Colloquiums archive 2024

As a model of quantum entanglement formation mediated by gravity, we consider gravitational interactions between particles with internal degrees of freedom. In this case, the internal degrees of freedom and the center of mass degrees of freedom of the particles become entangled due to relativistic effects (mass-energy equivalence), and quantum entanglement is formed between the particles. In this study, we consider a dust system with internal degrees of freedom and examine how its gravitational instability can be affected by quantum entanglement.

Recently I have become interested in the phenomena known as information scrambling. In this talk, I will briefly review the Hayden-Preskill thought experiment and recent research on scrambling. And I will talk about my recent calculations.

The Riemannian Penrose inequality gives the upper bound of the area of the outermost minimal surface in an asymptotically flat space with non-negative curvature. This inequality gives, roughly speaking, the upper-bound area of a black hole horizon. This inequality can be applied to a minimal surface, that is, a surface in a region with a strong gravitational field.

We introduce a surface called an attractive gravity probe surface, an AGPS, which is a generalization of the minimal surface, existing in a weak gravity region. We have shown that AGPS satisfies an areal inequality which is a generalization of the Riemannian Penrose inequality. We recently analyze the effect of the Maxwell field. We show that the lower bound of the surface area also exists and that the electric charge inside the surface cannot be larger than a critical value, which becomes the extremal charge of the black hole (i.e. Q=M) if the surface is a minimal surface. We could say that this critical charge is the extremality condition for an AGPS. 

My talk is based on our recent work arXiv:2407.20636 accepted to PRD.

Establishment of quantum gravity theory is a dream of physicists. Amounts of physicists challenged and suggested candidates of the theory. But we cannot assert that we have completed it so far because of difficulties with respect to quantization of gravity and conditions of an experiment to detect it. Therefore some trials with loose assumptions to investigate properties of quantum gravity are being done. 

 The BMV experiment is a good idea to consider and measure quantumness of gravity. However the Newton potential they quantized in the papers has no degrees of freedom of the gravity. Then the results are suspected that the quatumness is produced by quatumness of the source, not gravity. 

 We consider the lnearlized gravity and quantize it in order to test the dynamical contribution of quantized gravity, that is really quantumness of gravity in the same setup as the BMV experiment. We used the Unruh-DeWitt detector, which is a tool to research effects by quantum fields on a trajectory of the particle with the spin and we focused on the memory effect, which produces an eternal change of velocity or displacement of detectors due to radiations during a split of source particles in the BMV experiment. I will show you a review of the concept of quantumness of gravity and the BMV experiment at first, then our results expressed by the Bloch sphere of the detector. See you tomorrow. 

I introduce the criteria for initial singularities in homogeneous and/or isotropic inflationary universes, as established by Yoshida, Quintin (2018) and Nomura, Yoshida (2021). Additionally, I discuss a generalization of these criteria to cosmological spacetimes without assuming any symmetries, such as homogeneity or isotropy.

Using stochastic formalism, I discuss the information during the inflation and gain the meaningful entropy behavior as the guiding behavior for the quantum gravity theory. Arkani-Hamed et al., 2007, gain the inequality that an e-folding number of inflation is bounded by the area entropy of the cosmological horizon multiplied by a coefficient, and they conclude that eternal inflation violates this inequality. Using the analogy of the black hole information loss paradox, they interpret that inequality means the number of modes that become superhorizon in the inflation bounded by the degree of freedom in the inner cosmological horizon bound.  To reinterpret this inequality from the aspect of information, we focus on the entanglement entropy between the superhorizon modes and subhorizon modes, and we gain the same result that eternal inflation violates inequality. However, in the context of the black hole information loss paradox, the meaningful entropy behavior, called "Page curve", is considered to include the effect of quantum gravity in the theory. Therefore, to proceed analogy of the black hole, we discuss volume-weighting probability distribution as the global average of state like the discussion of gaining Page curve, and gain the stationary behavior of entropy in late-time we conclude the meaningful entropy behavior.

We can make use of the symmetries in the spacetime to reduce the system of partial-derivative equations into some of closed system of equations. In axially symmetric system, e.g., it is often used "Weyl metric" and "Belinski-Zakharov formalism," which divide the system into two parts: components of Killing direction (t, \phi) and 2-dim. space (\rho, z). In this talk, we will check the soliton formalism--superposing solutions of non-linear equations--in the wormhole spacetime and discuss how to generate "multiple" wormhole solution which connects multiple asymptotically flat regions. It is implied that we can obtain 2n-throat wormhole analytically by considering the boundary conditions.

