arXiv subjects

Hideki Maeda

Publications and source records attributed to Hideki Maeda.

At least 19 recordsLinked to original sources

arXiv2025

Chronology Protection of Rotating Black Holes in a Viable Lorentz-Violating Gravity

We study causal properties of the recently found rotating black-hole solution in the low-energy sector of Horava gravity as a viable Lorentz-violating (LV) gravity in four dimensions with the LV Maxwell field and a cosmological constant $\Lambda (>-3/a^2)$ for an arbitrary rotation parameter $a$. The region of non-trivial causality violation containing closed timelike curves is exactly the same as in the Kerr-Newman or the Kerr-Newman-(Anti-)de Sitter solution. Nevertheless, chronology is protected in the new rotating black hole because the causality violating region becomes physically inaccessible by exterior observers due to the new three-curvature singularity at its boundary that is topologically two-torus including the usual ring singularity at $(r,\theta)=(0,\pi/2)$. As a consequence, the physically accessible region outside the torus singularity is causal everywhere.

hep-th↗

arXiv2025

Exact plane symmetric black bounce with a perfect-fluid exterior obeying a linear equation of state

We investigate an exact two-parameter family of plane symmetric solutions admitting a hypersurface-orthogonal Killing vector in general relativity with a perfect fluid obeying a linear equation of state $p=\chi\rho$ in $n(\ge 4)$ dimensions, obtained by Gamboa in 2012. The Gamboa solution is identical to the topological Schwarzschild-Tangherlini-(anti-)de~Sitter $\Lambda$-vacuum solution for $\chi=-1$ and admits a nondegenerate Killing horizon only for $\chi=-1$ and $\chi\in[-1/3,0)$. We identify all possible regular attachments of two Gamboa solutions for $\chi\in[-1/3,0)$ at the Killing horizon without a lightlike thin shell, where $\chi$ may have different values on each side of the horizon. We also present the maximal extension of the static and asymptotically topological Schwarzschild-Tangherlini Gamboa solution, realized only for $\chi\in(-(n-3)/(3n-5),0)$, under the assumption that the value of $\chi$ is unchanged in the extended dynamical region beyond the horizon. The maximally extended spacetime describes either (i) a globally regular black bounce whose Killing horizon coincides with a bounce null hypersurface or (ii) a black hole with a spacelike curvature singularity inside the horizon. The matter field inside the horizon is not a perfect fluid but rather an anisotropic fluid that can be interpreted as a spacelike (tachyonic) perfect fluid. A fine-tuning of the parameters is unnecessary for the black bounce, but the null energy condition is violated everywhere except on the horizon. In the black-bounce (black-hole) case, the metric in the regular coordinate system is $C^\infty$ only for $\chi=-1/(1+2N)$ with odd (even) $N$ satisfying $N>(n-1)/(n-3)$, and if one of the parameters in the extended region is fine-tuned.

gr-qc↗

arXiv2025

Planar black holes and wormholes with a flat exterior

We present $n(\ge 4)$-dimensional planar black holes and wormholes with a flat exterior, which are originated by an exact solution in general relativity. The nonvacuum regions of these objects are described by the extended dynamical region inside a nondegenerate Killing horizon of Gamboa's static plane symmetric solution with a perfect fluid obeying a linear equation of state $p=\chi\rho$ for $\chi\in[-1/3,0)$. The matter field inside the horizon is not a perfect fluid but an anisotropic fluid that may be interpreted as a {\it spacelike} (tachyonic) perfect fluid. While it satisfies the null and strong energy conditions in the black hole case, it violates all the standard energy conditions in the wormhole case. The metric on the horizon is not analytic but at least $C^{1,1}$ in the single-null coordinates in both cases, so it is regular and there is no lightlike massive thin shell on the horizon.

