Searcharxiv⌕ Search

arXiv subjects

Yoshimune Tomikawa

Publications and source records attributed to Yoshimune Tomikawa.

At least 19 recordsLinked to original sources
arXiv2026

Exact solutions for static spherically symmetric spacetime with a perfect fluid in Rastall theory

In general relativity, exact Liouvillian solutions for a static and spherically symmetric spacetime with a perfect fluid and the equation of state $p(r)=wρ(r)$ are known only for $w=0,-\frac{1}{6}, -\frac{1}{5}, -\frac{1}{3}, -1$. We extend this setup to Rastall's theory, presenting the relation between the Rastall parameter and the constant $w$, and deriving exact solutions that correspond to the known counterparts in general relativity, except for $w=-\frac{1}{6}$. Furthermore, we find that, when $w\neq \frac{1}{3}, -1$, there exist several types of solutions whose behavior changes depending on the choice of constants.

gr-qc↗
arXiv2025

Quasilocal inequalities for attractive gravity probe surface

We discuss the local and quasilocal properties of the loosely trapped surface (LTS) and the attractive gravity probe surface (AGPS), which have been proposed to characterize the strength of gravity in both strong and weak gravity regions using the mean curvature. In terms of local mass defined in a region surrounded by the two AGPSs and of Geroch quasilocal mass, we present several inequalities concerning their size and area, which are of particular interest. We also propose the improved concepts of the LTS/AGPS, which we call LTS Plus (LTS+) and AGPS Plus (AGPS$+$), defined in terms of expansions of outgoing and ingoing null geodesic congruences on those surfaces. Then, the similar inequalities are proven in terms of appropriately defined local mass and the Hawking quasilocal mass.

gr-qc↗
arXiv2025

Attractive gravity probe surface in Einstein-Maxwell system

We derive areal inequalities for five types of attractive gravity probe surfaces, which were proposed by us in order to characterize the strength of gravity in different ways including weak gravity region, taking into account of contributions of electric and magnetic charges, angular momentum, gravitational waves, and matters. These inequalities are generalizations of the Riemannian Penrose inequality for minimal surfaces, and lead to the concept of extremality for a given surface whose condition is given in terms of the gravitational mass and the electromagnetic charges. This means that the extremality is a characteristic property not only of black hole horizons or minimal surfaces but also of surfaces in weak gravity region. We also derive areal inequalities and extremality conditions for surfaces in asymptotically locally anti-de Sitter spacetimes.

gr-qc↗
arXiv2024

Loosely trapped surface for slowly rotating black hole

We construct the marginal loosely trapped surface (marginal LTS) for the Kerr spacetime with a small Kerr parameter perturbatively, where the LTS condition is saturated. An LTS is a surface that specifies the strong gravity region, which is a generalization of the photon sphere in the Schwarzschild spacetime. It turns out that there are an infinite number of marginal LTSs. At the leading order of the small Kerr parameter, all of the marginal LTSs have the same area. However, one can see that the maximal marginal LTS among them is uniquely determined at the higher order.

gr-qc↗
arXiv2024

A generalization of photon sphere based on escape/capture cone

In asymptotically flat spacetimes, bearing the null geodesics reaching the future null infinity in mind, we propose new concepts, the "dark horizons" as generalizations of the photon sphere. They are defined in terms of the structure of escape/capture cones of photons with respect to a unit timelike vector field. More specifically, considering a two-sphere that represents a set of emission directions of photons, the dark horizons are located at positions where a hemisphere is marginally included in the capture and escape cones, respectively. We show that both of them are absent in the Minkowski spacetime, while they exist in spacetimes with black hole(s) under a certain condition. We derive the general properties of the dark horizons in spherically symmetric spacetimes and explicitly calculate the locations of the dark horizons in the Vaidya spacetime and the Kerr spacetime.

gr-qc↗
arXiv2023

Asymptotic behavior of null geodesics near future null infinity IV: Null-access theorem for generic asymptotically flat spacetime

In our previous papers [arXiv:2106.03150, arXiv:2110.10917, arXiv:2208.00822], we analyzed the asymptotic behavior of future directed null geodesics near future null infinity and then we showed a proposition on the accessibility of the null geodesics to future null infinity in a specific class of asymptotically flat spacetimes. In this paper, we adopt the retarded time of the Bondi coordinate as the parameter for the null geodesics and then see that one can relax the assumptions imposed in our previous studies. As a consequence, we obtain a new null-access theorem for generic asymptotically flat spacetimes.

gr-qc↗
arXiv2022

Asymptotic behavior of null geodesics near future null infinity. III. Photons towards inward directions

