arXiv subjects

Yohsuke Takamori

Publications and source records attributed to Yohsuke Takamori.

At least 19 recordsLinked to original sources

arXiv2026

Strong deflection of massive particles via the geodesic deviation equation

We develop a formulation of the strong deflection limit for the scattering of particles following timelike geodesics in asymptotically flat, static, and spherically symmetric spacetimes. For fixed specific energy, as the angular momentum approaches its critical value from above, the particle passes arbitrarily close to the associated unstable circular orbit, undergoes many windings around it, and the deflection angle diverges logarithmically. Using the geodesic deviation equation, we show covariantly that the coefficient of this logarithmic divergence is determined by the radial instability exponent of the critical trajectory, defined per unit azimuthal angle. We express this instability exponent in terms of local curvature data on the unstable circular orbit, thereby providing both kinematic and geometric interpretations of the strong deflection limit. In general relativity, its matter dependence enters only through a single local scalar combination constructed from the static-frame energy density and the principal radial and tangential pressures.

gr-qc↗

arXiv2025

Gravitational lensing and accretion disk imaging of a Buchdahl dense core

In this paper, we investigate the gravitational lensing and accretion disk imaging characteristics of a dense core modeled by the Buchdahl spacetime. By imposing the appropriate energy conditions and ensuring the absence of curvature singularities, we delineate the parameter space in which the dense core mimics key gravitational features of black holes while exhibiting unique deviations. We derive the photon orbital equation and calculate deflection angles, clearly distinguishing between weak- and strong-deflection regimes. Furthermore, we construct a mapping from the illuminated, geometrically thin accretion disk onto the observer's screen -- focusing on the isoradial curves corresponding to a representative source ring. For compactness values below a critical threshold, only a finite number of disk images are formed. In this range, their secondary and higher-order images typically display double-loop structures, with each loop individually capturing the entire source ring. Notably, the highest-order image sometimes appears as a single, crescent-shaped loop that does not enclose the screen's center, implying the existence of a cutoff angle that restricts the imaged portion of the source ring. In contrast, for compactness values above the critical threshold, an infinite sequence of double-loop structures appears -- a behavior closely linked to the presence of a photon sphere. These findings suggest that the lensing signatures of dense cores can distinguish them from black holes, offering new insights for high-resolution observations.

gr-qc↗

arXiv2024

Parametrized-Post-Newtonian Test of Black Hole Spacetime for Galactic Center Massive Black Hole Sgr A*: Formulation and $χ^2$ Fitting

We have performed a parametrized post-Newtonian (PPN) test of a black hole spacetime using observational data of the star S0-2/S2 orbiting the massive black hole at our galactic center Sgr A*. After introducing our PPN model of black hole spacetime, we report the result of $χ^2$ fitting of the PPN model with the observational data. A new finding through our PPN model is a detectability of the gravitational lens effect on the null geodesics connecting S0-2 and observer under the present observational uncertainties, if a PPN parameter is about one order larger than the value for general relativity case. On the other hand, the effect of black hole spin on the S0-2's motion is not detectable. Thus our present PPN test is performed with spherically symmetric vacuum black hole spacetime. The resultant value of the PPN parameter, which corresponds to the minimum $χ^2$, implies that the gravitational field of Sgr A* is not of Schwarzschild metric or that there exists a sufficient amount of dark matters around Sgr A* to be detected by present telescopes. However, the difference between the minimum $χ^2$ and the $χ^2$ of Schwarzschild case is not large enough to ensure a statistical significance of non-Schwarzschild result. A more precise statistical analysis than $χ^2$ statistics is necessary to extract a statistically significant information of the gravitational field of Sgr A* from present observational data. We will report a result by a Bayesian analysis in next paper.

gr-qc↗

arXiv2024

General formulae for the periapsis shift of a quasi-circular orbit in static spherically symmetric spacetimes and the active gravitational mass density

