I will talk about light rays in nano-Hertz gravitational waves, especially focusing on a basic theory on pulsar timing arrays. Recent development is also mentioned briefly.
The quantum nature of the Schwarzschild black hole interior is investigated through the Wheeler-DeWitt (WDW) equation. We derive the Hamiltonian for the gravitational system corresponding to the black hole interior and obtain the associated WDW equation. By varying the gravitational constant as a parameter controlling quantum effects, we examine how the solutions of the WDW equation change with respect to this parameter. In the parameter regime where quantum effects are negligible, we find that the wave packet solutions closely follow the classical trajectory of the black hole interior. On the other hand, as quantum effects are enhanced, the wave packet deviates from the classical trajectory and exhibits behavior suggestive of singularity avoidance.
Extreme mass ratio inspirals (EMRIs) are among one of main sources of gravitational waves detectable by LISA. A lot of efforts have been devoted to construct theoretical templates of gravitational waves from EMRIs toward the launch of LISA around 2035. There are high precision results for simple orbits such as circular orbits. It is also important for more realistic orbits to compute the gravitational waves accurately. In this talk, we will discuss an analytic method to compute EMRI gravitational waves for highly eccentric orbits.
宇宙重力波望遠鏡LISAで観測できると期待される波源のひとつに極端質量比連星から放出される重力波がある。約10年後にせまった打ち上げに向け、重力波理論波形の構築が精力的に行われている。円軌道など比較的簡単な軌道については高精度な計算結果がある。しかし、観測で想定されるより現実的な軌道の場合に高精度計算を行うことは課題のひとつとなっている。本講演では、軌道離心率が高い場合でも適用可能な解析的計算手法を紹介する。
I would describe how the criterion for primordial black hole formation is related to the existence of circular photon orbits in the underlying static spacetime. This talk is based on the paper [arXiv:2409.05544].
We present a method to determine the physical parameters of a Kerr–Newman black hole from its shadow. In a system consisting of a Kerr–Newman black hole, an observer, and a light source, the relevant parameters are the mass, specific angular momentum, electric charge, inclination angle, and observer distance. We examine both cases where the observer is located at a finite distance and at spatial infinity. Our analysis shows that, from spatial infinity, the shadow contour uniquely determines the dimensionless parameters, meaning that no two distinct sets of parameters produce identical shadow shapes. We also prove analytically that the shadow observed from a finite distance is not unique. The proposed method provides a unified framework for analyzing black hole shadows and can be applied to a broad class of rotating charged black hole solutions.
In stationary and axisymmetric spacetimes, the deflection angle of light rays exhibits a logarithmic divergence as the distance of closest approach tends to the radius of the unstable photon circular orbit (UPCO). In this talk, I show that, within the strong deflection limit, the coefficient of this divergence admits a fully local and coordinate-invariant representation expressed in terms of Newman–Penrose curvature scalars evaluated along the limit curve of the UPCO. This framework reveals that the magnitude of the logarithmic divergence is governed by the radial tidal response of a null geodesic congruence relative to the UPCO, thereby clarifying the physical origin of the divergence coefficient. Furthermore, through well-established correspondences, this local geometric description yields geometric expressions for both the Lyapunov exponent associated with the UPCO and the quasinormal mode frequencies. Taken together, these results provide a unified perspective on optical and dynamical phenomena governed by the UPCO, based on local geometry.
Astrophysical black holes are powered by accretion flows—magnetized plasma spiraling inward and releasing gravitational energy. Magnetic-field amplification drives strong radiation and launches outflows such as relativistic jets. General relativistic radiative transfer is therefore essential for probing black-hole spacetime, accretion physics in strong gravity, and jet-launching mechanisms through direct comparison with observations. We developed general relativistic multi-wavelength radiative transfer code RAIKOU, which computes images and spectra from radio to gamma-ray bands. We introduce our demonstrating that future ultra-high resolution observations can constrain the spin of black holes and relevant plasma dynamics near the event horizon.