This study investigates the formation of primordial black holes (PBHs) resulting from the collapse of adiabatic fluctuations with large amplitudes and non-Gaussianity. Recently, it was shown that fluctuations with large amplitudes lead to the formation of type B PBHs, characterized by the existence of the bifurcating trapping horizons, distinct from the more common type A PBHs without a bifurcating trapping horizon. We focus on the local type non-Gaussianity, characterized by parameter . Then we examine how the non-Gaussianity influences the dynamics and the type of PBH formed, particularly focusing on type II fluctuations, where the areal radius varies non-monotonically with the coordinate radius. Our findings indicate that, for β > −2, the threshold for distinguishing between type A and type B PBHs decreases with increasing β similarly to the threshold for black hole formation. Additionally, for large positive values of β, the threshold for type B PBHs approaches that for type II fluctuations. We also find that, for a sufficiently large negative value of β ≲ −4.0, the threshold value is in the type II region of μ, i.e., there are fluctuations of type II which do not form black holes. Lastly, we calculate the PBH mass for several values of β. Then we observe that the final mass monotonically increases with the initial amplitude within the parameter region of type A PBHs, which differs from previous analytical expectations.

strong gravity region, generalizing the photon sphere in　Schwarzschild spacetime. It turns out that there are an infinite number of marginal LTSs.  At leading order in the small Kerr parameter, all of the marginal LTSs have the same area. However, at higher orders, the maximal marginal LTS among them is uniquely determined.

  One of the most intriguing phenomena in quantum field theory in curved spacetime (QFTCS) is Hawking radiation from black holes. However, the temperature of Hawking radiation is significantly lower than that of the cosmic microwave background (CMB), making it extremely challenging to observe directly in astrophysical black holes.

According to the equivalence principle in general relativity, Hawking radiation is thought to be analogous to the Unruh effect: uniformly accelerating observers or detectors perceive a thermal bath at the Unruh temperature. In laboratory experiments, such as electron acceleration with ultra-strong lasers, it is possible to achieve uniform particle acceleration, raising the prospect of testing the Unruh effect and, by extension, Hawking radiation in controlled settings.

The Unruh effect occurs in the comoving frame of the accelerated particle, while observations are conducted in the laboratory frame. Therefore, to experimentally verify the Unruh effect, we must identify observable effects in the laboratory frame that stem from it. One promising candidate is the back-reaction of the Unruh effect: when a uniformly accelerating particle experiences a thermal bath, it thermalizes by emitting or absorbing energy quanta. These emissions or absorptions manifest as radiation observable from the laboratory frame.

In quantum electrodynamics, several phenomena are associated with radiation from accelerated charges. It is crucial to determine which of these phenomena involve the back-reaction of the Unruh effect. In this talk, we will explore whether Thomson scattering, Larmor radiation, and radiation from Cozzella’s gapless detector model could serve as manifestations of the back-reaction of the Unruh effect.

  As revealed by Kopp et al., a Type II primordial black hole (PBH) represents a hidden class of PBHs formed from Type II primordial fluctuations. Type II and Type I fluctuations are distinguished by the presence or absence of a neck-throat structure on their time slices.

Starting from these Type II perturbations, the nonlinear evolution governed by the Einstein equations results in two distinct horizon configurations characterized by the presence or absence of a bifurcating trapping horizon. These are classified as Type II-B and Type II-A PBHs, respectively. 

 Since this classification was introduced through a numerical study of PBH formation, we analytically compare the initial fluctuation type with the resulting spacetime using the Lemaître–Tolman–Bondi solution. Unlike in the radiation-dominated era, we demonstrate that Type II-A PBHs are not formed during the matter-dominated era. This result holds independently of the specific profile of the curvature fluctuations.

  TBA

  During the ringdown phase, the final stage of black hole (BH) binary mergers, the frequency of gravitational waves is characterized only by the mass and angular momentum of the merged BH. Therefore, it is called quasinormal mode (QNM), and its use to test general relativity (GR) is often discussed. However, in order to confirm that observed deviations from the theoretical waveform cannot be explained by GR, it is necessary to take into account effects of some factors, such as matter distribution, on the QNM.

In this colloquium, I will consider how the QNM waveform changes when spherically symmetric and stationary matter accretion is added to the Schwarzschild BH. I will derive the master equation at the general spherically symmetric background and set up background spacetime and source term using the equation of motion of the fluid. I will also briefly describe the numerical method and discuss the results and some issues.

  To evaluate the feasibility of traversable wormholes, the effect of angular momentum would be considerable. Because of non-spherical symmetricity, Einstein's equations in 4 dimensions must be dealt with as partial differential equations(cohomogeneity-2 problem). [Dzhunushaliev et al. (2013)] constructed stationary rotating wormhole solutions in 4+1 dimensional spacetime with equal angular momenta. This prescription can turn Einstein's equations into ordinary differential equations while keeping the rotation effects(cohomogeneity-1 problem).  This paper also shows that the effect of rotation could make the energy condition weaker. In this study, we reveal this relation between the rotation and energy condition in the view of geometrical points.