We study the periapsis shift of a quasi-circular orbit in general static spherically symmetric spacetimes. We derive two formulae in full order with respect to the gravitational field, one in terms of the gravitational mass $m$ and the Einstein tensor and the other in terms of the orbital angular velocity and the Einstein tensor. These formulae reproduce the well-known ones for the forward shift in the Schwarzschild spacetime. In a general case, the shift deviates from that in the vacuum spacetime due to a particular combination of the components of the Einstein tensor at the radius $r$ of the orbit. The formulae give a backward shift due to the extended-mass effect in Newtonian gravity. In general relativity, in the weak-field and diffuse regime, the active gravitational mass density, $ρ_{A}=(ε+p_{r}+2p_{t})/c^{2}$, plays an important role, where $ε$, $p_{r}$, and $p_{t}$ are the energy density, the radial stress, and the tangential stress of the matter field, respectively. We show that the shift is backward if $ρ_{A}$ is beyond a critical value $ρ_{c}\simeq 2.8\times 10^{-15} \mbox{g}/\mbox{cm}^{3} (m/M_{\odot})^{2}(r/\mbox{au})^{-4}$, while a forward shift greater than that in the vacuum spacetime instead implies $ρ_{A}<0$, i.e., the violation of the strong energy condition, and thereby provides evidence for dark energy. We obtain new observational constraints on $ρ_{A}$ in the Solar System and the Galactic Centre.

gr-qc↗

arXiv2023

Periapsis shifts in dark matter distribution around a black hole

We consider the periapsis shifts of bound orbits of stars on static clouds around a black hole. The background spacetime is constructed from a Schwarzschild black hole surrounded by a static and spherically symmetric self-gravitating system of massive particles, which satisfies all the standard energy conditions and physically models the gravitational effect of dark matter distribution around a nonrotating black hole. Using nearly circular bound orbits of stars, we obtain a simple formula for the precession rate. This formula explicitly shows that the precession rate is determined by a positive contribution (i.e., a prograde shift) from the conventional general-relativistic effect and a negative contribution (i.e., a retrograde shift) from the local matter density. The four quantities for such an orbit (i.e., the orbital shift angle, the radial oscillation period, the redshift, and the star position mapped onto the celestial sphere) determine the local values of the background model functions. Furthermore, we not only evaluate the precession rate of nearly circular bound orbits in several specific models but also simulate several bound orbits with large eccentricity and their periapsis shifts. The present exact model demonstrates that the retrograde precession does not mean any exotic central objects such as naked singularities or wormholes but simply the existence of significant energy density of matters on the star orbit around the black hole.

gr-qc↗

arXiv2023

Origin of an Orbiting Star Around the Galactic Supermassive Black Hole

The tremendous tidal force that is linked to the supermassive black hole (SMBH) at the center of our galaxy is expected to strongly subdue star formation in its vicinity. Stars within 1" from the SMBH thus likely formed further from the SMBH and migrated to their current positions. In this study, spectroscopic observations of the star S0-6/S10, one of the closest (projected distance from the SMBH of about 0.3") late-type stars were conducted. Using metal absorption lines in the spectra of S0-6, the radial velocity of S0-6 from 2014 to 2021 was measured, and a marginal acceleration was detected, which indicated that S0-6 is close to the SMBH. The S0-6 spectra were employed to determine its stellar parameters including temperature, chemical abundances ([M/H], [Fe/H], [alpha/Fe], [Ca/Fe], [Mg/Fe], [Ti/Fe]), and age. As suggested by the results of this study, S0-6 is very old (> ~10 Gyr) and has an origin different from that of stars born in the central pc region.

astro-ph.GA↗

arXiv2022

Periapsis shifts in dark matter distribution with a dense core

We consider the periapsis shifts in dark matter distribution with a dense core. We model the dark matter distribution as an isotropic gas sphere, the Emden polytropic sphere of index 5 in general relativity. This model has a parameter range where all the energy conditions are satisfied in the entire region. Within the parameter range, the asymptotic analysis for stellar motion allows us to identify two competing effects on the bounded motion: the general-relativistic effect and a local-density effect of matter. Furthermore, using nearly circular bound orbits, we demonstrate that retrograde periapsis shifts occur near the center, where the local-density effect dominates over the general-relativistic effect, whereas prograde periapsis shifts occur in the far region, where the general-relativistic effect dominates over the local-density effect. This result means that a natural explanation for the retrograde periapsis shifts is not the existence of exotic objects (e.g., naked singularities or wormholes) but the local distribution of physically reasonable matter on the stellar orbit. Furthermore, it also implies that the periapsis shift plays a crucial role in distinguishing black hole alternatives, such as dark matter cores, from a pure black hole.

