Colloquiums archive 2023

We investigate a violation of the Leggett-Garg inequalities (LGIs) due to gravitational interaction in a hybrid system consisting of a harmonic oscillator and a spatially localized superposed particle. The violation of the LGIs was discussed using the two-time quasi-probability in connection with the entanglement generated by gravitational interaction [reference]. However, relation between gravitational induced entanglement and violation of the LGIs is not still so clear because there are some cases that the LGIs can be violated even though the gravitational interaction is switched off. We try another type of measurement and aim to establish complete understanding of violation of the LGIs in the system with gravity induced entanglement.

[reference]

Leggett-Garg inequalities for testing quantumness of gravity

A.Matsumura, Y.Nambu and K.Yamamoto

PRA (2022) 012214

Dark energy models in $F(R)$ gravity generally possess a weak singularity, which could be cured by $R^2$ correction. However, the potential structure around the origin ($\phi=0$), corresponding to the intermediate epoch of the cosmic history, is significantly altered. The high energy excitation produced due to the nonadiabatic change of the scalar field's effective mass would be problematic, especially for BBN. In addition, the (gravitational) reheating mechanism is missing in some of the $R^2$-corrected models. We shall that the warm inflation scenario could be a remedy for resolving these two problems simultaneously.

In this colloquium, I discuss the probability distribution of the spins of primordial black holes (PBHs) formed in the matter-dominated universe.

I focus on cosmological perturbations that follow Gaussian distribution and discuss their linear-order effects on the tidal torque they generate.

By the time the fluid gravitationally collapses to form a PBH, nonlinear effects contribute strongly, and in order to account for this effect, I apply the Zel'dovich approximation.

I also make use of the peak theory that the Gaussian field follows and then evaluate the probability distribution of the PBH spins.

I propose to give the threshold of the fluctuations for PBH formation based on the magnitude of the spins produced by them. [Slides]

Recently, there has been a lot of discussion on the quantum nature of gravity for observational purposes. One of the main issues there is the relation between the number of DOFs for the gravitational field and the quantum features like entanglement among detectors.

To clarify this relation, we consider the quantum noise induced by the gravitational field. This quantum stochastic noise causes the Langevin-like motion on the geodesic deviation between detectors. And decoherence phenomena occur in the interferometry system.

In this talk, I will review the previous works for the GR case, introducing some techniques known in the contexts of open quantum systems. Then, I will discuss the scalar-tensor theory case for comparison, to see the influence of the additional DOF on the system. [Slides]

In 2017, Bose et al. proposed a thought tabletop experiment to observe gravitational effect induced by spatially superposed mass source, and this is expected to be the first step to look into quantum nature of gravity. However, they suppose that gravity is weak enough and consider Newton gravity in non-relativistic regime. Therefore, we could not distinguish gravity and other quantum interaction, e.g. Coulomb interaction, in their setup. To see the quantum nature unique to gravity, we need to consider relativistic phenomena more or less. In this talk, we consider gravitational lensing on spatially superposed curved spacetime. This work is in progress and collaborated with Yasusada Nambu.

We introduce a general formalism of the non-adiabatic response and apply it to the Friedmann equation with a free scalar field. The Friedmann equation describes the dynamics of the scale factor of the FLRW universe, and in this equation, we often deal with an energy-momentum tensor in the adiabatic limit. In this talk, we show how the scale factor excites the quantum state and estimate how much the excitation corrects the Friedmann equation. As a result, in this modern universe, we can neglect the non-adiabatic correction. However, the formalism of the non-adiabatic response might be helpful in analyzing the dynamics of the early universe, the evaporation of the black hole, and so forth.

I will give an introduction to Sorce-Wald formalism (https://arxiv.org/abs/1707.05862) on gedanken experiments to destroy a black hole by dropping energy, angular momentum, and charge into it. This formalism is based on the Iyer-Wald's Noether charge method and enables us to evaluate the increase of mass, angular momentum, and charge due to the perturbations around a stationary black hole up to the second order in perturbations. 

One may expect that asymptotically flat spacetimes would be approximated to the flat spacetime near infinity. However, in four dimensions, there is a difference in the behavior of null geodesics. Especially, the null energy flow to infinity affects null geodesics in the same order with the centrifugal force. I will show this effect and give the sufficient condition that null geodesics reach infinity.

