arXiv subjects

Naoki Tsukamoto

Publications and source records attributed to Naoki Tsukamoto.

At least 19 recordsLinked to original sources

arXiv2026

Gravitational lensing outside and inside of a marginally unstable photon sphere at a $Z_2$-symmetric wormhole throat in strong deflection limits

The deflection angles of rays diverge logarithmically near outside and inside of a photon sphere and they could be detected by near-future space observations on black hole shadows. We show that the deflection angles of the rays near a photon sphere at the throat of an example among some commonly used types of wormholes or one of the simple wormholes, which is often studied by the Event Horizon Telescope collaborations, does diverge not logarithmically but in power. This is because it has a marginally unstable photon sphere at a $Z_2$-symmetric wormhole throat and the wormhole has not a common nor simple but a special property. We investigate numerically gravitational lensing of rays with the deflection angles diverging in power outside and inside of a marginally unstable photon sphere at $Z_2$-symmetric wormhole throat in strong deflection limits. We apply our numerical method to the commonly-used simple wormhole spacetime, a Damour-Solodukhin wormhole spacetime, and a Simpson-Visser black-bounce spacetime. Our numerical results imply universal property of the deflection angle by the marginally unstable photon sphere on $Z_2$-symmetric wormhole throat in the strong deflection limits as similar to the deflection angles of ray bent by a marginally unstable photon sphere off a throat in the strong deflection limits which have a different power. We also correct the coefficients of power-divergent terms of deflection angles of the rays bent nearly outside of the marginally unstable photon sphere at the $Z_2$-symmetric wormhole throat in a semi-analytic approach investigated by the author and others.

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arXiv2026

Strong-deflection expansion of the deflection angle near a degenerate photon sphere

We present a strong-deflection expansion for the deflection angle of light rays scattered near a degenerate photon sphere in asymptotically flat, static, and spherically symmetric spacetimes. Our prescription isolates the divergent contribution to the deflection-angle integral arising from the ray's passage near the marginal orbit in a way that remains well defined at marginality, thereby yielding a unique leading power-law term. When expressed in terms of the radius of closest approach, the leading coefficient in the strong deflection limit factorizes into a universal branch constant and a local factor determined by the third derivative of the effective potential at the degenerate photon sphere. Passing to the expansion in terms of the impact parameter then only multiplies the coefficient by an additional local conversion factor. We show that the local factor in the closest-approach expansion admits an invariant representation through the areal-radius derivative of a dimensionless tidal measure constructed from the electric part of the Weyl tensor. In general relativity, we further relate this quantity to the areal-radius derivative of a weighted null-energy density profile. Analytic examples validate this factorization and yield closed-form expressions for the leading divergent coefficients in representative marginal configurations.

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arXiv2026

Dyonic hairy black holes in $U(1)$ gauge-invariant scalar-vector-tensor theories: Cubic and quartic SVT sectors

We construct and classify asymptotically flat, static, and spherically symmetric hairy black hole solutions in $U(1)$ gauge-invariant scalar-vector-tensor (SVT) theories carrying both electric and magnetic charges. Extending previous analyses restricted to ${\cal L}_{\rm SVT}^{2}$, we incorporate the cubic and quartic SVT sectors, ${\cal L}_{\rm SVT}^{3}$ and ${\cal L}_{\rm SVT}^{4}$, respectively. At the covariant level, the quartic SVT sector can generate higher-order derivatives, and we derive a condition that removes them before specializing to dyonic backgrounds, where they are generically present. We then classify the scalar hair according to the symmetry of the theory. In shift-symmetric theories, horizon regularity together with Noether-current conservation determines the scalar charge in terms of the remaining solution parameters, corresponding to secondary hair. When the couplings depend explicitly on the scalar field $\phi$, independent scalar integration constants appear in the asymptotic solutions, allowing branches with primary hair. We also find that the magnetic charge activates the $\tilde f_3$ interaction in the cubic SVT sector, which does not contribute in purely electric static and spherically symmetric configurations, thereby producing hairy solutions supported by the magnetic charge. The scalar field also exhibits interaction-dependent asymptotic falloff rates. Combining these expansions with numerical integration, we connect the near-horizon and asymptotic regimes for all branches in the cubic sector and for one of the two quartic branches. For the remaining quartic branch, our result is restricted to the local near-horizon expansion.