A new sufficient condition for photons emitted near future null infinity to reach future null infinity is derived by studying null geodesics in the Bondi coordinates in asymptotically flat spacetimes. In our previous works [arXiv:2106.03150, arXiv:2110.10917], such a condition was established for photons emitted in outward or tangential directions to constant radial surfaces. This paper improves our previous result by including photons emitted in inward directions. In four dimensions, imposing the same assumptions on the metric functions as previously, we prove that photons reach future null infinity if their initial values of $|dr/du|$ are smaller than a certain quantity, where $r$ and $u$ are the radial and retarded time coordinates, respectively. This quantity is determined by the asymptotic properties of the metric and is connected to the conjectured maximal luminosity. In higher dimensions, photons emitted with $dr/du>-(1-1/\sqrt{3})\approx -0.423$ are shown to reach future null infinity without the assumptions on the metric functions.

gr-qc↗
arXiv2022

Attractive gravity probe surfaces in higher dimensions

A generalization of the Riemannian Penrose inequality in $n$-dimensional space ($3\le n<8$) is done. We introduce a parameter $α$ ($-\frac{1}{n-1}<α< \infty$) indicating the strength of the gravitational field, and define a refined attractive gravity probe surface (refined AGPS) with $α$. Then, we show the area inequality for a refined AGPS, $A \le ω_{n-1} \left[ (n+2(n-1)α)Gm /(1+(n-1)α) \right]^{\frac{n-1}{n-2}}$, where $A$ is the area of the refined AGPS, $ω_{n-1}$ is the area of the standard unit $(n-1)$-sphere, $G$ is Newton's gravitational constant and $m$ is the Arnowitt-Deser-Misner mass. The obtained inequality is applicable not only to surfaces in strong gravity regions such as a minimal surface (corresponding to the limit $α\to \infty$), but also to those in weak gravity existing near infinity (corresponding to the limit $α\to -\frac{1}{n-1}$).

gr-qc↗
arXiv2022

Four types of attractive gravity probe surfaces

We reexamine the concept of the attractive gravity probe surface recently proposed as an indicator for strength of gravity. Then, we propose three new variant concepts and show refined inequalities for the four types of the AGPSs by taking account of the angular momentum, gravitational waves and matters.

gr-qc↗
arXiv2022

Asymptotic behavior of null geodesics near future null infinity II: curvatures, photon surface and dynamically transversely trapping surface

Bearing in mind our previous study on asymptotic behavior of null geodesics near future null infinity, we analyze the behavior of geometrical quantities such as a certain extrinsic curvature and Riemann tensor in the Bondi coordinates. In the sense of asymptotics, the condition for an $r$-constant hypersurface to be a photon surface is shown to be controlled by a key quantity that determines the fate of photons initially emitted in angular directions. As a consequence, in four dimensions, such a non-expanding photon surface can be realized even near future null infinity in the presence of enormous energy flux for a short period of time. By contrast, in higher-dimensional cases, no such a photon surface can exist. This result also implies that the dynamically transversely trapping surface, which is proposed as an extension of a photon surface, can have an arbitrarily large radius in four dimensions.

gr-qc↗
arXiv2021

Asymptotic behavior of null geodesics near future null infinity: Significance of gravitational waves

We investigate the behavior of null geodesics near future null infinity in asymptotically flat spacetimes. In particular, we focus on the asymptotic behavior of null geodesics that correspond to worldlines of photons initially emitted in the directions tangential to the constant radial surfaces in the Bondi coordinates. The analysis is performed for general dimensions, and the difference between the four-dimensional cases and the higher-dimensional cases is stressed. In four dimensions, some assumptions are required to guarantee the null geodesics to reach future null infinity, in addition to the conditions of asymptotic flatness. Without these assumptions, gravitational waves may prevent photons from reaching null infinity. In higher dimensions, by contrast, such assumptions are not necessary, and gravitational waves do not affect the asymptotic behavior of null geodesics.

gr-qc↗
arXiv2021

Area bound for surfaces in generic gravitational field

We define an attractive gravity probe surface (AGPS) as a compact 2-surface $S_α$ with positive mean curvature $k$ satisfying $r^a D_a k / k^2 \ge α$ (for a constant $α>-1/2$) in the local inverse mean curvature flow, where $r^a D_a k$ is the derivative of $k$ in the outward unit normal direction. For asymptotically flat spaces, any AGPS is proved to satisfy the areal inequality $A_α\le 4π[ ( 3+4α)/(1+2α) ]^2(Gm)^2$, where $A_α$ is the area of $S_α$ and $m$ is the Arnowitt-Deser-Misner (ADM) mass. Equality is realized when the space is isometric to the $t=$constant hypersurface of the Schwarzschild spacetime and $S_α$ is an $r=\mathrm{constant}$ surface with $r^a D_a k / k^2 = α$. We adapt the two methods of the inverse mean curvature flow and the conformal flow. Therefore, our result is applicable to the case where $S_α$ has multiple components. For anti-de Sitter (AdS) spaces, a similar inequality is derived, but the proof is performed only by using the inverse mean curvature flow. We also discuss the cases with asymptotically locally AdS spaces.

