Colloquiums archive 2021

In non-relativistic Kepler problem, it is well known that an additional conserved charge called Runge-Lenz vector exists. The Runge-Lenz vector extends the SO(3) symmetry in hydrogen atom to SO(4). Considering the unitary representation of SO(4), the energy spectrum and the electron orbital are obtained.

In this seminar, we consider to derive the wave function in momentum representation, respecting the SO(4) symmetry. As the results, the wave function can be expressed as an embedding map of a 3d-sphere in a 4d-Euclid space. Furthermore, we also consider the representation of the parabola orbit which corresponds to the ISO(3) symmetry.

  We succeeded in generalizing Penrose inequality to surfaces in weak gravitational field, which I explained in QG colloquium last year and which is shown in our paper PTEP 2021 (2021) 8, 083E02. The generalization was done in four dimensions.

  In this talk, I show a higher-dimensional generalization. We also refine the inequality.

  We investigate the emergent time scenario in quantum cosmology based on the Page-Wotters approach. Using a quantum cosmological model with a qubit clock, it is demonstrated how the entanglement between the qubit clock and the geometry derives emergence of a time parameter which defines evolution of the timeless quantum state of the universe. We show the univerese wave function conditioned by a qubit clock obeys the standard Schrödinger equation and the Fisher information for the clock state, which quantifies entanglement between the universe and the clock, contributes as a negative energy density. 

  Self-gravitating systems have distinct thermodynamical properties and have attracted much attention. One of the most interesting such properties is the gravothermal catastrophe. The gravothermal catastrophe is a thermodynamical instability of the self-gravitating many-particle system, which is associated with the negative specific heat of the system.

  Apart from the classical gravothermal catastrophe, asymptotically AdS spacetimes have also been attractive in the context of the AdS/CFT correspondence and the AdS turbulent instability. Due to the confined structure and the nonlinearity of the field equations, arbitrary small perturbations may form a black hole. However, the final states have not been understood yet because the final states may depend on the symmetry of the system, initial conditions of perturbations, and the dimension of the spacetime.

  In this talk, we consider a self-gravitating system in an asymptotically AdS spacetime as an approach to obtain a candidate for the final states and analyze the stability of the system. Particularly, we focus on the dimension dependence of stability and show the existence of the critical dimension for the stability in both Newtonian gravity case and AdS spacetime case. Furthermore, we will see that the critical dimensions for the two cases are the same value. [Slides]

  The entanglement entropy (EE) and the logarithmic negativity(LE) for two disjoint intervals in CFT_{1+1} was not able to evaluate analytically except for free CFT. We present a method to analytically evaluate them for the large c Liouville CFT. We can use it independent of the strength of the interaction, and then the resulting EE and LN from it are consistent with the free scalar field calculation. It is valid to exploit for the theory with the large c limit and the level 2 null vector as well, if not for the Liouville theory. We can see that the EE and LN are completely determined by the topology of replica manifold through the BPZ equation stem from the level 2 null vector.

  Soft theorems in quantum field theory(QFT), which remove infrared(IR) divergence in transition probabilities, and asymptotic symmetries and memory effects in classical field theory are closely related. This relation is called the “IR triangle.”  The possibility that an infinite number of asymptotic symmetry charges can exist on a black hole as “soft hairs” is considered to give us some hints for the information loss problem. Besides this theoretical viewpoint, this relation is also interesting in observational aspects because gravitational memory effects may be detected by future generation gravitational wave interferometers.

  In our previous study, by setting a large time box, we constructed a dressed state formalism in QFT that includes the IR triangle (Ref[1]). In this talk, I will briefly show how the IR triangle appears in our formalism in quantum electrodynamics as an example. After that, we will investigate the possibility of “soft-graviton theory” by considering the relation between Lorentz covariance/invariance and asymptotic symmetry. Finally, I will discuss implications to gravitational memory effects from “soft-graviton theory” with a self-interacting real-scalar field. If we have enough time, I will also talk about some prospects. [Slides]

Ref[1] : Phys. Rev. D 104, 125004 (2021)

  Through the application of the positive mass theorem, I will review the rigidity of spacetimes in general relativity. In particular, I will pick up a no-go theorem for strictly stationary spacetimes and uniqueness of static black holes. [Slides]

  Machine Learning is being increasingly integrated into physics community, and indeed in the recent years we have seen numerous applications of machine learning to various physics problems, and even more predictions regarding which physics problems we will be able to solve with machine learning in the near future. The foremost reason is attributable to the power of extracting valuable information from data and solving inverse problem. 