We propose a simple and efficient method for calculating the quasinormal modes. After revisiting Leaver's method, we present a simple way of calculation. We employ Nollert's method and its extension to calculate quasinormal frequencies efficiently. We also extend this method to couped systems.
According to the AdS/CFT correspondence, CFTs may have dual counterparts of gravity theories in asymptotically AdS spacetimes. Due to the duality, the two-point correlation functions of CFTs on the boundary geometry have characteristic singularities called bulk-cone singularities. The singularities appear when the two points on the AdS boundary are connected by a bulk null geodesic. Thus, the bulk-cone singularities are the key information to examine the dual geometry. In this talk, we study the bulk-cone singularities of CFTs dual to AdS exotic compact objects (ECOs), such as an AdS gravastar. We see how specific signatures appear in the ECOs case compared to the black hole case.
AdS/CFT対応によると、CFTには双対なAdS時空上の重力理論が存在しうる。双対性によってCFTの二点相関関数には特徴的な特異点が現れ、バルク円錐特異点と呼ばれる。バルク円錐特異点は、AdS境界上の二点がバルク内のヌル測地線でつながるときに現れ、与えられたCFTから双対な漸近AdS時空の幾何学を調べることができる。本講演では、AdS時空がExotic compact objectである場合のバルク円錐特異点を調べ、ブラックホールの場合と比べどのような違いが現れるかを見る。
Gravitational waves interact with the background spacetime through their intrinsic spin, and this interaction manifests as spin effects during scattering processes. Since spin effects become more pronounced for longer wavelengths, they may play an important role for long-wavelength gravitational waves, such as those emitted by binary systems, in addition to wave effects. In the case of gravitational lensing by compact objects like black holes, the influence of the light ring also becomes slightly noticeable. In this study, we numerically solved the Teukolsky equation with a source term corresponding to an equal-mass circular binary to analyze the lensing effects of gravitational waves by a Kerr black hole. Our analysis simultaneously takes into account spin effects, wave effects, and the influence of the light ring, and examines how these factors are reflected in the amplification factor. The results provide valuable insights for deepening our understanding of gravitational wave propagation in strong gravitational fields.
重力波はスピンと背景時空との相互作用によって、散乱過程においてスピンの影響が現れる。スピン効果は波長が長いほど顕著になるため、連星から放出される重力波のように波長が長い場合には、波動効果に加えてスピン効果も重要になる可能性がある。また、ブラックホールのようなコンパクト天体による重力レンズの場合、ライトリングの影響も僅かながら現れる。本研究では、等質量円軌道連星をソース項とする Teukolsky 方程式を数値的に解くことで、Kerr ブラックホールによる重力波レンズ効果を解析した。解析では、スピン効果・波動効果・ライトリングの影響を同時に考慮し、それらが増幅因子にどのように反映されるかを理論的に検討した。得られた結果は、強重力場における重力波伝播の理解を深める上で重要な手がかりを与える。
In the vicinity of black holes and other ultracompact objects, strong gravity allows light rays (null geodesics) to follow intricate trajectories. In particular, the photon region, where photons can be trapped, offers information about the geometric properties of the spacetime through gravitational lensing and black hole shadow observations.
In this talk, we introduce a geometric framework for defining photon regions in arbitrary stationary axisymmetric spacetimes. We also focus on the stability of the bound photon orbits that constitute the photon region, and discuss how the characteristics of the photon region are related to the global structure of the spacetime.
ブラックホールを含む超コンパクト天体の周囲では，強重力によって光線（ヌル測地線）が複雑な軌道をとり得る．特に，光子が閉じ込められる領域である光子領域（photon region）の性質は，重力レンズ効果やシャドウ観測を通じて時空の幾何を反映する重要な情報源となる．
本講演では，任意の定常軸対称時空に対して光子領域を幾何学的に定義する枠組みを紹介し，その構成要素である束縛光子軌道の安定性に着目することで，光子領域の性質が時空の大域的特徴とどのように結びつくかを議論する．
Recent observations have revealed that narrow, nearly light-speed jets are ejected from the centers of several active galaxies. Blandford-Znajek (BZ) process is considered a leading candidate for the energy source of such jets. However, it has recently been suggested that black hole charge may inhibit BZ process, and this debate continues. This presentation will discuss analytical results concerning the capture solid angle of a test charged particle in Kerr spacetime with a BZ split-monopole magnetic field, as used in the original BZ paper (1977).