gr-qc↗

arXiv2024

Fake Schwarzschild and Kerr black holes

We present exact solutions describing a fake Schwarzschild black hole that cannot be distinguished from the Schwarzschild black hole by observations. They are constructed by attaching a spherically symmetric dynamical interior solution with a matter field to the Schwarzschild exterior solution at the event horizon without a lightlike thin shell. The dynamical region inside a Killing horizon of a static spherically symmetric perfect-fluid solution obeying an equation of state $p=\chi\rho$ for $\chi\in[-1/3,0)$ can be the interior of a fake Schwarzschild black hole. The matter field inside such a black hole is an anisotropic fluid that violates at least the weak energy condition and can be interpreted as a spacelike (tachyonic) perfect fluid. While the author constructed the first model of fake Schwarzschild black holes using Semiz's solution for $\chi=-1/5$, we present another one using Whittaker's solution for $\chi=-1/3$ in this paper. We also present a model of fake Kerr black holes whose interior is filled with a different matter field violating only the dominant energy condition near the event horizon. Because it contradicts the conservation theorem, this configuration of black holes is, in fact, precluded by the dominant energy condition.

gr-qc↗

arXiv2024

Extremal rotating BTZ black holes cannot be dressed in (anti-)self-dual Maxwell field

Under the (anti-)self-dual condition for orthonormal components of the Faraday tensor, the 3D Einstein-Maxwell system with a negative cosmological constant $\Lambda$ admits a solution obtained by Kamata and Koikawa and later by Cataldo and Salgado in the most general form. Actually, Clement first obtained this solution and interpreted it as a regular particle-like solution without horizon. Nevertheless, it has been erroneously stated in some literature that this Clement-Cataldo-Salgado (CCS) solution, locally characterized by a single parameter, describes a black hole even in the charged case as it reduces to the extremal rotating Banados-Teitelboim-Zanelli (BTZ) solution in the vacuum limit and its curvature invariants are constant. In this paper, we supplement Clement's interpretation by showing that there appears a parallelly propagated curvature singularity corresponding to an infinite affine parameter along spacelike geodesics at the location of the Killing horizon in the extremal rotating BTZ solution when the (anti-)self-dual Maxwell field is added. If the spatial coordinate $\theta$ is periodic, closed timelike curves exist near the singularity. It is also shown that the CCS solution is of the Cotton type N (in contrast to charged rotating BTZ black holes which are of type I away from the horizon), and the energy-momentum tensor of the Maxwell field is of the Hawking-Ellis type II. The metric solves the Einstein-$\Lambda$ equations also with a massless scalar field or a null dust fluid. We demonstrate that it belongs to the Kundt shear-free, non-twisting, non-expanding class of geometries, whereas extremal rotating BTZ black holes have expanding principal null directions. It means that the CCS metric represents the specific null ("radiative") Maxwell field generated by a singular source, rather than an extremal rotating BTZ black hole dressed in an (anti-)self-dual Maxwell field.

hep-th↗

arXiv2024

Existence and absence of Killing horizons in static solutions with symmetries

Without specifying a matter field nor imposing energy conditions, we study Killing horizons in $n(\ge 3)$-dimensional static solutions in general relativity with an $(n-2)$-dimensional Einstein base manifold. Assuming linear relations $p_{\rm r}\simeq\chi_{\rm r} \rho$ and $p_2\simeq\chi_{\rm t} \rho$ near a Killing horizon between the energy density $\rho$, radial pressure $p_{\rm r}$, and tangential pressure $p_2$ of the matter field, we prove that any non-vacuum solution satisfying $\chi_{\rm r}<-1/3$ ($\chi_{\rm r}\ne -1$) or $\chi_{\rm r}>0$ does not admit a horizon as it becomes a curvature singularity. For $\chi_{\rm r}=-1$ and $\chi_{\rm r}\in[-1/3,0)$, non-vacuum solutions admit Killing horizons, on which there exists a matter field only for $\chi_{\rm r}=-1$ and $-1/3$, which are of the Hawking-Ellis type~I and type~II, respectively. Differentiability of the metric on the horizon depends on the value of $\chi_{\rm r}$, and non-analytic extensions beyond the horizon are allowed for $\chi_{\rm r}\in[-1/3,0)$. In particular, solutions can be attached to the Schwarzschild-Tangherlini-type vacuum solution at the Killing horizon in at least a $C^{1,1}$ regular manner without a lightlike thin shell. We generalize some of those results in Lovelock gravity with a maximally symmetric base manifold.