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arXiv2025

Gravitational lensing inside and outside of a marginally unstable photon sphere in a general, static, spherically symmetric, and asymptotically-flat spacetime in strong deflection limits

It is believed that rays bent inside and outside photon spheres could affect partially the black hole shadow images by the Event Horizon Telescope and the rays near photon spheres would be detected by near-future space observations. The investigation of the rays near the photon spheres in not only black hole spacetimes but also exotic spacetimes would be important since one will need them to exclude black hole mimickers. The deflection angles of the rays deflected by the photon spheres diverge logarithmically and we can treat them by a strong-deflection-limit analysis. The error of the strong-deflection-limit analysis becomes large if antiphoton spheres exist in the spacetimes and the analysis breaks down when the photon spheres and the antiphoton spheres degenerate to form a marginally unstable photon sphere. This is because the deflection angles of the rays bent by the marginally unstable photon sphere diverge in powers. In this paper, we extend Eiroa, Romero, and Torres's method to gravitational lensing of rays inside and outside of the marginally unstable photon sphere in a general, static, spherically symmetric, and asymptotically-flat spacetime in strong deflection limits and we apply it to a Reissner-Nordstr\"{o}m spacetime and a Hayward spacetime with the marginally unstable photon sphere. We have also confirmed that the deflection angles in the strong deflection limits by the method converge correctly to the deflection angle without approximations, while there are the mismatches of the coefficient of the power-divergent term of the deflection angles of the rays deflected just outside of the marginally unstable photon sphere in a semianalytic calculation by the author previously.

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arXiv2025

Linear perturbations of dyonic black holes in the lowest-order $U(1)$ gauge-invariant scalar-vector-tensor theories

We study linear perturbations on top of the static and spherically symmetric background of dyonic black hole solutions endowed with electric and magnetic charges, as well as a scalar hair, in the lowest-order $U(1)$ gauge-invariant scalar-vector-tensor theories. The presence of magnetic charges in the background solutions gives rise to a mixing between the odd-parity and even-parity sectors of perturbations, which makes it impossible to analyze each sector separately. Thus, we expand the action up to second order in both odd-parity and even-parity perturbations and derive the general conditions for the absence of ghosts and Laplacian instabilities. We apply these general conditions to extended Einstein-Maxwell-scalar theories, which encompass numerous types of concrete models from the literature known to have dyonic black hole solutions with the scalar hair, and examine their stabilities. Our general framework for studying stability conditions and dynamics of perturbations can be applied to a wide variety of theories, including nonlinear electrodynamics coupled to a scalar field, as well as to calculations of black hole quasinormal modes.

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arXiv2025

Circular light orbits of a general, static, and spherical symmetrical wormhole with $Z_2$ symmetry

Recently, the ring images or the shadow images of the centers of the galaxy M87 and the Milky way have been reported by Event Horizon Telescope Collaboration. It is believed that the ring images imply that the central objects form unstable light circular orbits. Some of wormholes with $Z_2$ symmetry against a throat are wrongly excluded from the candidates at the centers of M87 and the Milky way due to the overlooking the unstable light circular orbits on the throat. A general asymptotically-flat, static, and spherical symmetrical wormhole without a thin shell has at least one unstable circular light orbit at the throat or elsewhere. If the wormhole has $Z_2$ symmetry against the throat, it has the unstable circular light orbits on the throat or it has stable circular light orbits on the throat and unstable ones near the throat. We need to analyze the throat carefully to make sure we do not unfairly rule out the $Z_2$-symmetrical wormholes. In this study, we categorize the numbers of the circular light orbits of the $Z_2$-symmetrical wormhole and their stability from the derivatives of an effective potential at the throat and we investigate the circular light orbits around a Simpson-Visser black-bounce spacetime, a Damour-Solodukhin wormhole spacetime, a Reissner-Nordström black-hole-like wormhole spacetime or a charged Damour-Solodukhin wormhole spacetime as examples. We give complete treatments including degenerated circular light orbits made from more than one stable and unstable circular light orbits on and off the throat.

