arXiv subjects

Umpei Miyamoto

Publications and source records attributed to Umpei Miyamoto.

At least 19 recordsLinked to original sources

arXiv2026

The critical radius of compressible capillary drops: viscosity, thermodynamics, and diffuse-interface scales

A compressible capillary drop differs from an incompressible one in that its radius is a dynamical degree of freedom. When the drop is sufficiently small, this spherical mode can become unstable, defining a critical radius set by the competition between surface tension and compressibility. This paper examines the robustness and physical meaning of that critical radius. For a non-relativistic viscous fluid, starting from the viscous compressible equations and the free-surface stress condition, we derive the radial dispersion relation and show that shear and bulk viscosities change the eigenvalues but not the onset radius. A thermodynamic argument identifies the same radius as the point where the energy of a uniformly compressed drop changes from locally stable to unstable, explaining why the threshold is not set by viscous dissipation. This energetic interpretation can also be applied to a special-relativistic fluid, where the non-relativistic mass-density factor is replaced by the corresponding enthalpy-density factor. We then compare the critical radius with diffuse-interface length scales in two Cahn--Hilliard free-energy models to determine whether the instability can occur within the range of validity of the sharp-interface description. In a symmetric quartic model the critical radius is much smaller than the interface thickness, so the instability is absent throughout that range. In a shallow-well model, however, the critical radius can become parametrically larger than the interface thickness, leaving a range of sharp-interface drops that are unstable. Whether such a range exists therefore depends on the diffuse-interface free-energy model.

physics.flu-dyn↗

arXiv2026

Determining Kerr black hole spin and inclination from a segment of the critical curve in black hole images

We present a method for determining the spin parameter $a/M$ and inclination angle $i$ of a non-extremal Kerr black hole from segments of the critical curve identified in black hole images. Although the critical curve itself is not directly observable, higher-order photon rings accumulate near it, and in realistic observations localized portions of the resulting brightness enhancement may be available for identifying segments of the critical curve. We introduce standardized segments of the critical curve and define three observables that characterize their geometry. We show that these observables uniquely determine $(a/M,i)$, together with an auxiliary parameter $r_{nl}\in[0,1]$ specifying the location of the identified segment along the critical curve, within the domain considered. Thus, even a segment of the critical curve contains sufficient geometric information to constrain the black hole spin and inclination without reconstructing the full critical curve. The framework is naturally suited to realistic observations and may be extended to more general rotating black hole spacetimes.

gr-qc↗

arXiv2026

A linear-algebraic formulation of dimensional analysis with constraints

Dimensional analysis, especially Buckingham's $\pi$ theorem, reduces the number of variables by rewriting a relation in terms of dimensionless quantities. When variables are tied by definitions, constitutive laws, or other constraints, however, eliminating variables in advance can be awkward. We formulate dimensional analysis with constraints as linear algebra in logarithmic variables. Dimensional transformations and constraints are represented by subspaces, the effective number of independent dimensionless quantities is characterized by their intersection, and a matrix representation yields a systematic redundancy elimination procedure. Examples from falling motion, drag force, and stock-market indicators illustrate the scope and limitations of the method.

math-ph↗

arXiv2025

Determining parameters of Kerr-Newman black holes by shadow observation from finite distance and spatial infinity

We present a method for determining the physical parameters of a Kerr-Newman black hole through shadow observation. In a system comprising a Kerr-Newman black hole, an observer, and a light source, the relevant parameters are mass $M$, specific angular momentum $a$, electric charge $Q$, inclination angle $i$, and distance $r_o$. We consider the cases where the observer is at either a finite distance or spatial infinity. Using our method, the dimensionless parameters $(a/M, Q/M, i)$ can be determined by observing the shadow contour of the Kerr-Newman black hole from spatial infinity. We analytically prove that the shadow contour of the Kerr-Newman black hole observed from spatial infinity is unique, where uniqueness is defined as the absence of two congruent shadow contours for distinct sets of dimensionless parameter values. This method is versatile and can be applied to a range of black hole solutions with charge. Additionally, we show analytically that the shadow contour of a Kerr-Newman black hole observed from a finite distance $r_o$ is not unique, meaning that the parameters of a Kerr-Newman black hole at finite distance cannot be determined from shadow observations. This result reveals a new challenge and provides a clear direction for further research on black hole shadows.

gr-qc↗

arXiv2024

Determining parameters of Kerr black holes at finite distance by shadow observation