　In this colloquium, I will give an introduction about machine learning (including deep learning), mainly supervised learning. After that, a neural network model applying into holographic QCD for constructing a gravity dual from lattice QCD data suggested by K. Hashimoto et al. will be explained in detail. 

  For the second half of the colloquium, I will focus on the modifications to the above model in order to find the time and spatial metric components separately, discontinuous on the Ricci Scalar function predicted from the training and neural ODE that is going to solve this issue. [Slides]

  A tabletop experiment of the quantumness of gravity has been explored for the last few years such as BMV proposals. Its main purpose is to find out whether the gravitational field is also superposed for superposed mass source.
  I will talk about a new quantum gravity witness using Leggett-Garg inequality (LGI) collaborated with Osawa-kun, Maeda-kun and Nambu-san. LGI is a correlation inequality of temporally separated systems.
  Also, I will give a brief introduction about quantum witness using gravitational time dilation of quantum clock. It is expected to pick out the quantum property peculiar to the gravity unlike BMV proposals or LGI analysis. [Slides]

  Vacuum decay is a transition from a classically stable state to a lower energy state, which may be described by a quantum tunneling process. Vacuum decay in a black hole (BH) spacetime was considered in some researches and it was shown that the four-dimensional Schwarzschild BH acts as a nucleation site for the decay. However, the physical meaning of the vacuum decay in BH spacetimes has not yet been sufficiently clear and researches from various viewpoints are needed.
  Based on the above background, we analyze vacuum decay in rotating BTZ black hole spacetimes. Especially, we look on to a contribution of spins on decay. In addition to the result and discussion of the BTZ case, I briefly introduce our attempts towards Kerr case in the last part of the talk. [Slides]

  In recent years, gravitational wave observations have started. Especially, tidal deformation of neutron stars (NSs) is one of their main targets, which is useful to test modified gravity theories owing to strong gravity inside the NS.
  For this purpose, we consider the tidal deformation phenomena under the F(R) gravity. At the beginning of this talk, I will give introductory reviews of the tidal deformation, and F(R) gravity respectively. And I will show some results in on-going work. [Slides]

  Because of a superradiance, a rotating black hole makes a cloud of axion around a black hole. But when we consider an interaction between a magnetic field around black hole and an axion, axion may converse into a photon and escape to infinity. That will cause the decay of an axion cloud. Recently, Yoo-san calculated the decay rate of an axion cloud in monopole and uniform magnetic field. In this talk, I will give a quick review of that and talk about a calculation in arbitrary magnetic fields. I will also talk about the result in dipole magnetic fields.

Event web-page is here.

  This talk is based on my preliminary idea for testing gravity theories via astronomical observations. Let me focus on a star orbiting a massive object such as a black hole. As is well known, for non-Newtonian gravitational potential, the orbiting star experiences the orbital shift. A significant appearance of orbital shift is the shift of pericenter (apocenter), where the pericenter (apocenter) is the closest (farthest) point to the gravitational center on the orbit. Usual method for detecting the orbital shift may be observations of the position of the star. (The observation of stellar position is called the “astrometry”.)
  Here I try to introduce a “spectroscopic” counterpart to the orbital shift, which is a phenomenon appearing in the spectrum/frequency of photons coming from the star.(The observation of photon’s spectrum is called the “spectroscopy”.) If we can successfully recognize the spectroscopic phenomenon, it may offer us a new tool for testing gravity theories. I show an application of my idea to the star, named S0-2, orbiting around the massive black hole (Sgr A*) at the center of our galaxy.

 In this talk, we will consider mutual information (MI) of finite temperature and rotating system using gauge/gravity duality. MI is considered to measure correlation between two regions. So, calculating the MI, we can learn how hotter temperature and faster rotation affect correlation. Gravity dual of finite temperature and rotating system is Kerr AdS spacetime. Holographic calculation is performed by using Hubeny- Rangamani - Takayanagi (HRT)formula. First, I will review some property of Mutual Information. Then, we will calculate MI holographically in BTZ BH. In this case, we can calculate MI analytically, and by taking some limits, we can learn the effect on MI of hotter temperature and faster rotation. Last, we will calculate MI in higher dimensional cases numerically and discuss the results.