gr-qc↗

arXiv2022

Testing the Non-circularity of the Spacetime around Sagittarius A* with Orbiting Pulsars

A disformal Kerr black hole solution is a rotating black hole solution in a modified gravity theory which breaks the circular condition of spacetime differently from the case of the Kerr spacetime. In this paper, assuming that Sagittarius A* (Sgr A*) is a disformal Kerr black hole, we examine the potential to test the spacetime geometry with a hypothetical pulsar whose orbital elements are similar to those of the S2/S0-2 star. By numerically solving the equations of motion for the pulsar and photons emitted from it, we calculate the apparent position of the pulsar and the time of arrival (TOA) of the emitted pulse signals. Our analysis shows that the magnitude of the difference in the TOAs reaches the order of $10\>{\rm ms}$ if the deviation from the Kerr spacetime is significant. The time difference is mainly caused by the non-circularity of the spacetime at the $1.5$ post-Newtonian order. The accuracy of the TOA measurement by a future radio telescope named the Square Kilometer Array (SKA) is between about $0.1\>{\rm ms}$ and $10\>{\rm ms}$ for a normal pulsar. Thus, we expect that the SKA can distinguish the disformal Kerr black hole from the Kerr black hole through the non-circularity of the spacetime around Sgr A*.

gr-qc↗

arXiv2021

Axion Cloud Decay due to the Axion-photon Conversion with Background Magnetic Fields

We consider an axion cloud around a black hole with background magnetic fields. We calculate the decay rate of the axion cloud due to the axion-photon conversion associated with the axion-photon coupling. For simplicity, we consider the situation where the axion configuration is dominated by a solution for the eigenvalue equation equivalent to that for the Hydrogen atom, and the coupling term can be evaluated by a successive perturbation method. For the monopole background, we find the decay rate of the axion cloud is given by $\sim q^2κ^2(GM)^5μ^8$, where $μ$, $M$, $G$, $κ$ and $q$ are the axion mass, black hole mass, gravitational constant, coupling constant of the axion-photon coupling and monopole charge, respectively. For the uniform background magnetic field, we obtain the decay rate of the axion cloud $\sim B_0^2κ^2 (GM)^7μ^6$, where $B_0$ is the magnetic field strength. Applying our formula to the central black hole in our galaxy, we find that the value of the decay rate for the case of the uniform magnetic field is comparable to the growth rate of the superradiant instability with $κ\sim 10^{-12}{\rm GeV^{-1}}$, $B_0\sim 10^3{\rm G}$ and $μ\sim 10^{-18}{\rm eV}$. The ratio is $10^5$ times larger for the monopole magnetic field with the same values of the parameters.

hep-ph↗

arXiv2020

Constraints on the dark mass distribution surrounding Sgr A*: simple $χ^2$ analysis for the redshift of photons from orbiting stars

Sagittarius A* (Sgr A*) is the central supermassive black hole with the mass $\sim 4\times 10^6 M_{\odot}$ in the Milky Way and stars are orbiting around it. In May 2018, one of the nearest stars to Sgr A* named S0-2/S2 experienced the pericenter passage. The redshift of photons from S0-2 had varied from $4000\>{\rm km\>s^{-1}}$ to $-2000\>{\rm km\>s^{-1}}$ during the pericenter passage, which is within $0.5\>{\rm yr}$. In this paper, we show that this steep variation of the redshift gives a strong constraint on a dark mass distribution inside the orbit of S0-2. By applying a simple $χ^2$ analysis to the observed redshift, we can easily distinguish between the two models, the point mass model and the point mass plus an extended mass model without the best-fitting parameter search. Our redshift data during the pericenter passage in 2018 with Subaru/IRCS bound the amount of the extended mass inside the orbit of S0-2 less than $0.5\,\%$ ($\sim 2 \times 10^4 M_\odot$) of the mass of Sgr A*. This constraint obtained by our simple analysis is comparable to previous works with the best-fitting parameter search to the motion of S0-2 including the effect of the extended mass. We consider both the power-law and the Plummer models for the dark mass distribution model, but the significant difference between these results is not found.

