arXiv subjects

Kei-ichi Maeda

Publications and source records attributed to Kei-ichi Maeda.

At least 19 recordsLinked to original sources

arXiv2026

Dynamics of Binary System around a Supermassive Black Hole :Binary Scattering and Eccentric vZLK Oscillations

We study the dynamics of a binary orbiting a supermassive black hole (SMBH), focusing on both binary scattering in unbound orbits and eccentric von Zeipel-Lidov-Kozai (vZLK) oscillations in bound orbits. The motion is described in a local inertial frame in Kerr spacetime, where tidal effects are encoded in the Riemann curvature. For unbound (parabolic and hyperbolic) orbits, we identify four scattering regimes-adiabatic, tidally affected, chaotic, and disruptive-depending on the binary semi-major axis. As the binary becomes softer, tidal interactions near periapsis lead to strong eccentricity excitation, large changes in the orbital parameters, and eventually chaotic behavior or tidal disruption, with a sensitive dependence on the argument of periapsis. For eccentric bound (elliptic) orbits, the vZLK mechanism differs qualitatively from the standard one, although the $z$-component of the angular momentum in the local inertial frame remains approximately conserved. The evolution proceeds on a dynamical timescale and exhibits step-like changes driven by repeated periapsis passages, which can be interpreted as a sequence of scattering events. We refer to this behavior as scattering-type vZLK oscillations. The rotation of the SMBH also modifies the oscillation profiles, although its effect is less significant than the dependence on the initial orbital parameters. These results suggest a unified picture of periapsis-driven tidal dynamics in galactic nuclei.

gr-qc↗

arXiv2025

Dynamical von Zeipel-Lidov-Kozai Oscillations of a Binary on a Spherical Orbit around a Rotating Supermassive Black Hole

We study the dynamics of a binary system orbiting a rotating supermassive black hole (SMBH). Using Fermi-Walker transport, we construct a local inertial reference frame in the Kerr spacetime and set up a Newtonian binary system. Assuming the binary moves on a spherical orbit with constant radius around the black hole, we derive the equations of motion governing its dynamics. We focus on von Zeipel-Lidov-Kozai (vZLK) oscillations, which arise when the binary is compact and its initial inclination exceeds a critical angle. In our previous work on a circular orbit in the equatorial plane, we found that for hard binary systems, these oscillations in eccentricity and inclination follow a regular pattern, whereas in soft binaries, they exhibit chaotic behavior with irregular periods and amplitudes, yet remain stable. In this study, we extend our analysis to a spherical orbit in the Kerr background. The libration of the binary's orbit in the latitudinal direction affects the vZLK oscillations: as the libration angle increases, the oscillation period shortens, and the maximum eccentricity grows, particularly when the oscillations become chaotic. Notably, when the binary is sufficiently soft yet remains stable, the oscillation period is reduced to the dynamical timescale rather than the secular timescale. This effect arises due to the interaction between the SMBH spin and the binary's angular momentum. As the Kerr rotation parameter increases or the radius of the spherical orbit decreases, both the enhancement of maximum eccentricity and the reduction in oscillation period become more pronounced.

gr-qc↗

arXiv2024

Einstein Cluster as Central Spiky Distribution of Galactic Dark Matter

Using the Einstein cluster models, we construct a fully relativistic, spherically symmetric, spiky structure of matter distribution near a supermassive black hole. We introduce and discuss three simple toy models, together with a more realistic model, which includes a Hernquist-type distribution with a typical galaxy scale. We find that the innermost stable circular orbit (ISCO) depends on the details of the environment, and lies between the photon radius (at $3M_{\rm BH}$) and the ISCO radius of an isolated black hole of mass $M_{\rm BH}$ (at $6M_{\rm BH}$).

gr-qc↗

arXiv2024

Black hole thermodynamics in generalized Proca theories

We investigate thermodynamics of static and spherically symmetric black holes (BHs) in generalized Proca (GP) theories by applying the Iyer-Wald prescription. BH solutions in GP theories are divided into the two classes. The first class corresponds to the solutions obtained by the direct promotion of the BH solutions in shift-symmetric Horndeski theories, while the second class consists of the solutions which are obtained only in GP theories and contain a nonzero electromagnetic field. For BH solutions in the first class, we confirm that the BH entropy and its thermodynamic mass remain the same as those in the counterpart solution in shift-symmetric Horndeski theories. We also calculate the thermodynamical variables of the several static and spherically-symmetric BH solutions in the second class, and investigate the thermodynamical stability when there exist two BH solutions.

gr-qc↗

arXiv2023

Chaotic von Zeipel-Lidov-Kozai Oscillations of Binary System around Rotating Supermassive Black Hole

