Abstract We show that 3-dimensional AdS spacetime can be semiclassically unstable due to strongly interacting quantum field effects. In our previous paper, we have pointed out the possibility of such an instability of AdS₃ by inspecting linear perturbations of the (covering space of) static BTZ black hole with AdS₄ gravity dual in the context of holographic semiclassical problems. In the present paper, we further study this issue from thermodynamic viewpoint by constructing asymptotically AdS₃ semiclassical solutions and computing free energies of the solutions. We find two asymptotically AdS₃ solutions to the semiclassical Einstein equations with non-vanishing source term: the one whose free energy is smaller than that of the BTZ with vanishing source term and the other whose free energy is smaller than that of the global AdS₃ with no horizon (thus manifestly zero-temperature background). The instability found in this paper implies the breakdown of the maximal symmetries of AdS₃, and its origin is different from the well-known semiclassical linear instability since our holographic semiclassical Einstein equations in 3-dimensions do not involve higher order derivative terms.

Abstract In this paper, we consider how to formulate semiclassical problems in the context of the AdS/CFT correspondence, based on the proposal of Compere and Marolf. Our prescription involves the effective action with self-action term for boundary dynamical fields, which can be viewed as imposing mixed boundary conditions for the gravity dual. We derive the semiclassical Einstein equations sourced by boundary CFT stress-energy tensor. Analyzing perturbations of the holographic semiclassical Einstein equations, we find a universal parameter γ_d which controls the contribution from boundary CFTs and specifies dynamics on the AdS boundary. As a simple example, we examine the semiclassical Einstein equations in 3-dimensions with 4-dimensional AdS gravity dual, and show that the boundary BTZ black hole with vanishing expectation value of the stress-energy tensor becomes unstable due to the backreaction from quantum stress-energy tensor when the parameter γ_d exceeds a certain critical value.

Abstract We examine the averaged null energy condition (ANEC) for strongly coupled fields, along the event horizon of an evaporating black hole by using the AdS/CFT duality. First, we consider a holographic model of a 3-dimensional evaporating black hole with a perturbed 4-dimensional black droplet geometry as the bulk dual, and investigate how negative energy flux going into the boundary black hole horizon appears. We show that the ingoing negative energy flux always appears at the boundary black hole horizon when the horizon area decreases. Second, we test the ANEC in a holographic model whose boundary geometry is a 4-dimensional asymptotically flat spacetime, describing the formation and subsequent evaporation of a spherically symmetric black hole. By applying the “bulk-no-shortcut principle”, we show that the ANEC is always satisfied when the local null energy is averaged with a weight function along the incomplete null geodesic on the event horizon from beginning of the formation to the final instant of the black hole evaporation. Our results indicate that the total ingoing negative energy flux is compensated by a large amount of positive energy flux in the early stage of the black hole formation.

We consider averaged null energy conditions (ANEC) for strongly coupled quantum field theories in even (two and four) dimensional curved spacetimes by applying the no-bulk-shortcut principle in the context of the AdS/CFT duality. In the same context but in odd-dimensions, the present authors previously derived a conformally invariant averaged null energy condition (CANEC), which is a version of the ANEC with a certain weight function for conformal invariance. In even-dimensions, however, one has to deal with gravitational conformal anomalies, which make relevant formulas much more complicated than the odd-dimensional case. In two-dimensions, we derive the ANEC by applying the no-bulk-shortcut principle. In four-dimensions, we derive an inequality which essentially provides the lower-bound for the ANEC with a weight function. For this purpose, and also to get some geometric insights into gravitational conformal anomalies, we express the stress-energy formulas in terms of geometric quantities such as the expansions of boundary null geodesics and a quasi-local mass of the boundary geometry. We argue when the lowest bound is achieved and also discuss when the averaged value of the null energy can be negative, considering a simple example of a spatially compact universe with wormhole throat.