gr-qc↗

arXiv2023

Charged rotating BTZ solution revisited: New coordinates and algebraic classifications

We revisit the charged rotating Ba\~nados-Teitelboim-Zanelli (BTZ) solution in the three-dimensional Einstein-Maxwell-$\Lambda$ system. After the erroneous announcement of its discovery at the end of the original BTZ paper in 1992, the solution was first obtained by Cl\'ement in the paper published in 1996 by coordinate transformations from the charged non-rotating BTZ solution. While Cl\'ement's form of the solution is valid only for ${\Lambda<0}$, we present a new form for a wider range of $\Lambda$ by uniform scaling transformations and a reparametrization. We also introduce new coordinates corresponding to the Doran coordinates in the Kerr spacetime, in which the metric and also its inverse are regular at the Killing horizon, and described by elementary functions. Lastly, we show that (i) the algebraic Cotton type of the spacetime is type III on the Killing horizon and type I away from the horizon, and (ii) the energy-momentum tensor for the Maxwell field is of the Hawking-Ellis type I everywhere.

gr-qc↗

arXiv2023

Energy conditions for non-timelike thin shells

We study energy conditions for non-timelike thin shells in arbitrary $n(\ge 3)$ dimensions. It is shown that the induced energy-momentum tensor $t_{\mu\nu}$ on a shell $\Sigma$ is of the Hawking-Ellis type I if $\Sigma$ is spacelike and either of type I, II, or III if $\Sigma$ is null. Then, we derive simple equivalent representations of the standard energy conditions for $t_{\mu\nu}$. In particular, on a spacelike shell or on a null shell with non-vanishing surface current, $t_{\mu\nu}$ inevitably violates the dominant energy condition. If the surface pressure on the null shell is vanishing in addition, $t_{\mu\nu}$ is of type III and violates all the standard energy conditions. Those fully general results are obtained without imposing a spacetime symmetry and can be used in any theory of gravity. Lastly, several applications of the main results are presented in general relativity in four dimensions.

gr-qc↗

arXiv2022

Vacuum-dual static perfect fluid obeying $p=-(n-3)\rho/(n+1)$ in $n(\ge 4)$ dimensions

We obtain the general $n(\ge 4)$-dimensional static solution with an $(n-2)$-dimensional Einstein base manifold for a perfect fluid obeying a linear equation of state $p=-(n-3)\rho/(n+1)$. It is a generalization of Semiz's four-dimensional general solution with spherical symmetry and consists of two different classes. Through the Buchdahl transformation, the class-I and class-II solutions are dual to the topological Schwarzschild-Tangherlini-(A)dS solution and one of the $\Lambda$-vacuum direct-product solutions, respectively. While the metric of the spherically symmetric class-I solution is $C^\infty$ at the Killing horizon for $n=4$ and $5$, it is $C^1$ for $n\ge 6$ and then the Killing horizon turns to be a parallelly propagated curvature singularity. For $n=4$ and $5$, the spherically symmetric class-I solution can be attached to the Schwarzschild-Tangherlini vacuum black hole with the same value of the mass parameter at the Killing horizon in a regular manner, namely without a lightlike massive thin-shell. This construction allows new configurations of an asymptotically (locally) flat black hole to emerge. If a static perfect fluid hovers outside a vacuum black hole, its energy density is negative. In contrast, if the dynamical region inside the event horizon of a vacuum black hole is replaced by the class-I solution, the corresponding matter field is an anisotropic fluid and may satisfy the null and strong energy conditions. While the latter configuration always involves a spacelike singularity inside the horizon for $n=4$, it becomes a non-singular black hole of the big-bounce type for $n=5$ if the ADM mass is larger than a critical value.