  Evaluating the evolution of long-wavelength cosmological fluctuations is crucial for linking inflation models with observed structures. The scalar-type fluctuation is represented as curvature perturbations, and the delta N formalism is effective for their evaluation. The delta N formalism finds relationships between the background spacetime geometry, the equations of motion, and their perturbed counterparts, to calculate curvature perturbations. Specifically, in this formalism, one often assumes the homogeneity and isotropy of the background spacetime, and this holds locally even in the presence of long-wavelength perturbations.

In this talk, I will discuss the delta N formalism assuming that the background spacetime is homogeneous but anisotropic. As a concrete example, I will use an inflationary model that includes a U(1) vector field in addition to the inflaton. In the first half of the talk, I will evaluate linear fluctuations, and in the second half, I will discuss the evaluation of nonlinear fluctuations.

  In quantum field theory (QFT) in curved spacetime, it is widely recognized that a consistent quantum field description leads to a higher-order curvature effect, known as the trace anomaly of the regularized stress-energy tensor(RSET). This phenomenon has been well investigated with black holes and cosmological spacetimes, and its consequences, such as the possible vacuum state and RSET, have been explored. In recent years, this area of research has expanded to include the case with horizonless objects to analyze the impact on stellar physics and the quantum field distribution.

  In this colloquium, I will begin with a review of trace anomalies and then introduce the EFT approach for semiclassical gravity. This approach provides a convenient way to discuss such effects in arbitrary spacetime. Next, I will present some preliminary results on the consistent description of quantum fields on horizonless geometry. This work is a collaboration with S. Mukohyama and K. Okabayashi in YITP, Kyoto U.

In 2017, Bose et al. proposed a thought tabletop experiment to observe the gravitational effect induced by a spatially superposed quantum mass source, and this is seen as a promising first step in exploring the quantum nature of gravity.

Since they supposed that gravity is weak enough and consider Newton gravity, some people are now working on the relativistic extension of Bose et al.'s porposal to discuss the quantum effect unique to gravity. In this talk, we explore gravitational lensing on spatially superposed curved spacetime. We calculate the propagation of a massless quantum scalar field propagating on the weak gravitational field induced by z spatially superposed quantum mass source. Finally, we propose an observable which reveals Einstein rings and also closely related to the gravity-induced entanglement between the scalar field and the mass source.

Recent theoretical research has been conducted to examine how the accumulation of matter affects the metrics of black hole solutions. One notable approach is to use perturbation methods to model and derive particle trajectories in the vicinity of these cosmic entities. This method provides a detailed understanding of how accretion affects the surrounding geometry.

This study focuses on scrutinizing the metric resulting from perfect fluid accretion onto a Schwarzschild black hole. By visualizing timelike geodesics and orbits around black holes, we deepen our understanding of the effects of accretion. Furthermore, we use the osculating element method to further analyze the impact of matter in the geodesic equation, enhancing our understanding of its implications. In addition, by examining the redshift of test particles orbiting a black hole, we investigate its observable effects. 

Together, these multidimensional analyses enrich our understanding of the complex dynamics surrounding black holes and the influence of surrounding matter.

It has already been known that the power spectrum of radiations coming from vicinity of BH becomes the thermal spectrum with Hawking temperature. In this talk, I will show a careful analysis of this thermal spectrum, and then suggest/discuss that the radiations coming from the region r < 4M (for Schwarzschild case) give the thermal power spectrum, otherwise the power spectrum does not become thermal. The radius r=4M may be understood as a "thermal power surface" around BH.

It is known that in the 2nd-order WKB approximation, positive and negative parts of the black hole quasi-normal mode frequency are closely related to the Lyapnov exponent and angular velocity of the null unstable geodesics.  The null geodesics can be easily calculated in general spherically symmetric spacetimes, and we may extract information about the quasi-normal mode through its null geodesic counterpart. If the spacetime differs from the Schwarzschild spacetime since the Einstein tensor in the background spacetime gives us the effective stress-energy tensor, the non-vacuum effects are reflected in the difference of Lyapnov exponent and angular velocity from those in the Schwarzschild spacetime. That is, the difference of the quasi-normal mode from the Schwarzschild case can be characterized by the effective stress-energy tensor through the null geodesic counterpart. The contents of this colloquium are as follows:

1. Review of 2nd order WKB method of QNM

2. Unstable null geodesics in spherically symmetric spacetimes

3. Review of PRD79 064016 "Geodesic stability, Lyapunov exponents, and quasinormal modes"

4. Non-vacuum effects on QNM and its null geodesic counterpart