In this paper, we investigate the dynamics of a binary system that orbits a rotating supermassive black hole. Our approach employs Fermi-Walker transport to construct a local inertial reference frame, and to set up a Newtonian binary system. We consider a scenario in which a circular geodesic observer is positioned around a Kerr black hole, and thereby derive the equations of motion governing the binary system. To eliminate the interaction terms between the center of mass (CM) of the binary and its relative coordinates, we introduce a small acceleration for the observer. This adjustment leads to the CM closely following the observer's orbit, deviating from a circular geodesic. Here, we first focus on elucidating the stability conditions in a hierarchical triple system. Subsequently, we discuss the phenomenon of von Zeipel-Lidov-Kozai (vZLK) oscillations, which manifest when the binary system is compact and the initial inclination exceeds a critical angle. In hard binary systems, these oscillations exhibit regular behavior, while in soft binary systems, they exhibit a chaotic character, characterized by irregular periods and amplitudes, albeit remaining stable. Additionally, we observe an orbital flip under circumstances of large initial inclination. As for the motion of the CM, we observe deviations from a purely circular orbit that transform into stable yet chaotic oscillations characterized by minute amplitude variations.

gr-qc↗

arXiv2023

Black hole thermodynamics in Horndeski theories

We investigate thermodynamics of static and spherically symmetric black holes (BHs) in the Horndeski theories. Because of the presence of the higher-derivative interactions and the nonminimal derivative couplings of the scalar field, the standard Wald entropy formula may not be directly applicable. Hence, following the original formulation by Iyer and Wald, we obtain the differentials of the BH entropy and the total mass of the system in the Horndeski theories, which lead to the first-law of thermodynamics via the conservation of the Hamiltonian. Our formulation covers the case of the static and spherically symmetric BH solutions with the static scalar field and those with the linearly time-dependent scalar field in the shift-symmetric Horndeski theories. We then apply our results to explicit BH solutions in the Horndeski theories. In the case of the conventional scalar-tensor theories and the Einstein-scalar-Gauss-Bonnet theories, we recover the BH entropy obtained by the Wald entropy formula. In the shift-symmetric theories, in the case of the BH solutions with the static scalar field we show that the BH entropy follows the ordinary area law even in the presence of the nontrivial profile of the scalar field. On the other hand, in the case of the BH solutions where the scalar field linearly depends on time, i.e., the stealth Schwarzschild and Schwarzschild-(anti-) de Sitter solutions, the BH entropy also depends on the profile of the scalar field. By use of the entropy, we find that there exists some range of the parameters in which Schwarzschild$-$(AdS) BH with non-trivial scalar field is thermodynamically stable than Schwarzschild$-$(AdS) BH without scalar field in general relativity.

gr-qc↗

arXiv2023

Dynamics of Binary System around Supermassive Black Hole

We discuss motion of a binary system around a supermassive black hole. Using Fermi-Walker transport, we construct a local inertial reference frame and set up a Newtonian binary system. Assuming a circular geodesic observer around a Schwarzschild black hole, we write down the equations of motion of a binary. Introducing a small acceleration of the observer, we remove the interaction terms between the center of mass (CM) of a binary and its relative coordinates. The CM follows the observer's orbit, but its motion deviates from an exact circular geodesic. We first solve the relative motion of a binary system, and then find the motion of the CM by the perturbation equations with the small acceleration. We show that there appears the Kozai-Lidov (KL) oscillations when a binary is compact and the initial inclination is larger than a critical angle. In a hard binary system, KL oscillations are regular, whereas in a soft binary system, oscillations are irregular both in period and in amplitude, although stable. We find an orbital flip when the initial inclination is large. As for the motion of the CM, the radial deviations from a circular orbit become stable oscillations with very small amplitude.

gr-qc↗

arXiv2023

Cosmological Dynamics of Cuscuta-Galileon Gravity

We study cosmological dynamics of the cuscuta-galileon gravity with a potential term by using the dynamical system approach. This model is galileon generalization of the cuscuton gravity where we add a potential term to the theory in order to obtain the radiation and matter dominated eras. The exponential potential can provide the sequence of the thermal history of the Universe correctly, i.e. starting from radiation dominance, passing through matter dominant era, and then approaching de Sitter expansion stage. This model has no ghosts and the Laplacian instability for both scalar and tensor perturbations. We also discuss the observational constraints on the model parameters. It turns out that the model actually has three degrees of freedom unlike the original cuscuton theory.

gr-qc↗

arXiv2022

Gravitational collapse and formation of a black hole in a type II minimally modified gravity theory