astro-ph.GA↗

arXiv2019

A Significant Feature in the General Relativistic Time Evolution of the Redshift of Photons Coming from a Star Orbiting Sgr A*

The star S0-2, orbiting the Galactic central massive black hole candidate Sgr A*, passed its pericenter in May 2018. This event is the first chance to detect the general relativistic (GR) effect of a massive black hole, free from non-gravitational physics. The observable GR evidence in the event is the difference between the GR redshift and the Newtonian redshift of photons coming from S0-2. Within the present observational precision, the 1st post-Newtonian (1PN) GR evidence is detectable. In this paper, we give a theoretical analysis of the time evolution of the 1PN GR evidence, under a presupposition that is different from used in previous papers. Our presupposition is that the GR/Newtonian redshift is always calculated with the parameter values (the mass of Sgr A*, the initial conditions of S0-2, and so on) determined by fitting the GR/Newtonian motion of S0-2 with the observational data. It is then revealed that the difference of the GR redshift and the Newtonian one shows two peaks before and after the pericenter passage. This double-peak-appearance is due to our presupposition, and reduces to a single peak if the same parameter values are used in both GR and Newtonian redshifts as considered in previous papers. In addition to this theoretical discussion, we report our observational data obtained with the Subaru telescope by 2018. The quality and the number of Subaru data in 2018 are not sufficient to confirm the detection of the double-peak-appearance.

gr-qc↗

arXiv2019

Relativistic redshift of the star S0-2 orbiting the Galactic center supermassive black hole

General Relativity predicts that a star passing close to a supermassive black hole should exhibit a relativistic redshift. We test this using observations of the Galactic center star S0-2. We combine existing spectroscopic and astrometric measurements from 1995-2017, which cover S0-2's 16-year orbit, with measurements in 2018 March to September which cover three events during its closest approach to the black hole. We detect the combination of special relativistic- and gravitational-redshift, quantified using a redshift parameter, $Υ$. Our result, $Υ=0.88 \pm 0.17$, is consistent with General Relativity ($Υ=1$) and excludes a Newtonian model ($Υ=0$ ) with a statistical significance of 5 $σ$.

astro-ph.GA↗

arXiv2017

Radial Velocity Measurements of an Orbiting Star Around Sgr A*

During the next closest approach of the orbiting star S2/S0-2 to the Galactic supermassive black hole (SMBH), it is estimated that RV uncertainties of ~ 10 km/s allow us to detect post-Newtonian effects throughout 2018. To evaluate an achievable uncertainty in RV and its stability, we have carried out near-infrared, high resolution (R ~ 20,000) spectroscopic monitoring observations of S2 using the Subaru telescope and the near-infrared spectrograph IRCS from 2014 to 2016. The Br-gamma absorption lines are used to determine the RVs of S2. The RVs we obtained are 497 km/s, 877 km/s, and 1108 km/s in 2014, 2015, and 2016, respectively. The statistical uncertainties are derived using the jackknife analysis. The wavelength calibrations in our three-year monitoring are stable: short-term (hours to days) uncertainties in RVs are < 0.5 km/s, and a long-term (three years) uncertainty is 1.2 km/s. The uncertainties from different smoothing parameter, and from the partial exclusion of the spectra, are found to be a few km/s. The final results using the Br-gamma line are 497 +- 17 (stat.) +- 3 (sys.) km/s in 2014, 877 +- 15 (stat.) +- 4 (sys.) km/s in 2015, and 1108 +- 12 (stat.) +- 4 (sys.) km/s in 2016. When we use two He I lines at 2.113\mum in addition to Br-gamma, the mean RVs are 513 km/s and 1114 km/s for 2014 and 2016, respectively. The standard errors of the mean are 16.2 km/s (2014) and 5.4 km/s (2016), confirming the reliability of our measurements. The difference between the RVs estimated by Newtonian mechanics and general relativity will reach about 200 km/s near the next pericenter passage in 2018. Therefore our RV uncertainties of 13 - 17 km/s with Subaru enable us to detect the general relativistic effects in the RV measurements with more than 10 sigma in 2018.