gr-qc↗

arXiv2022

Conformally Schwarzschild cosmological black holes

We thoroughly investigate conformally Schwarzschild spacetimes in different coordinate systems to seek for physically reasonable models of a cosmological black hole. We assume that a conformal factor depends only on the time coordinate and that the spacetime is asymptotically flat Friedmann-Lema\^{\i}tre-Robertson-Walker universe filled by a perfect fluid obeying a linear equation state $p=w\rho$ with $w>-1/3$. In this class of spacetimes, the McClure-Dyer spacetime, constructed in terms of the isotropic coordinates, and the Thakurta spacetime, constructed in terms of the standard Schwarzschild coordinates, are identical and do not describe a cosmological black hole. In contrast, the Sultana-Dyer and Culetu classes of spacetimes, constructed in terms of the Kerr-Schild and Painlev\'{e}-Gullstrand coordinates, respectively, describe a cosmological black hole. In the Sultana-Dyer case, the corresponding matter field in general relativity can be interpreted as a combination of a homogeneous perfect fluid and an inhomogeneous null fluid, which is valid everywhere in the spacetime unlike Sultana and Dyer's interpretation. In the Culetu case, the matter field can be interpreted as a combination of a homogeneous perfect fluid and an inhomogeneous anisotropic fluid. However, in both cases, the total energy-momentum tensor violates all the standard energy conditions at a finite value of the radial coordinate in late times. As a consequence, the Sultana-Dyer and Culetu black holes for $-1/3<w\le 1$ cannot describe the evolution of a primordial black hole after its horizon entry.

gr-qc↗

arXiv2022

Criteria for energy conditions

In model building studies, it is important to check the energy conditions for the corresponding energy-momentum tensor determined by the gravitational field equations in order to single out physically reasonable models. In this process, one often encounters a situation where the energy-momentum tensor has one off-diagonal "space-time" component in the frame with an orthonormal basis in a given spacetime. We derive useful criteria of energy-momentum tensors for their Hawking-Ellis types and the standard energy conditions in such situations. As demonstrations, we apply those criteria to four different systems.

gr-qc↗

arXiv2021

Simple traversable wormholes violating energy conditions only near the Planck scale

We present a static and axisymmetric traversable wormhole spacetime with vanishing Arnowitt-Deser-Misner (ADM) mass which is characterized by a length parameter $l$ and a deformation parameter $a$ and reduces to the massless Kerr vacuum wormhole as $l\to 0$. The spacetime is analytic everywhere and regularizes a ring-like conical singularity of the massless Kerr wormhole by virtue of a localized exotic matter which violates the standard energy conditions only near the wormhole throat. In the spherically symmetric case ($a=0$), the areal radius of the wormhole throat is exactly $l$ and all the standard energy conditions are respected outside the proper radial distance approximately $1.60l$ from the throat. While the curvature at the throat is beyond the Planck scale if $l$ is identical to the Planck length $l_{\rm p}$, our wormhole may be a semi-classical model for $l\simeq 10l_{\rm p}$. With $l=10l_{\rm p}$, the total amount of the negative energy supporting this wormhole is only $E\simeq -26.5m_{\rm p}c^2$, which is the rest mass energy of about $-5.77\times 10^{-4}{\rm g}$. It is shown that the geodesic behavior on the equatorial plane does not qualitatively change by the localization of an exotic matter.

gr-qc↗

arXiv2021

Quest for realistic non-singular black-hole geometries: Regular-center type

We propose seven criteria to single out physically reasonable non-singular black-hole models and adopt them to four different spherically symmetric models with a regular center and their rotating counterparts. In general relativity, all such non-singular black holes are non-generic with a certain matter field including a class of nonlinear electromagnetic fields. According to a criterion that the effective energy-momentum tensor should satisfy all the standard energy conditions in asymptotically flat regions, the well-known Bardeen and Hayward black holes are discarded. In contrast, the Dymnikova and Fan-Wang black holes respect the dominant energy condition everywhere. Although the rotating Fan-Wang black hole contains a curvature singularity, the rotating Dymnikova black hole is free from scalar polynomial curvature singularities and closed timelike curves. In addition, the dominant energy condition is respected on and outside the event horizons in the latter case. The absence of parallelly propagated curvature singularities remains an open question.