We consider the memory effect in even dimensional spacetimes of dimension d >= 4 arising from a burst of gravitational radiation. When d = 4, the natural frames in the stationary eras before and after the burst differ by the composition of a boost and supertranslation, and this supertranslation characterizes the 'memory effect', i.e. the permanent displacement of test particles near infinity produced by the radiation burst. However, we show that when d > 4, this supertranslation and the corresponding memory effect vanish. Consequently, when d > 4, it is natural to impose stronger asymptotic conditions at null infinity that reduce the asymptotic symmetry group to the Poincare group. Conversely, when d = 4, the asymptotic symmetry group at null infinity must be taken to be the BMS group.

We investigate a stress-energy tensor for a conformal field theory (CFT) at strong coupling inside a small five-dimensional rotating Myers-Perry black hole with equal angular momenta by using the holographic method. As a gravitational dual, we perturbatively construct a black droplet solution by applying the "derivative expansion" method, generalizing the work of Haddad [Classical Quantum Gravity 29, 245001 (2012)] and analytically compute the holographic stress-energy tensor for our solution. We find that the stress-energy tensor is finite at both the future and past outer (event) horizons and that the energy density is negative just outside the event horizons due to the Hawking effect. Furthermore, we apply the holographic method to the question of quantum instability of the Cauchy horizon since, by construction, our black droplet solution also admits a Cauchy horizon inside. We analytically show that the null-null component of the holographic stress-energy tensor negatively diverges at the Cauchy horizon, suggesting that a singularity appears there, in favor of strong cosmic censorship.

We explicitly calculate the gravitational wave memory effect for classical point particle sources in linearized gravity off an even dimensional Minkowski background. We show that there is no memory effect in d > 4 dimensions, in agreement with the general analysis of Hollands et al (2016 arXiv: 1612.03290).

We investigate a holographic model of superfluid flows with an external repulsive potential. When the strength of the potential is sufficiently weak, we analytically construct two steady superfluid flow solutions. As the strength of the potential is increased, the two solutions merge into a single critical solution at a critical strength, and then disappear above the critical value, as predicted by a saddle-node bifurcation theory. We also analyze the spectral function of fluctuations around the solutions under a certain decoupling approximation.

We study the linear stability of asymptotically anti-de Sitter black holes in general relativity in spacetime dimension d >= 4. Our approach is an adaptation of the general framework of Hollands and Wald, which gives a stability criterion in terms of the sign of the canonical energy, epsilon The general framework was originally formulated for static or stationary and axisymmetric black holes in the asymptotically flat case, and the stability analysis for that case applies only to axisymmetric perturbations. However, in the asymptotically anti-de Sitter case, the stability analysis requires only that the black hole have a single Killing field normal to the horizon and there are no restrictions on the perturbations (apart from smoothness and appropriate behavior at infinity). For an asymptotically anti-de Sitter black hole, we define an ergoregion to be a region where the horizon Killing field is spacelike; such a region, if present, would normally occur near infinity. We show that for black holes with ergoregions, initial data can be constructed such that epsilon < 0, so all such black holes are unstable. To obtain such initial data, we first construct an approximate solution to the constraint equations using the WKB method, and then we use the Corvino-Schoen technique to obtain an exact solution. We also discuss the case of charged asymptotically anti-de Sitter black holes with generalized ergoregions.

Recently, Durkee and Reall have conjectured a criterion for linear instability of rotating, extremal, asymptotically Minkowskian black holes in dimensions, such as the Myers-Perry black holes. They considered a certain elliptic operator, , acting on symmetric trace-free tensors intrinsic to the horizon. Based in part on numerical evidence, they suggested that if the lowest eigenvalue of this operator is less than the critical value -1/4 ( called "effective BF-bound"), then the black hole is linearly unstable. In this paper, we prove an extended version of their conjecture. Our proof uses a combination of methods such as (1) the "canonical energy method" of Hollands-Wald, (2) algebraically special properties of the near horizon geometries associated with the black hole, (3) the Corvino-Schoen technique, and (4) semiclassical analysis. Our method of proof is also applicable to rotating, extremal asymptotically Anti-deSitter black holes. In that case, we find additional instabilities for ultra-spinning black holes. Although we explicitly discuss in this paper only extremal black holes, we argue that our results can be generalized to near extremal black holes.