astro-ph.GA↗

arXiv2013

An Alternative Numerical Method for the Stationary Pulsar Magnetosphere

Stationary pulsar magnetospheres in the force-free system are governed by the pulsar equation. In 1999, Contopoulos, Kazanas, and Fendt (hereafter CKF) numerically solved the pulsar equation and obtained a pulsar magnetosphere model called the CKF solution that has both closed and open magnetic field lines. The CKF solution is a successful solution, but it contains a poloidal current sheet that flows along the last open field line. This current sheet is artificially added to make the current system closed. In this paper, we suggest an alternative method to solve the pulsar equation and construct pulsar magnetosphere models without a current sheet. In our method, the pulsar equation is decomposed into Ampere's law and the force-free condition. We numerically solve these equations simultaneously with a fixed poloidal current. As a result, we obtain a pulsar magnetosphere model without a current sheet, which is similar to the CKF solution near the neutron star and has a jet-like structure at a distance along the pole. In addition, we discuss physical properties of the model and find that the force-free condition breaks down in a vicinity of the light cylinder due to dissipation that is included implicitly in the numerical method.

astro-ph.HE↗

arXiv2013

Stable Bound Orbits of Massless Particles around a Black Ring

We study the geodesic motion of massless particles in singly rotating black ring spacetimes. We find stable stationary orbits of massless particles in toroidal spiral shape in the case that the thickness parameter of a black ring is less than a critical value. Furthermore, there exist nonstationary massless particles bounded in a finite region outside the horizon. This is the first example of stable bound orbits of massless particles around a black object.

hep-th↗

arXiv2012

Black Hole Universe: Construction and Analysis of Initial Data

We numerically construct an one-parameter family of initial data of an expanding inhomogeneous universe model which is composed of regularly aligned black holes with an identical mass. They are initial data for vacuum solutions of the Einstein equations. We call this universe model the "black hole universe" and analyze the structure of these initial data. We study the relation between the mean expansion rate of the 3-space, which corresponds to the Hubble parameter, and the mass density of black holes. The result implies that the same relation as that of the Einstein-de Sitter universe is realized in the limit of the large separation between neighboring black holes. The applicability of the cosmological Newtonian $N$-body simulation to the dark matter composed of black holes is also discussed. The deviation of the spatial metric of the cosmological Newtonian $N$-body system from that of the black hole universe is found to be smaller than about 1% in a region distant from the particles, if the separation length between neighboring particles is 20 times larger than their gravitational radius. By contrast, the deviation of the square of the Hubble parameter of the cosmological Newtonian $N$-body system from that of the black hole universe is about 20% for the same separation length.

gr-qc↗

arXiv2010

Chaos in Geodesic Motion around a Black Ring

We study bound orbits of a free particle around a singly rotating black ring. We find there exists chaotic motion of a particle which is gravitationally bound to the black ring by using the Poincare map.

hep-th↗

arXiv2010

Perturbative Analysis of a Stationary Magnetosphere in an Extreme Black Hole Spacetime : On the Meissner-like Effect of an Extreme Black Hole

It is known that the Meissner-like effect is seen in a magnetosphere without an electric current in black hole spacetime: no non-monopole component of magnetic flux penetrates the event horizon if the black hole is extreme. In this paper, in order to see how an electric current affects the Meissner-like effect, we study a force-free electromagnetic system in a static and spherically symmetric extreme black hole spacetime. By assuming that the rotational angular velocity of the magnetic field is very small, we construct a perturbative solution for the Grad-Shafranov equation, which is the basic equation to determine a stationary, axisymmetric electromagnetic field with a force-free electric current. Our perturbation analysis reveals that, if an electric current exists, higher multipole components may be superposed upon the monopole component on the event horizon, even if the black hole is extreme.

gr-qc↗