Under certain conditions, it is shown that the positivity of the Geroch/Hawking quasi-local mass holds for the attractive gravity probe surfaces in any higher spatial dimensions than three. We also comment on the Arnowitt-Deser-Misner mass.

A recent paper, in the context of quantum gravity, claimed that we can make the “quantum switch” protocol by considering the superposition of the shells. Quantum switch has been studied as one of the higher-order quantum operations in quantum information theory. Higher-order quantum operations are currently the subject of much research, as they are expected to expand the usefulness of quantum computers in engineering and to further our understanding of quantum mechanics in physics. It is very interesting to study the quantum properties of gravitational systems using such quantum information-theoretic protocols. I have learned about quantum switches and will introduce them in this colloquium.

One of the modified gravity theories is f(Q) gravity, which has been actively studied under a special gauge called coincident gauge in recent years. This theory is based on a different geometry of spacetime than GR, and the fundamental degrees of freedom of gravity are given by not only the metric but also the connection. Therefore, situations arise in which the intuition and theorems that have been used up to now do not work.

In this talk, we start from the most general metric-affine geometry, derive relations, and then carefully show how to get to f(Q) gravity. As an application, the identity of the coincident gauge is also discussed.

　During inflation, quantum vacuum fluctuations are known to exit the horizon moment by moment and become classical. At this time, the already classicized fluctuations are affected by quantum fluctuations exiting the horizon at a later time. The method to deal with it successfully is stochastic formalism. Additionally, stochastic \delta N, which combines stochastic formalism and \delta N formalism, describes fluctuations nonlinearly on the super-horizon scale.

　In this colloquium, I will mainly talk about a simplified derivation of stochastic formalism and a method for calculating the power spectrum of curvature fluctuations by stochastic \delta N. There will be a discussion of Primordial Black Holes as an application of stochastic \delta N [Eemeli Tomberg (2023)], which will be mentioned at the end of the talk.

   The final phase of black hole (BH) binary mergers, quasinormal mode (QNM), is characterized solely by the mass of the merged BH and is therefore considered suitable for testing general relativity (GR). However, in order to confirm that the observed deviations from the theoretical waveform cannot be explained by GR, it is necessary to take into account the effects of some factors, such as mass accretion, on the QNM.

   In this colloquium, I will consider the QNM when there is spherically symmetric and stationary mass accretion on the Schwarzschild BH. I will set the background when there is accretion and discuss how to derive the master equation and the source term. 

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). Therefore, [Dzhunushaliev et al. (2013)] constructed stationary rotating wormhole solutions in 4+1 dimensional spacetime with equal angular momenta. This prescription is able to turn Einstein's equations into ordinary differential equations while keeping the rotation effects(cohomogeneity-1 problem). In this study, we impose asymptotically flat boundary conditions on both sides of the wormhole and construct more general solutions by considering the "asymmetry" degrees of freedom near the wormhole throat, which has never been suggested by [Dzhunushaliev et al. (2013)]. We also discuss the relation between mass and angular momentum. [Slides]

The program is HERE.

The motion of a closed string in $AdS_5\times S^5$ spacetime is known to be integrable. However, integrability depends on boundary conditions. Since various boundary conditions can be considered for open strings, we can expect that integrability may be violated in some cases.

In this talk, we consider several boundary conditions for the open string of a test Nambu Goto string moving in $AdS_3$ spacetime. We observed initial value sensitivities and turbulence at certain boundary conditions. This implies that there are boundary conditions under which the open string motion becomes non-integrable. 

Let me talk about my idea that treats the issue indicated by the title of this talk.

I am considering a discretized spacetime whose structure is consistent with discretized Einstein equation, and assuming that matters are certain oscillation modes of the building blocks of the discretized spacetime.

In my framework for discretizing the spacetime, I think it is necessary to introduce a probability for describing the time evolution of the discretized spacetime and matters on it.

Now, within this model, I am trying to derive phenomenologically, for the matters, the Schrodinger equation (quantum mechanical probability of matters) and the so-called "principle of equal probability" (the basic assumption in statistical mechanics) from the probability that I have introduced for describing the time evolution in my discretized model of spacetime and matters.