We propose a new method to determine the physical parameters of Kerr black holes (namely, specific angular momentum $a$, inclination angle $i$, and distance $D$ from an observer) only from the shadow's information such as the size and shape. Key points in our method are (i) to treat the distance as a free parameter, (ii) to expand the shadow's outline as a Fourier series, and (iii) to construct principal components from the Fourier coefficients. These points enable us to obtain a one-to-one mapping between three principal components, being observables characterizing the size and deviation of shadow's shape from a circular disk, and the values of three parameters ($D/M, a/M, i$), where $M$ is the mass of black hole. Our method is applicable to various type of black holes and even to ones with accretion disks.

gr-qc↗

arXiv2023

Stability of hypersurfaces of constant mean curvature with free boundary in two parallel hyperplanes

Surfaces with constant mean curvature (CMC) are critical points of the area with volume constraint. They serve as a mathematical model of surfaces of soap bubbles and tiny liquid drops. CMC surfaces are said to be stable if the second variation of the area is nonnegative for all volume-preserving variations satisfying the given boundary condition. In this paper, we examine the stability of CMC hypersurfaces in general Euclidean space possibly having boundaries on two parallel hyperplanes. We reveal the stability of equilibrium hypersurfaces without self-intersection for the first time in all dimensions. The analysis is assisted by numerical computations.

math.DG↗

arXiv2023

Stability of hypersurfaces with constant mean curvature trapped between two parallel hyperplanes

Static equilibrium configurations of continua supported by surface tension are given by constant mean curvature (CMC) surfaces which are critical points of a variational problem to extremize the area while keeping the volume fixed. CMC surfaces are used as mathematical models of a variety of continua, such as tiny liquid drops, stars, and nuclei, to play important roles in both mathematics and physics. Therefore, the geometry of CMC surfaces and their properties such as stability are of special importance in differential geometry and in a variety of physical sciences. In this paper we examine the stability of CMC hypersurfaces in arbitrary dimensions, possibly having boundaries on two parallel hyperplanes, by investigating the second variation of the area. We determine the stability of non-uniform liquid bridges or unduloids for the first time in all dimensions and all parameter (the ratio of the neck radius to bulge radius) regimes. The analysis is assisted by numerical computations.

math-ph↗

arXiv2023

Determining parameters of a spherical black hole with a thin accretion disk by observing its shadow

We revisit the classic system of a spherically symmetric black hole in general relativity (i.e., a Schwarzschild black hole) surrounded by a geometrically thin accretion disk. Our purpose is to examine whether one can determine three parameters of this system (i.e., black hole mass $M$, distance between the black hole and an observer $r_o$, inclination angle $i$) solely by observing the accretion disk and the black hole shadow. A point in our analysis is to allow $r_o$ to be finite, which is set to be infinite in most relevant studies. First, it is shown that one can determine the values of $(r_o/M, i)$, where $M/r_o$ is the so-called angular gravitational radius, from the size and shape of shadow. Then, it is shown that if one additionally knows the accretion rate $\dot{M}$ (respectively, mass $M$) by any independent theoretical or observational approach, one can determine the values of $(M, r_o, i)$ [respectively, $(\dot{M}, r_o, i)$] without degeneracy, in principle, from the value of flux at any point on the accretion disk.

gr-qc↗

arXiv2019

Escape probability of a photon emitted near the black hole horizon

We investigate the escape of photons from the vicinity of the horizon to infinity in the Kerr-Newmann black hole spacetime. We assume that a light source is at rest in a locally nonrotating frame and photons are emitted isotropically. Then, we evaluate the escape probability of the emitted photons. The main result of this paper is the following. If the black hole is extremal with the nondimensional spin parameter $a_*> 1/2$, however close to the horizon the light source would be, the escape probability remains nonzero. The near-horizon limit value of the escape probability is a monotonically increasing function of $a_*$ and takes a maximum $\sim$29.1\% at $a_*=1$, i.e., for the extremal Kerr case. On the other hand, if the black hole is extremal with $0\leq a_*\leq 1/2$ or if the black hole is subextremal, the near-horizon limit value is zero.