We study the spherically symmetric collapse of a cloud of dust in VCDM, a class of gravitational theories with two local physical degrees of freedom. We find that the collapse corresponds to a particular foliation of the Oppenheimer-Snyder solution in general relativity (GR) which is endowed with a constant trace for the extrinsic curvature relative to the time $t$ constant foliation. For this solution, we find that the final state of the collapse leads to a static configuration with the lapse function vanishing at a radius inside the apparent horizon. Such a point is reached in an infinite time-$t$ interval, $t$ being the cosmological time, i.e. the time of an observer located far away from the collapsing cloud. The presence of this vanishing lapse endpoint implies the necessity of a UV completion to describe the physics inside the resulting black hole. On the other hand, since the corresponding cosmic time $t$ is infinite, VCDM can safely describe the whole history of the universe at large scales without knowledge of the unknown UV completion, despite the presence of the so-called shadowy mode.

gr-qc↗

arXiv2022

VCDM and Cuscuton

We investigate two Type-IIa Minimally Modified Gravity theories, namely VCDM and Cuscuton theories. We confirm that all acceptable Cuscuton solutions are always solutions for VCDM theory. However, the inverse does not hold. We find that VCDM allows for the existence of exact General Relativity (GR) solutions with or without the presence of matter fields and a cosmological constant. We determine the conditions of existence for such GR-VCDM solutions in terms of the trace of the extrinsic curvature and on the fields which define the VCDM theory. On the other hand, for the Cuscuton theory, we find that the same set of exact GR solutions (such as Schwarzschild and Kerr spacetimes) is not compatible with timelike configurations of the Cuscuton field and therefore cannot be considered as acceptable solutions. Nonetheless, in Cuscuton theory, there could exist solutions which are not the same but close enough to GR solutions. We also show the conditions to determine intrinsic-VCDM solutions, i.e. solutions which differ from GR and do not belong to the Cuscuton model. We finally show that in cosmology a mapping between VCDM and the Cuscuton is possible, for a generic form of the VCDM potential. In particular, we find that for a quadratic potential in VCDM theory, this mapping is well defined giving an effective redefinition of the Planck mass for the cosmological background solutions of both theories.

gr-qc↗

arXiv2022

A Possible Solution to the Helium Anomaly of EMPRESS VIII by Cuscuton Gravity Theory

We discuss cosmology based on the cuscuton gravity theory to resolve the anomaly of the observational $^4$He abundance reported by the EMPRESS collaboration. We find that the gravitational constant $G_{\rm cos}$ in Friedmann equation should be smaller than the Newton's constant ${G_{\rm N}}$ such that ${ΔG_{\rm N}}/{G_{\rm N}} \equiv (G_{\rm cos}-G_{\rm N})/{G_{\rm N}} = -0.085_{-0.028}^{+0.026} \quad(68 \% \text { C.L. })$ in terms of big-bang nucleosynthesis, which excludes ${ΔG_{\rm N}}=0$ at more than 95~$\% \text { C.L. }$ To fit the data, we obtain a negative mass squared of a non-dynamical scalar field with the Planck-mass scale as $\sim - {\mathcal{O}}(1) {M_{\rm PL}^2} (μ/{0.5 M_{\rm PL}})^{4}$ with the cuscuton mass parameter $μ$. This fact could suggest the need for modified gravity theories such as the cuscuton gravity theory with a quadratic potential, which can be regarded as the low-energy Hořava-Lifshitz gravity and might give a hint of quantum gravity.

gr-qc↗

arXiv2022

Cuscuta-Galileon cosmology: Dynamics, gravitational "constant"s and the Hubble Constant

We discuss cosmology based on a Cuscuta-Galileon gravity theory, which preserves just two degrees of freedom. Although there exists no additional degrees of freedom, introduction of a potential of a scalar field changes the dynamics. The scalar field is completely determined by matter fields. Giving an exponential potential as an example, we discuss the cosmological dynamics. The gravitational "constant" $G_{\rm F}$ appeared in the effective Friedmann equation becomes time dependent. We also present how to construct a potential when we know the evolution of the Hubble parameter. When we assume the $Λ$CDM cosmology for the background evolution, we find the potential form. We then analyze the density perturbations, which equation is characterized only by a change of the gravitational "constant"$G_{\rm eff}$, which also becomes time dependent. From the observational constraints such as the constraint from the big-bang nucleosynthesis and the constraint on time-variation of gravitational constant, we restrict the parameters in our models. Taking into account the time dependence of the gravitational constant in the effective Friedmann equation, we may have a chance to explain the Hubble tension problem.

gr-qc↗

arXiv2022

Kink-antikink collision in a Lorentz-violating $ϕ^4$ model

In this work, kink-antikink collision in a two-dimensional Lorentz-violating $ϕ^4$ model is considered. It is shown that the Lorentz-violating term in the proposed model does not affect the structure of the linear perturbation spectrum of the standard $ϕ^4$ model, and thus there exists only one vibrational mode. The Lorentz-violating term impacts, however, the frequency and spatial wave function of the vibrational mode. As a consequence, the well-known results on $ϕ^4$ kink-antikink collision will also change. Collisions of kink-antikink pairs with different values of initial velocities and Lorentz-violating parameters are simulated using the Fourier spectral method. Our results indicate that models with larger Lorentz-violating parameters would have smaller critical velocities $v_c$ and smaller widths of bounce windows. Interesting fractal structures existing in the curves of maximal energy densities of the scalar field are also found.