My idea is still under construction and may be thought as a foolish one, so I welcome your frank feeling of my idea. 

This is a review of methodologies to model and understand gravitational collapse from ideal fluid with/without pressure such as Lemitre--Tolmann--Bondi solution and 3+1 formalism in spherically symmetric system.

In this system, one could confront the existence of weak singularity such that having infinite energy density at the locus of a derivative of the areal radius with respect to radial coordinate vanishes R'=0, so-called shell crossing singularity.

Otherwise, the locus can be understood as a wormhole structure of the Kruskal--Szekeres type in some particular cases.

The study of quantum systems involving thin shells and gravity offers a solvable framework for investigating quantum effects of gravity, such as the back reaction problems of Hawking radiation. However, the quantum aspects of the gravitational interaction between two shells have not been extensively explored.

In this presentation, we will review a method to track the time evolution of a system with a shell and its associated spacetime geometry. Furthermore, we will extend this method to consider the case of two interacting shells.

We will show you the results of the numerical calculation and discuss the characterisation of the spacetime geometry created by the quantum matter in the end of this talk.

In astrophysical situations, both massless and massive particles are accelerated or decelerated by several mechanisms. For photons, deceleration, or redshift, can occur due to the cosmic expansion, difference of gravitational potential, and so on. For massive particles, acceleration, or energy gain, such as the Penrose process around a black hole has been investigated so far. In this talk, we investigate particle acceleration/deceleration by spacetime dynamics. We focus on a spacetime with a dynamical spherical shell and see its relation to the particle acceleration/deceleration. As an application, we also see shadow formation due to collapse of the shell.

We have numerically simulated the formation of vacuum bubbles considering a small bump in a single-field  inflationary model, for what large backward quantum fluctuations can prevent the inflaton from overshooting the barrier and make it trapped. Such a scenario leads to two coexistent channels for PBH production: from large adiabatic curvature fluctuations and from false vacuum bubbles. In particular, we have studied several aspects, including consistent initial conditions for the bubble formation, its dynamics and the scaling size behaviour. Our numerical results confirm that the analytical logarithmic relation between the non-Gaussian curvature fluctuation and its Gaussian counterpart previously considered in the literature successfully predicts the formation of vacuum bubbles for relatively small non-gaussianities when a bump is included in the inflationary potential. Moreover, the abundance of peaks generated from the bubble channel dominates over those coming from the collapse of adiabatic fluctuations for large values of non-gaussianities, but smaller than previously found using analytical estimates. [Slides]

In active galactic nuclei and gamma-ray burst sources, it is considered that a black hole exists and accretion plasma onto the black holes causes various high-energy astronomical phenomena. In many cases, high-energy emission and relativistic jets are observed from the central region, and the magnetic field is considered to play an important role. Understanding the strength and shape of the magnetic field around a black hole is extremely important.

  In this talk, we consider the magnetic field distribution as the magnetosphere around a black hole and the motion of charged particles there. Although the vacuum magnetosphere is discussed here, it is assumed that the flow of many charged particles (positive and negative charges) creates the charge distribution and/or current distribution, and in the future, I would like to analyze the current system in the black hole magnetosphere; i.e., force-free magnetosphere. I would also like to consider the problem of the plasma source of the relativistic jet. [Slides]

   Few parameters dependent generalised entropy includes Tsallis entropy, Renyi entropy, Sharma-Mittal entropy, Barrow entropy, Kaniadakis entropy, etc as particular representatives. Its relation to physical systems is not always clear. In this paper, we propose the microscopic thermodynamic description for an arbitrary generalised entropy in terms of the particle system. It is shown that the change in the volume of the phase space of the particle system in the micro-canonical description or the difference in the integration measure in the phase space in the canonical description may lead to generalised entropy. Our consideration may help us understand the structure of quantum gravity.

Based on arXiv:2304.09014 [gr-qc].  [Slides]

First, I will give a brief review of quasi-normal modes (QNM) in Schwarzschild spacetime. In particular, I will show how to calculate the complex frequencies of the QNMs based on the well-known Leaver's method. In the latter part, I will talk about the analyses of the QNMs by numerical integration in the time domain. Then, finally, prospects of calculation of QNMs in time-dependent dirty black holes will be briefly mentioned. [Note]