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arXiv2024

Neutral particle collisions near Gibbons-Maeda-Garfinkle-Horowitz-Strominger black holes after shadow observations

A Gibbons-Maeda-Garfinkle-Horowitz-Strominger (GMGHS) black hole with a magnetic charge (or an electric charge) has noteworthy features that its scalar curvature near the event horizon of the black hole with the almost maximal charge can be extremely large. The large curvature, which is related with the gravity on a finite-sized object or between two points, causes high center-of-mass energy for two neutral particles near the almost maximally charged GMGHS black hole. Recently, the Event Horizon Telescope Collaboration gave the bound on the charge of black holes from the shadow and mass observations of black holes under an assumption that the diameter of observed rings are proportion to that of photon spheres. The photon sphere would be less related with the curvature, since it is determined by the behavior of one photon or one ray neither two photons nor two rays. Thus, the high-energy neutral particle collision and the black hole shadow observations would be complementary to distinguish the GMGHS black hole from other black hole solutions. In this paper, we investigate a new way to compare the center-of-mass energy for neutral particle collisions in the GMGHS spacetime and other black hole spacetimes. From the shadow observations and the mass observations under the assumptions on the effect of black hole charges, we can put constraints on the center-of-mass energy of the particles. We apply our method to shadow and mass observations of M87* and Sagittarius A*. We find that the center-of-mass energy of neutral particles near the GMGHS black holes cannot be extremely large under the observational constraints, and conclude that the GMGHS spacetimes are hardly distinguishable from the Reissner-Nordström spacetimes by the particle collisions if we apply the shadow and mass observations at $1 σ$ probability.

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arXiv2024

Constraints on the black-hole charges of M87* and Sagittarius A* by changing rates of photon spheres can be relaxed

The Event Horizon Telescope (EHT) Collaboration observed ring images called the shadows of M87* and Sagittarius~A* (Sgr~A*), which are supermassive objects in M87 and our galaxy, respectively, and their general relativistic magnetohydrodynamic simulations of black holes imply that the observed rings are formed by the gravitational lensing of synchrotron radiations from a hot plasma near outside of supermassive black holes. The EHT Collaboration gave constrains on the electrical or alternative charges of M87* and Sgr A* under an assumption that the radius of the observed ring should be proportional to the changing rates of photon spheres by the charges. Since the validness of this assumption is not sure, it is worth to checking the same constraints under another assumption. In this paper, we consider the changing rates of not only the photon spheres but also lensing rings in a simple model and we test whether aforementioned constraint is robust. We conclude that EHT Collaboration's constraints based on the changing rates of the photon spheres can be relaxed compared to that based on the changing rate of the lensing rings while we do not claim that the observed rings are formed by the photon spheres and the lensing rings in our simple model. We concentrate on Reissner-Nordström black hole spacetimes in this paper, but our result implies the relaxation of the bound of the charge parameters on other black hole spacetimes.

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arXiv2024

Relation between circular photon orbits and the stability of wormholes with the thin shell of a barotropic fluid

We cut a general, static, spherically symmetric spacetime and paste its copy to make a wormhole with a thin shell of any barotropic fluid in general relativity. We show that the stability of the thin-shell wormhole is characterized by a set of circular photon orbits called an (anti)photon sphere in the original spacetime if a momentum flux passing through a throat is prohibited. Our result will be useful to classify the stability of the thin shell on the throat against linearized spherically symmetric perturbations.