近年の様々な観測から、いくつかの活動的な銀河の中心からは、細く絞られた光速に近いジェットが噴き出していることが分かっている。このようなジェットのエネルギー源の候補の一つとして、Blandford-Znajek(BZ)過程が有力視されているが、近年BHの帯電がBZ過程を妨げる可能性が指摘され、現在も議論が続いている。本講演では、BZ論文(1977)で用いられたBZ split-monopole磁場を伴うKerr時空中のテスト荷電粒子の捕獲立体角に関する解析結果について議論する。
We study the motion of a charged test particle in the spacetime with a spherically symmetric black hole which is immersed in a monopole magnetic field. We show that since the radial motion of the charged test particle is govern by completely the same equation as that in the case of no magnetic field. This result implies that the black hole will acquire the electric charge if it is surrounded by the collisionless plasma composed of protons and electrons which obey the Maxwell velocity distribution. The drastically different situation appears in the tangential motions of charged test particles due to the magnetic field. The trajectory of a charged test particle in the black hole with the magnetic field of the order of 10 Gauss near the black hole is confined on a very thin cone as long as the specific angular momentum of the particle is not much larger than the gravitational radius of the black hole times the speed of light. This result leads to a possibility that a plasma lump can hover over the black hole and is very hot, in the monopole magnetic field.
In this talk, we introduce the properties of spherical accretion flows onto the Ellis-Bronnikov wormhole. We derive solutions for spherical accretion flows not only for the case of zero ADM mass, but also for the non-zero ADM mass. Furthermore, we discuss the image of the wormhole when the spherical accretion flow serves as the light source, highlighting in particular the differences compared to black holes.
本公演では、まずEllis-Bronnikovワームホールへの球対称降着流の性質を紹介する。先行研究で行われていたADM質量がゼロの場合だけでなく、ADM質量を持つ場合についても球対称降着流の解を導出する。また、球対称降着流を光源とした場合のワームホールの像についても議論し、特にブラックホールとの違いについて紹介したい。
TBA
We study how surrounding accreting matter perturbs the spacetime around black holes, motivated by the fact that many astrophysical black holes interact with ambient material rather than existing in a pure vacuum. Using a first-order perturbative expansion of the Einstein equations, we model stationary, spherically symmetric perfect-fluid distributions and examine their influence on geodesic motion. This perturbative approach offers an analytically tractable way to incorporate matter effects while retaining a clear connection to the Schwarzschild solution. We use the osculating orbit element method to compare unperturbed and perturbed trajectories and to evaluate changes in observable quantities such as redshift.
Post-Newtonian (PN) templates are often used to describe the gravitational waves (GWs) from compact binary inspirals approximately. Most of the analytic PN templates used currently are restricted to equatorial and circular orbits. In this talk, I show the analytic PN templates for generic bound orbits, based on the PN formulas for the secular evolution derived by black hole perturbation theory.
ポストニュートン波形は、コンパクト連星からのインスパイラル重力波をよく近似する理論波形として、データ解析をはじめ様々な場面で良く用いられている。現在用いられている解析的ポストニュートン波形は、赤道面上の円軌道に制限されているものがほとんどである。本発表では、ブラックホール摂動論を用いて求められる永年進化の解析公式をもとにした、一般束縛軌道に対する解析的ポストニュートン波形の導出について紹介する。
I will present, from my perspective, an overview of studies on the supermassive black hole candidate Sgr A* at the center of the Milky Way and the surrounding stars, known as the S-stars. The overview will cover results from radio and infrared observations as well as research based on general relativity.