gr-qc↗

arXiv2019

Explosive particle creation by instantaneous change of boundary condition

We investigate the dynamic Casimir effect (DCE) of a $1+1$ dimensional free massless scalar field in a finite or semi-infinite cavity for which the boundary condition (BC) instantaneously changes from the Neumann to Dirichlet BC or reversely. While this setup is motivated by the gravitational phenomena such as the formation of strong naked singularities or wormholes, and the topology change of spacetimes or strings in quantum gravity, the analysis is quite general. For the Neumann-to-Dirichlet cases, we find two components of diverging flux emanate from the point where the BC changes. We carefully compare this result with that of Ishibashi and Hosoya (2002) obtained in the context of a quantum version of cosmic censorship hypothesis, and show that one of the diverging components was overlooked by them and is actually non-renormalizable, suggesting to bring non-negligible backreaction or semiclassical instability. On the other hand, for the Dirichlet-to-Neumann cases, we reveal for the first time that only one component of diverging flux emanates, which is the same kind as that overlooked in the Neumann-to-Dirichlet cases. This result suggests not only the robustness of the appearance of diverging flux in instantaneous limits of DCE but also that the type of divergence sensitively depends on the combination of initial and final BCs.

hep-th↗

arXiv2018

Systematical study of pulsar light curves with special relativistic effects

We systematically study pulsar light curves, taking into account the special relativistic effect, i.e., the Doppler factor due to the fast spin of the neutron stars, together with the time delay, which comes from the difference of the travel times depending on the position of the spots. For this purpose, first we derive the basic equations with the general expression of the metric for the static, spherically symmetric spacetime, where for simplicity we adopt the pointlike spot approximation for the antipodal spots associated with the magnetic polar cap model. Then, we calculate the light curves from the neutron star models in general relativity, with various angle between rotational and magnetic axes and the inclination angle. As the results, unlike the case for a slowly rotating stellar model, we find that the light curve from a fast rotating stellar model depends not only the stellar compactness but also the stellar radius. We also find that the amplitude of the light curve becomes larger as the stellar radius increases and as the stellar compactness decreases. Thus, via careful observations of the light curves from the rotating neutron star, one would determine the stellar compactness together with the stellar radius, if it rotates fast enough.

astro-ph.HE↗

arXiv2018

Pulse profiles of highly compact pulsars in general relativity

Gravitational light bending by compact stars is an important astrophysical phenomenon. The bending angle depends on the stellar compactness, which is the ratio of stellar mass $M$ to radius $R$. In this paper, we investigate the pulse profile of highly compact rotating neutron stars for which the bending angle exceeds $π/2$. When $M/R > 0.284$ (the bending angle becomes equal to $π/2$ for the stellar model with $M/R=0.284$), such a large bending happens, resulting in that a photon emitted from any position on the stellar surface can reach an observer. First, we classify the parameter plane of inclination angle $i$ and angle $Θ$ between the rotation axis and the normal on the hot spot by the number of photon paths reaching the observer. Then, we estimate the time-dependent flux of photons emitted from two hot spots on the rotating neutron star, associated with the magnetic polar caps, for various combinations of $i$ and $Θ$, and for two values of compactness, assuming that the stellar rotation is not so fast that the frame dragging and the stellar deformation are negligible. As the result, we find that the pulse profiles of highly compact neutron stars are qualitatively different from those for the standard neutron stars. In particular, the ratio of the maximum observed flux to the minimum one is significantly larger than that for the standard neutron stars. This study suggests that one would be able to constrain the equation of state for neutron stars through the observation of pulse profile with angles $i$ and $Θ$ determined by other methods.

astro-ph.HE↗

arXiv2017

Sensitivity of pulsar light curves to spacetime geometry and efficacy of analytic approximations

In order to examine the pulse profile from a pulsar, we derive the formula for describing the flux from antipodal hot spots with any static, spherically symmetric spacetime. We find that the pulse profiles are almost independent of the gravitational geometry outside the star when the compactness of neutron stars is low enough, e.g., the stellar mass and radius are $1.4M_\odot$ and 14 km, respectively. On the other hand, the pulse profiles depend strongly on the gravitational geometry when the compactness of neutron stars is so high, e.g., the stellar mass and radius are $1.8M_\odot$ and 10 km, respectively. Thus, one may probe the spacetime geometry outside the star and even distinguish gravitational theories via the observation of pulse profile with the help of another observations for the stellar compactness, if the compactness of central object is high enough. We also derive the 1st and 2nd order approximation of the flux with respect to a parameter defined by the radio of the gravitational radius of considered spacetime to the stellar radius. Then, we find that the relative error from full order numerical results in the bending angle becomes $\sim 20-30\%$ with the 1st order and $\sim 5-10\%$ with the 2nd order approximations for a typical neutron star, whose mass and radius are $1.4M_\odot$ and 12 km, respectively. Our results with the 1st order approximation for the Schwarzschild spacetime are different from those obtained in the literature, which suggests that the 1st order approximation has been misunderstood to yield highly accurate prediction.