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arXiv2023

Comment on "Horizon-scale tests of gravity theories and fundamental physics from the Event Horizon Telescope image of Sagittarius A*"

Vagnozzi et al. constrained the additional parameter of spacetimes with a photon sphere from the observation of the shadow of Sagittarius A* under the assumption that a distance to the Sagittarius A* and its mass parameter was estimated from other observations. They claimed that a Damour-Solodukhin wormhole with an additional parameter $λ$ is not an asymptotically-flat spacetime and that they gave the first robust observational constraint on the parameter $λ$ of the Damour-Solodukhin wormhole. However, they overlooked the fact that: (A) the Damour-Solodukhin wormhole spacetime is asymptotically flat, (B) the throat of the Damour-Solodukhin wormhole works as an effective photon sphere for $λ>\sqrt{2}/2$, and (C) not only a usual mass parameter but also the parameter $λ$ contributes the mass of the Damour-Solodukhin wormhole. Because of the overlook (C), we realize that their constraint on the parameter $λ$ is invalid. This is because their method corresponds to the following way: They estimated the mass parameter from the other observations under the assumption $λ=0$ even though the value of the parameter $λ$ strongly affects the determination of the mass parameter, and then, they used the value of the mass parameter to constrain $λ$ from the observation of the shadow. We conclude that we should constrain the mass parameter and $λ$ from the shadow observation and other observations without the assumption $λ=0$.

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arXiv2023

Gravitational lensing by using the 0th order of affine perturbation series of the deflection angle of a ray near a photon sphere

The 0th order of affine perturbation series of the deflection angle of a ray near a photon sphere is more accurate than a deflection angle in a strong deflection limit, which is used often, because the later has hidden error terms. We investigate gravitational lensing by using 0th order affine perturbation series of the deflection angle in a general asymptotically-flat, static, and spherical symmetric spacetime with the photon sphere. We apply our formula to Schwarzschild black hole, Reissner-Nordström black hole, and Ellis-Bronnikov wormhole spacetimes as examples. By comparing observables by using the deflection angles, we show that we can ignore the effect of the hidden error terms in the deflection angle in the strong deflection limit on the observables in a usual lens configuration with the photon sphere since the hidden error terms are tiny. On the other hand, in a retro lensing configuration, the deflection angle in the strong-deflection-limit analysis have error of several percent and the 0th order of affine perturbation series of the deflection angle has almost half of the error. Thus, in the retro lensing configuration, we should use the 0th order of affine perturbation series of the deflection angle rather than the deflection angle in the strong-deflection-limit analysis. The 0th order of affine perturbation series of the deflection angle can give a brighter magnification by a dozen percent than the one by using the deflection angle in the strong-deflection-limit analysis.

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arXiv2022

Affine perturbation series of the deflection angle of a ray near the photon sphere of a Reissner-Nordström black hole

We investigate the affine perturbation series of the deflection angle of a ray near the photon sphere of an extreme Reissner-Nordström black hole. We compare the 0th and 1st orders of the affine perturbation series with the deflection angle in a strong deflection limit. We conclude that the 0th order of the affine perturbation series is more accurate than the deflection angle in the strong deflection limit and that we should improve a strong-deflection-limit analysis by using the 0th order of the affine perturbation series.

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arXiv2022

Nonlogarithmic divergence of a deflection angle by a marginally unstable photon sphere of the Damour-Solodukhin wormhole in a strong deflection limit

Static, spherically symmetric black holes and compact objects without an event horizon have unstable (stable) circular orbits of a light called photon (antiphoton) sphere. A Damour-Solodukhin wormhole has been suggested as a simple black hole mimicker and the difference of its metric tensors from a black hole is described by a dimensionless parameter $λ$. The wormhole with two flat regions has two photon spheres and an antiphoton sphere for $λ<\sqrt{2}/2$ and a photon sphere for $λ\geq \sqrt{2}/2$. When the parameter $λ$ is $\sqrt{2}/2$, the photon sphere is marginally unstable because of degeneration of the photon spheres and antiphoton sphere. We investigate gravitational lensing by the wormhole in weak and strong gravitational fields. We find that the deflection angle of a light ray reflected by the marginally unstable photon sphere diverges nonlogarithmically in a strong deflection limit for $λ=\sqrt{2}/2$, while the deflection angle reflected by the photon sphere diverges logarithmically for $λ\neq \sqrt{2}/2$. We extend a strong deflection limit analysis for the nonlogarithmic divergence case. We expect that our method can be applied for gravitational lenses by marginally unstable photon spheres of various compact objects.