gr-qc↗

arXiv2021

Hawking-Ellis type of matter on Killing horizons in symmetric spacetimes

Spherically, plane, or hyperbolically symmetric spacetimes with an additional hypersurface orthogonal Killing vector are often called ``static'' spacetimes even if they contain regions where the Killing vector is non-timelike. It seems to be widely believed that an energy-momentum tenor for a matter field compatible with these spacetimes in general relativity is of the Hawking-Ellis type I everywhere. We show in arbitrary $n(\ge 3)$ dimensions that, contrary to popular belief, a matter field on a Killing horizon is not necessarily of type I but can be of type II. Such a type-II matter field on a Killing horizon is realized in the Gibbons-Maeda-Garfinkle-Horowitz-Strominger black hole in the Einstein-Maxwell-dilaton system and may be interpreted as a mixture of a particular anisotropic fluid and a null dust fluid.

gr-qc↗

arXiv2021

Thakurta metric does not describe a cosmological black hole

Recently, the Thakurta metric has been adopted as a model of primordial black holes. We show that the spacetime described by this metric has neither black-hole event horizon nor black-hole trapping horizon and involves the violation of all the standard energy conditions as a solution of the Einstein equation. Therefore, this metric does not describe a cosmological black hole in the early universe. It is pointed out that a contradictory claim by the other group stems from an incorrect choice of sign.

gr-qc↗

arXiv2020

Nonstaticity with type II, III, or IV matter field in $f(R_{\mu\nu\rho\sigma},g^{\mu\nu})$ gravity

In all $n(\ge 3)$-dimensional gravitation theories whose Lagrangians are functions of the Riemann tensor and metric, we show that static solutions are absent unless the total energy-momentum tensor for matter fields is of type I in the Hawking-Ellis classification. In other words, there is no hypersurface-orthogonal timelike Killing vector in a spacetime region with an energy-momentum tensor of type II, III, or IV. This asserts that, if back-reaction is taken into account to give a self-consistent solution, ultra-dense regions with a semiclassical type-IV matter field cannot be static even with higher-curvature correction terms. As a consequence, a static Planck-mass relic is possible as a final state of an evaporating black hole only if the semiclassical total energy-momentum tensor is of type I.

gr-qc↗

arXiv2019

Junction conditions in scalar-tensor theories

We analyze junction conditions at a null or non-null hypersurface $Σ$ in a large class of scalar-tensor theories in arbitrary $n(\ge 3)$ dimensions. After showing that the metric and a scalar field must be continuous at $Σ$ as the first junction conditions, we derive the second junctions conditions from the Einstein equations and the equation of motion for the scalar field. Subsequently, we study $C^1$ regular matching conditions as well as vacuum conditions at $Σ$ both in the Jordan and Einstein frames. Our result suggests that the following configurations may be possible; (i) a vacuum thin-shell at null $Σ$ in the Einstein frame, (ii) a vacuum thin-shell at null and non-null $Σ$ in the Jordan frame, and (iii) a non-vacuum $C^1$ regular matching at null $Σ$ in the Jordan frame. Lastly, we clarify the relations between the conditions for $C^1$ regularity and also for vacuum $Σ$ in the Jordan and Einstein frames.

gr-qc↗

arXiv2019

Higher-dimensional Buchdahl and Janis-Robinson-Winicour transformations in the Einstein-Maxwell system with a massless scalar field

We present higher-dimensional generalizations of the Buchdahl and Janis-Robinson-Winicour transformations which generate static solutions in the Einstein-Maxwell system with a massless scalar field. While the former adds a nontrivial scalar field to a vacuum solution, the latter generates a charged solution from a neutral one with the same scalar field. Applying these transformations to (i) a static solution with an Einstein base manifold, (ii) a multi-center solution, and (iii) a four-dimensional cylindrically symmetric solution, we construct several new exact solutions.

gr-qc↗