gr-qc↗
arXiv2021

On uniqueness of static spacetime with conformal scalar in higher dimensions

We discuss the uniqueness of asymptotically flat and static spacetimes in the $n$-dimensional Einstein-conformal scalar system. This theory potentially has a singular point in the field equations where the effective Newton constant diverges. We will show that the static spacetime with the conformal scalar field outside a certain surface $S_p$ associated with the singular point is unique.

gr-qc↗
arXiv2020

Loosely trapped surface and dynamically transversely trapping surface in Einstein-Maxwell system

We study the properties of the loosely trapped surface (LTS) and the dynamically transversely trapping surface (DTTS) in Einstein-Maxwell systems. These concepts of surfaces were proposed by the four of the present authors in order to characterize strong gravity regions. We prove the Penrose-like inequalities for the area of LTSs/DTTSs. Interestingly, although the naively expected upper bound for the area is that of the photon sphere of a Reissner-Nordstroem black hole with the same mass and charge, the obtained inequalities include corrections represented by the energy density or pressure/tension of electromagnetic fields. Due to this correction, the Penrose-like inequality for the area of LTSs is tighter than the naively expected one. We also evaluate the correction term numerically in the Majumdar-Papapetrou two-black-hole spacetimes.

gr-qc↗
arXiv2020

Formation of dynamically transversely trapping surfaces and the stretched hoop conjecture

A dynamically transversely trapping surface (DTTS) is a new concept of an extension of a photon sphere that appropriately represents a strong gravity region and has close analogy with a trapped surface. We study formation of a marginally DTTS in time-symmetric, conformally flat initial data with two black holes, with a spindle-shaped source, and with a ring-shaped source, and clarify that $\mathcal{C}\lesssim 6πGM$ describes the condition for the DTTS formation well, where $\mathcal{C}$ is the circumference and $M$ is the mass of the system. This indicates that an understanding analogous to the hoop conjecture for the horizon formation is possible. Exploring the ring system further, we find configurations where a marginally DTTS with the torus topology forms inside a marginally DTTS with the spherical topology, without being hidden by an apparent horizon. There also exist configurations where a marginally trapped surface with the torus topology forms inside a marginally trapped surface with the spherical topology, showing a further similarity between DTTSs and trapped surfaces.

gr-qc↗
arXiv2020

Transversely trapping surfaces: Dynamical version

We propose new concepts, a dynamically transversely trapping surface (DTTS) and a marginally DTTS, as indicators for a strong gravity region. A DTTS is defined as a two-dimensional closed surface on a spacelike hypersurface such that photons emitted from arbitrary points on it in transverse directions are acceleratedly contracted in time, and a marginally DTTS is reduced to the photon sphere in spherically symmetric cases. (Marginally) DTTSs have a close analogy with (marginally) trapped surfaces in many aspects. After preparing the method of solving for a marginally DTTS in the time-symmetric initial data and the momentarily stationary axisymmetric initial data, some examples of marginally DTTSs are numerically constructed for systems of two black holes in the Brill-Lindquist initial data and in the Majumdar-Papapetrou spacetimes. Furthermore, the area of a DTTS is proved to satisfy the Penrose-like inequality, $A_0\le 4π(3GM)^2$, under some assumptions. Differences and connections between a DTTS and the other two concepts proposed by us previously, a loosely trapped surface [arXiv:1701.00564] and a static/stationary transversely trapping surface [arXiv:1704.04637], are also discussed. A (marginally) DTTS provides us with a theoretical tool to significantly advance our understanding of strong gravity fields. Also, since DTTSs are located outside the event horizon, they could possibly be related with future observations of strong gravity regions in dynamical evolutions.

gr-qc↗
arXiv2017

Extension of photon surfaces and their area: Static and stationary spacetimes

We propose a new concept, the transversely trapping surface (TTS), as an extension of the static photon surface characterizing the strong gravity region of a static/stationary spacetime in terms of photon behavior. The TTS is defined as a static/stationary timelike surface $S$ whose spatial section is a closed two-surface, such that arbitrary photons emitted tangentially to $S$ from arbitrary points on $S$ propagate on or toward the inside of $S$. We study the properties of TTSs for static spacetimes and axisymmetric stationary spacetimes. In particular, the area $A_0$ of a TTS is proved to be bounded as $A_0\le 4π(3GM)^2$ under certain conditions, where $G$ is the Newton constant and $M$ is the total mass. The connection between the TTS and the loosely trapped surface proposed by us [arXiv:1701.00564] is also examined.

gr-qc↗