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arXiv2022

Is there a trade-off relation between efficiency and power in a collisional Penrose process in an extreme Reissner-Nordström spacetime?

We investigate the power of a collisional Penrose process with an unbound energy extraction from an extreme Reissner-Nordström black hole. This process takes infinite time in a time coordinate at a constant radial coordinate outside of the black hole. For black holes as a power plant, the power of the process for an observer far away from the black hole can be useful. We define the power as energy gain from the extreme Reissner-Nordström black hole divided by the time interval of the process in a coordinate time; we estimate the upper bound of the power in a near-horizon limit, while the efficiency of the process can be arbitrary large in that limit. Thus, we conclude that there is no trade-off relation between the efficiency and power in the collisional Penrose process in extreme Reissner-Nordström spacetime.

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arXiv2022

Retrolensing by two photon spheres of a black-bounce spacetime

We investigate retrolensing by two photon spheres in a novel black-bounce spacetime suggested by Lobo et al. which can correspond to a Schwarzschild black hole, a regular black hole, and a traversable wormhole including an Ellis-Bronnikov wormhole. In a case, the wormhole has a throat which acts as a photon sphere and it has another photon sphere outside of the throat. With the sun as a light source, an observer, and the wormhole are lined up in this order, sunlight reflected slightly outside of the throat and barely outside and inside of the outer photon sphere can reach the observer. We show that the light rays reflected by the outer photon sphere are dominant in retrolensing light curves in the case.

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arXiv2022

Gravitational lensing by a Bronnikov-Kim wormhole under a weak-field approximation and in a strong deflection limit

We consider gravitational lensing under a weak-field approximation and in a strong deflection limit by a Bronnikov-Kim wormhole with the same metric as the one of a wormhole which has been suggested in Einstein-Dirac-Maxwell theory. The metric approaches into the metric of an extreme charged Reissner-Nordström black hole in a black hole limit and it becomes the metric of an spatial Schwarzschild wormhole in an ultrastatic limit. In both of the black hole limit and the ultrastatic limit, the coefficient of a divergent term and the constant term of the deflection angle of a light in the strong deflection limit can be obtained exactly without expanding of parameters of the spacetime. Interestingly, in the both limits to the black hole and the ultrastatic wormhole, we obtain exactly the same coefficient and constant term in the strong deflection limit.

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arXiv2022

Gravitational lensing by two photon spheres in a black-bounce spacetime in strong deflection limits

We investigate gravitational lensing by a primary photon sphere which is a sphere filled with unstable circular light orbits, and by a secondary photon sphere on a wormhole throat in a black-bounce spacetime which is suggested in [F. S. N. Lobo, M. E. Rodrigues, M. V. d. S. Silva, A. Simpson, and M. Visser, Phys. Rev. D 103, 084052 (2021)] in strong deflection limits. There is an antiphoton sphere between the primary photon sphere and the secondary photon sphere. If a light source and an observer are on the same side of the wormhole throat, in addition to an infinite number of images slightly outside of both the primary and secondary photon spheres, an infinite number of images formed by light rays reflected by the potential barrier near the antiphoton sphere, slightly inside the primary photon sphere, might be observed.

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arXiv2021

Retrolensing by light rays slightly inside and outside of a photon sphere around a Reissner-Nordström naked singularity

We investigate retrolensing of sunlights reflected by a photon sphere and by a potential barrier near an antiphoton sphere around a Reissner-Nordström naked singularity. We apply the deflection angles of light rays in strong deflection limits to the retrolensing. We show that the retrolensing by the photon sphere around the Reissner-Nordström naked singularity can be brighter than the one around a Reissner-Nordström black hole because of the existence of the rays which reflected by the potential barrier.

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