astro-ph.HE↗

arXiv2017

Escape probability of the super-Penrose process

We consider a head-on collision of two massive particles that move in the equatorial plane of an extremal Kerr black hole, which results in the production of two massless particles. Focusing on a typical case, where both of the colliding particles have zero angular momenta, we show that a massless particle produced in such a collision can escape to infinity with arbitrarily large energy in the near-horizon limit of the collision point. Furthermore, if we assume that the emission of the produced massless particles is isotropic in the center-of-mass frame but confined to the equatorial plane, the escape probability of the produced massless particle approaches $5/12$ and almost all escaping massless particles have arbitrarily large energy at infinity and an impact parameter approaching $2GM/c^2$, where $M$ is the mass of the black hole.

gr-qc↗

arXiv2017

Non-linear perturbation of black branes at large $D$

The Einstein equations describing the black-brane dynamics both in Minkowski and AdS background were recently recast in the form of coupled diffusion equations in the large-$D$(imension) limit. Using such results in the literature, we formulate a higher-order perturbation theory of black branes in time domain and present the general form of solutions for arbitrary initial conditions. For illustrative purposes, the solutions up to the first or second order are explicitly written down for several kind of initial conditions, such as a Gaussian wave packet, shock wave, and rather general superposed sinusoidal waves. These could be the first examples describing the non-trivial evolution of black-brane horizons in time domain. In particular, we learn some interesting aspects of black-brane dynamics such as the Gregory-Laflamme (GL) instability and non-equilibrium steady state (NESS). The formalism presented here would be applicable to the analysis of various black branes and their holographically dual field theories.

hep-th↗

arXiv2016

Consistent analytic approach to the efficiency of collisional Penrose process

We propose a consistent analytic approach to the efficiency of collisional Penrose process in the vicinity of a maximally rotating Kerr black hole. We focus on a collision with arbitrarily high center-of-mass energy, which occurs if either of the colliding particles has its angular momentum fine-tuned to the critical value to enter the horizon. We show that if the fine-tuned particle is ingoing on the collision, the upper limit of the efficiency is $(2+\sqrt{3})(2-\sqrt{2})\simeq 2.186$, while if the fine-tuned particle is bounced back before the collision, the upper limit is $(2+\sqrt{3})^{2}\simeq 13.93$. Despite earlier claims, the former can be attained for inverse Compton scattering if the fine-tuned particle is massive and starts at rest at infinity, while the latter can be attained for various particle reactions, such as inverse Compton scattering and pair annihilation, if the fine-tuned particle is either massless or highly relativistic at infinity. We discuss the difference between the present and earlier analyses.

gr-qc↗

arXiv2016

Vacuum excitation by sudden appearance and disappearance of a Dirichlet wall in a cavity

Vacuum excitation by time-varying boundary conditions is not only of fundamental importance but also has recently been confirmed in a laboratory experiment. In this paper, we study the vacuum excitation of a scalar field by the instantaneous appearance and disappearance of a both-sided Dirichlet wall in the middle of a 1D cavity, as toy models of bifurcating and merging spacetimes, respectively. It is shown that the energy flux emitted positively diverges on the null lines emanating from the appearance and disappearance events, which is analogous to the result of Anderson and DeWitt. This result suggests that the semiclassical effect prevents the spacetime both from bifurcating and merging. In addition, we argue that the diverging flux in the disappearance case plays an interesting role to compensate for the lowness of ambient energy density after the disappearance, which is lower than the zero-point level.

hep-th↗

arXiv2015

High efficiency of collisional Penrose process requires heavy particle production

The center-of-mass energy of two particles can become arbitrarily large if they collide near the event horizon of an extremal Kerr black hole, which is called the Ba$\rm \tilde n$ados-Silk-West (BSW) effect. We consider such a high-energy collision of two particles which started from infinity and follow geodesics in the equatorial plane and investigate the energy extraction from such a high-energy particle collision and the production of particles in the equatorial plane. We analytically show that, on the one hand, if the produced particles are as massive as the colliding particles, the energy-extraction efficiency is bounded by $2.19$ approximately. On the other hand, if a very massive particle is to be produced as a result of the high-energy collision, which has negative energy and necessarily falls into the black hole, the upper limit of the energy-extraction efficiency is increased to $(2+\sqrt{3})^2 \simeq 13.9$. Thus, higher efficiency of the energy extraction, which is typically as large as 10, provides strong evidence for the production of a heavy particle.

gr-qc↗