Until about a decade ago, black holes were regarded mainly as subjects of theoretical investigation. However, over the past ten years, the development of gravitational wave detections, precise monitoring of S-star motions, and the imaging of the black hole shadows have made black holes be the objects of “physics” based on observational data and general relativity. At this point, it may be particularly timely and rewarding for relativists to enter in studies of Sgr A* and the S-stars using observational data to probe gravitational theories.
天の川銀河中心の巨大BH候補天体 Sgr A* と、Sgr A*を周回する星々 S-stars について、私（斉田）の視点から、電波観測、赤外線観測、そして一般相対論に基づいた研究の概観をまとめます。10年ほど前までBHはもっぱら数理的な研究対象だったと思いますが、ここ10年ほどで、重力波、S-stars 運動、BH shadow によって、ようやく、観測データと一般相対論の両方に基づく「物理」としての研究が可能になったと思います。いま、相対論研究者が Sgr A* や S-stars の観測データに基づく重力理論研究へ参入するのが美味しいところかもしれません。
We discuss analytical evaluation of the deflection angle of massless particles in spherically symmetric spacetimes. First, we illustrate how one can derive full-order expressions for the deflection angle in the Schwarzschild spacetime, both in the weak and strong deflection limits, using the Picard-Fuchs equations. Next, we extend this method to charged spacetimes, taking the example of the Einstein-Maxwell-Dilaton spacetimes, which include the Riessner-Nordström spacetime. Lastly, we use the derived expressions for the deflection angle to solve the lens equation.
In curved spacetime, the trajectory of a light ray is described by a geodesic under the geometric optics approximation.However, this approximation is valid only locally and is not justified int the all spacetime regions.If it breaks down, the polarization of light can affect its propagation.In this presentation, we consider light propagating through an axion field in spinoptics approximation.When the polarization is taken into account, the photon-axion coupling introduces an additional acceleration term into the ray equation.This acceleration causes the trajectories to differ depending on the helicity of the light in the presence of an axion field.
曲がった時空において、光線の軌道は幾何光学近似のもとで測地線として記述される。しかし、この近似は局所的な領域でのみ有効であり、時空全域で正当化されるとは限らない。この近似が破綻する場合、光の偏光がその伝播に影響を及ぼすことがある。
本発表では、スピン光学近似の枠組みで、アクシオン場中を伝播する光を考察する。偏光を考慮すると、光子–アクシオン結合により、光線の方程式に追加の加速度項が導かれる。この項により、アクシオン場中では光子のヘリシティに応じて軌道の変化が見られることを示す。
Recently, the Event Horizon Telescope Collaboration reported on the observations of black hole shadows. They excluded a wormhole metric from their observations and they reinforced their claim that the observed objects must be suppermassive black holes. We reconsider their claims and related studies. And, when I was a Ph.D student, I was asked by Motoyuki Saijo, who was an assistant professor at Rikkyo University, whether the deflection angles of rays by any photon sphere always exhibit a logarithmic divergence. A few years ago, I applied Bozza's method to treat the power-divergent deflection angles of the rays. However, Tadashi Sasaki pointed out that the coefficient of a power-divergent term in a Reissner-Nordstrom spacetime was wrong due to my approximations. I will report that I classify the deflaction angles and that I apply Eiroa, Romero, and Torres's method to recalculate the coefficient of the power-divergent term.
最近、Event Horizon Telescopeコラボレーションがブラックホールシャドウの観測について報告した。彼らは観測からワームホール計量を排除することで、観測天体がブラックホールであるという主張を補強している。彼らの主張や関連する研究について見直す。また、立教大学助教だった西條統之さんから十数年前に光子球による光の曲がり角は必ずlog発散するかという質問を受け、数年前にBozzaの手法を応用して冪で発散する光の曲がり角について調べた。しかし、佐々木伸さんによって発表者の近似ではライスナー・ノルドシュトローム時空における冪発散する項の係数が正しく計算できていないことが指摘された。最近、発表者はEiroaらの手法を応用して冪発散する項の係数を再計算しているので進捗報告をする。
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 a static spherically symmetric black hole spacetime, it is known that the quasinormal 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.