 One obtain the evolution of the density fluctuation in perturbative way. Going to small scales this perturbative treatment is broken, and the system is strongly coupled (=non-linearity becomes important). If we obtain some correlation functions for the density fluctuation with higher loops, we take account of small scale physics, otherwise higher loops have some divergent behavior at the UV limit. In a traditional way, we can introduce an effective fluid as effects of small scale physics, and then this fluid can cancel out UV divergence on loop integrals. This procedure is called effective field theory of large scale structure (EFTofLSS). We extend EFTofLSS to that in modified gravity, and apply it to the DHOST theory which one-loop power spectrum have UV divergence.

 The propagation of magnetohydrodynamic (MHD) waves is studied in a black hole magnetosphere. By using a canonical type formulation for the propagation of MHD disturbances in magnetized plasma around a black hole, the basic properties and the numerical calculations of motion of the locus of simultaneous fronts of wave packets are presented. We define the “magneto-acostic metric” and the effective potential for MHD waves. Hence, we discuss the “magneto-acostic horizon”, which corresponds to the magnetosonic surface for ingoing flows, and “magneto-acostic ergoregion” where is the super-magnetosonic region for flows in the toroidal direction. We show the basic feature that MHD waves with negative angular momentum focus toward the disk’s inner edge region and/or the funnel region, while MHD waves with positive angular momentum propagate outward. This angular momentum transport by MHD wave would be enhanced to gas accretion rate, and would be related to the formation of relativistic jet in the black hole magnetosphere. [Slides]

 Photon spheres have attracted much attention from observational and mathematical viewpoints. In observations, they are related to the black hole shadows. In mathematics, they can be the visible structures characterizing strong gravitational fields.
 Since their naive definition, “spheres of circular photon orbits,” is too dependent of the spacetime symmetries, several generalized notions of photon spheres have been proposed so far.
 A photon surface was defined by Claudel et al. (2001) as a geometrical generalization of the Schwarzschild photon sphere. In this seminar, we see the examples of photon surfaces and discuss their utility and problems as the generalization of photon spheres. In particular, we focus on photon surfaces in spherically symmetric, but dynamical spacetimes. [Slides]

 Can we find a holographic description of Scattering amplitudes? What does that even look like, and how can we make that notion more concrete? To attempt to answer these questions, we start by giving brief introductions to Soft Theorems, which were shown to give Celestial Correlators strongly resembling those of conserved U(1) Kac-Moody current in 2D CFT. Utilizing techniques from the Celestial Correlator formalism and path integration, we motivate the existence of and determine various forms of effective actions on various hyper-surfaces at null infinity in free U(1) theory as an easily generalizable example. We discuss various implications of these forms and the correlation functions they induce. Finally, we discuss how we can obtain scattering amplitudes perturbatively through this description and discuss the current status of our work-in-progress and future prospects. [Slides]

 We propose statistical systems based on $p$-adic numbers. In the systems, the Hamiltonian is a standard real number which is given by a map from the $p$-adic numbers. Therefore we can introduce the temperature as a real number and calculate the thermodynamical quantities like free energy, thermodynamical energy, entropy, specific heat, etc. Although we consider a very simple system, which corresponds to a free particle moving in one dimensional space, we find that there appear the behaviors like phase transition in the system. Usually in order that a phase transition occurs, we need a system with an infinite number of degrees of freedom but in the system where the dynamical variable is given by $p$-adic number, even if the degree of the freedom is unity, there might occur the phase transition. [Slides]

 In the first part of the talk, I will give a review on the superradiant instability based on the paper  PRD22(1980) 2323-2326. In the second part, we consider an axion cloud around a black hole with background magnetic fields. and calculate the decay rate of the axion cloud due to the axion-photon conversion associated with the axion-photon coupling. Then the decay rate due to the axion photon conversion is compared with the growth rate of the superradiant instability. I will explain details of calculations  as far as possible, and therefore the talk would be longer than a standard seminar talk (I expect about 2 hours).

Ref:　https://arxiv.org/abs/2103.13227