Colloquiums 

  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