about its outlook.

When one considers a physical problem, there is often a corresponding inverse problem. For example, in a (direct) scattering problem with a given potential, one can, in principle, reconstruct the potential from the scattering data. This is the idea of the inverse scattering method, which is a typical example of an inverse problem. The analogue method is particularly effective for certain systems of partial differential equations, including the Einstein equations under specific assumptions, e.g., in vacuum or in electrovacuum spacetimes with F_{\mu\nu}F^{\mu\nu}=0. In this talk, I will briefly introduce the inverse scattering method in gravity and present an example of its application.

Simulations of PBH formation are crucial for understanding the initial conditions that lead to black hole formation and for studying their properties and cosmological impact. The Misner-Sharp formalism is a standard framework used typically in these simulations. Recently, a class of curvature perturbations known as type-II fluctuations, characterised by a non-monotonic areal radius, has attracted growing interest. However, when simulating PBH formation from type-II fluctuations using the standard Misner-Sharp approach, the evolution equations contain divergent terms (of the form 0/0), which hinder numerical progress and make the simulation impossible.
  In this talk, I will present a new methodology with the Misner-Sharp formalism that enables simulations of PBH formation from generic curvature fluctuations while avoiding the divergences associated with type-II curvature profiles. With the new method, we systematically study the black hole formation threshold across various fluctuation profiles and find for the profiles tested that, for sufficiently large curvatures in the linear component of the compaction function shape around its peak, the threshold lies deep within the type-II region.
References: ArXiv:2504.05813 , ArXiv:2504.05814 

We discuss the motion of charged particles in a vacuum magnetosphere around a rotating black hole with a geometrically thin disk. The magnetic field is created by a disk’s toroidal current, and the electric field is generated by the spacetime dragging effect. To discuss the particle’s motion, we consider the effective potential for a charged particle, and discuss the negative potential regions. Hence, we show the possibility of magnetic Penrose Process near the rotation axis and above the thin disk. For a supermassive black hole of mass 10^9 M_sun and magnetic field strength 1 T, it is possible to explain ultrahigh-energy cosmic rays of energy > 10^20 eV. 

Moving mirror model is known as a simple model to describe Hawking radiation. This can describe several evaporation processes by changing the trajectory of mirror. One of these is kink mirror, which demonstrates the end of evaporation. Using this model, there have been several studied investigating the entanglement partner of Hawking radiation. However, in this model, at first glance unphysical phenomenon appear. So, the negative energy flux is emitted from mirror. In this colloquium, I will first discuss this phenomenon and then talk about what happens when the boundary condition at mirror is modified.

We investigate primordial black holes (PBHs) formed from extremely large amplitudes of primordial curvature fluctuations, classified as type II. Type II fluctuations differ from type I by the presence of a stationary point on the initial time slice, when we see the areal radius as a function of the radial coordinate. Starting from these type II perturbations to form black holes, the nonlinear evolution governed by the Einstein equations generally results in two distinct types, A and B, of horizon configurations, respectively characterized by the absence and presence of a bifurcating trapping horizon where past and future trapping horizons meet. In this paper, we use the Lemaitre-Tolman-Bondi solution to show that type I/II and type A/B classifications are equivalent for a spherically symmetric dust fluid system, regardless of the fluctuation profile. However, this equivalence does not generally hold in the presence of pressure.

Entanglement entropy (EE) is widely used to quantify quantum correlations in field theory, with the well-known result in two-dimensional conformal field theory (CFT) predicting a logarithmic divergence with the ultraviolet (UV) cutoff. However, this expression lacks operational meaning: it remains unclear how much of the entanglement is physically extractable via local measurements. In this work, we investigate the operationally accessible entanglement by employing a pair of Unruh-DeWitt detectors, each interacting with complementary regions of a quantum field. We derive an upper bound on the entanglement that can be harvested by such detectors and show that it scales as a double logarithm with respect to the UV cutoff—significantly weaker than the single-logarithmic divergence of the standard CFT result. This work provides an operational perspective on field-theoretic entanglement and sets fundamental limits on its extractability.

Recently, it was proposed that the Page curve is reproduced by using the prescription of islands. The island prescription is first proposed in the framework of holography. By using the formula of the quantum extremal surface, it turns out that there is a region which is not covered by the entanglement wedge of the CFT after a sufficient amount of the Hawking radiation has got outside of the AdS spacetime. This region, which is called the island, is interpreted as a part of the entanglement wedge of (a dual of) the Hawking radiation. The same formula can be obtained by using the replica trick for theories with gravity, and hence, can be applied for any black holes without relying on holography. In this talk, we discuss islands in eternal black holes and evaporating black holes. 

We examine the possible characterization of ringdown waves in a dynamical Vaidya spacetime using the Penrose limit geometry around the dynamical photon sphere. In the case of static spherically symmetric spacetime, it is known that the quasi-normal frequency in the eikonal limit can be characterized by the angular velocity and the Lyapunov exponent for the null geodesic congruence on the orbit of the unstable circular null geodesic. This correspondence can be further backed up by the analysis of the Penrose limit geometry around the unstable circular null geodesic orbit. We try to extend this analysis to a Vaidya spacetime focusing on the dynamical photon sphere in it. Then we discuss to what extent the Penrose limit geometry can be relevant to the ringdown waves in the Vaidya spacetime comparing the results with the numerically calculated waveform in the Vaidya spacetime.

We will discuss how to formulate the semiclassical Einstein equations sourced by CFT stress-energy tensor in the holographic framework. As an application, we study dynamical as well as thermodynamic instability of topological AdS black holes due to the backreaction of quantum stress-energy tensor.  

This talk is based on 2412.18764 [hep-th] 2312.10311 [hep-th] 2301.12170 [hep-th]