hep-th↗

arXiv2021

ECO-spotting: looking for extremely compact objects with bosonic fields

Black holes are thought to describe the geometry of massive, dark compact objects in the universe. To further support and quantify this long-held belief requires knowledge of possible, if exotic alternatives. Here, we wish to understand how compact can self-gravitating solutions be. We discuss theories with a well-posed initial value problem, consisting in either a single self-interacting scalar, vector or both. We focus on spherically symmetric solutions, investigating the influence of self-interacting potentials into the compactness of the solutions, in particular those that allow for flat-spacetime solutions. We are able to connect such stars to hairy black hole solutions, which emerge as a zero-mass black hole. We show that such stars can have light rings, but their compactness is never parametrically close to that of black holes. The challenge of finding black hole mimickers to investigate full numerical-relativity binary setups remains open.

gr-qc↗

arXiv2020

Post-Newtonian Kozai-Lidov Mechanism and its Effect on Cumulative Shift of Periastron Time of Binary Pulsar

We study the Kozai-Lidov mechanism in a hierarchical triple system in detail by the direct integration of the first-order post Newtonian equations of motion. We analyse a variety of models with a pulsar to evaluate the cumulative shift of the periastron time of a binary pulsar caused by the gravitational wave emission in a hierarchical triple system with Kozai-Lidov mechanism. We compare our results with those by the double-averaging method. The deviation in the eccentricity, even if small, is important in the evaluation of the emission of the gravitational waves. We also calculate the cumulative shift of the periastron time by using obtained osculating orbital elements. If Kozai-Lidov oscillations occur, the cumulative shift curve will bend differently from that of the isolated binary. If such a bending is detected through the radio observation, it will be the first indirect observation of gravitational waves from a triple system.

gr-qc↗

arXiv2020

Current status of space gravitational wave antenna DECIGO and B-DECIGO

Deci-hertz Interferometer Gravitational Wave Observatory (DECIGO) is the future Japanese space mission with a frequency band of 0.1 Hz to 10 Hz. DECIGO aims at the detection of primordial gravitational waves, which could be produced during the inflationary period right after the birth of the universe. There are many other scientific objectives of DECIGO, including the direct measurement of the acceleration of the expansion of the universe, and reliable and accurate predictions of the timing and locations of neutron star/black hole binary coalescences. DECIGO consists of four clusters of observatories placed in the heliocentric orbit. Each cluster consists of three spacecraft, which form three Fabry-Perot Michelson interferometers with an arm length of 1,000 km. Three clusters of DECIGO will be placed far from each other, and the fourth cluster will be placed in the same position as one of the three clusters to obtain the correlation signals for the detection of the primordial gravitational waves. We plan to launch B-DECIGO, which is a scientific pathfinder of DECIGO, before DECIGO in the 2030s to demonstrate the technologies required for DECIGO, as well as to obtain fruitful scientific results to further expand the multi-messenger astronomy.

gr-qc↗

arXiv2020

Gravitational Waves from Hierarchical Triple Systems with Kozai-Lidov Oscillation

We study gravitational waves from a hierarchical three-body system up to first-order postNewtonian approximation. Under certain conditions, the existence of a nearby third body can cause periodic exchange between eccentricity of an inner binary and relative inclination, known as Kozai-Lidov oscillations. We analyze features of the waveform from the inner binary system undergoing such oscillations. We find that variation caused due to the tertiary companion can be observed in the gravitational waveforms and energy spectra, which should be compared with those from isolated binaries and coplanar three-body system. The detections from future space interferometers will make possible the investigation of the gravitational wave spectrum in mHz range and may fetch signals by sources addressed.

gr-qc↗

arXiv2020

Maximal Efficiency of Collisional Penrose Process with Spinning Particle II

We analyze the collisional Penrose process between a particle on the ISCO orbit around an extreme Kerr black hole and a particle impinging from infinity. We consider both cases with non-spinning and spinning particles. We evaluate the maximal efficiency, $η_{\text{max}}=(\text{extracted energy})/(\text{input energy})$, for the elastic collision of two massive particles and for the photoemission process, in which the ISCO particle will escape to infinity after the collision with a massless impinging particle. For non-spinning particles, the maximum efficiency is $η_{\text{max}} \approx 2.562$ for the elastic collision and $η_{\text{max}} \approx 7$ for the photoemission process. While for spinning particles we obtain the maximal efficiency $η_{\text{max}} \approx 8.442$ for the elastic collision and $η_{\text{max}} \approx 12.54$ for the photoemission process.

gr-qc↗