We consider linear gravitational perturbations of the Kerr brane, an exact solution of vacuum Einstein's equations in dimensions higher than four and a low-energy solution of string theory. Decomposing the perturbations in tensor harmonics of the trans-verse Ricci-flat space, we show that tensor- and vector-type metric perturbations of the Kerr brane satisfy respectively a massive Klein-Gordon equation and a Proca equation on the four-dimensional Kerr space, where the mass term is proportional to the eigenvalue of the harmonics. Massive bosonic fields trigger a well-known superradiant instability on a Kerr black hole. We thus establish that Kerr branes in dimensions D a parts per thousand yen 6 are gravi-tationally unstable due to superradiance. These solutions are also unstable against the Gregory-Laflamme instability and we discuss the conditions for either instability to occur and their rather different nature. When the transverse dimensions are compactified and much smaller than the Kerr horizon, only the superradiant instability is present, with a time scale much longer than the dynamical time scale. Our formalism can be also used to discuss other types of higher-dimensional black objects, taking advantage of recent progress in studying linear perturbations of four-dimensional black holes.

We perturbatively construct a three-dimensional rotating AdS black hole with a real scalar hair. We choose the mass of a scalar field slightly above the Breitenlohner-Freedman bound and impose a general boundary condition for the bulk scalar field at AdS infinity. We first show that rotating BTZ black holes are unstable against scalar field perturbations under our more general boundary condition. Next we construct a rotating hairy black hole perturbatively with respect to a small amplitude epsilon of the scalar field, up to O (epsilon(4)). Our hairy black hole is stationary and exhibits no dissipation, but the lumps of the non-linearly perturbed geometry break axial symmetry, thus providing the first example of a rotating black hole whose metric admits only one Killing vector field. Furthermore, we numerically show that the entropy of our hairy black hole is larger than that of the BTZ black hole with the same energy and the angular momentum. We briefly discuss if our rotating hairy black hole in lumpy geometry could be the endpoint of the instability.

We discuss a general method to study linear perturbations of slowly rotating black holes which is valid for any perturbation field, and particularly advantageous when the field equations are not separable. As an illustration of the method we investigate massive vector (Proca) perturbations in the Kerr metric, which do not appear to be separable in the standard Teukolsky formalism. Working in a perturbative scheme, we discuss two important effects induced by rotation: a Zeeman-like shift of nonaxisymmetric quasinormal modes and bound states with different azimuthal number m, and the coupling between axial and polar modes with different multipolar index. We explicitly compute the perturbation equations up to second order in rotation, but in principle the method can be extended to any order. Working at first order in rotation we show that polar and axial Proca modes can be computed by solving two decoupled sets of equations, and we derive a single master equation describing axial perturbations of spin s=0 and s=±1. By extending the calculation to second order we can study the superradiant regime of Proca perturbations in a self-consistent way. For the first time we show that Proca fields around Kerr black holes exhibit a superradiant instability, which is significantly stronger than for massive scalar fields. Because of this instability, astrophysical observations of spinning black holes provide the tightest upper limit on the mass of the photon: m γ4×10 -20eV under our most conservative assumptions. Spin measurements for the largest black holes could reduce this bound to m γ10 -22eV or lower. © 2012 American Physical Society.

We place further restriction on the possible topology of stationary asymptotically flat vacuum black holes in five spacetime dimensions. We prove that the horizon manifold can be either a connected sum of Lens spaces and "handles" S (1) x S (2), or the quotient of S (3) by certain finite groups of isometries (with no "handles"). The resulting horizon topologies include Prism manifolds and quotients of the Poincare homology sphere. We also show that the topology of the domain of outer communication is a cartesian product of the time direction with a finite connected sum of S (1) x S (2), and CP (2)'s, minus the black hole itself. We do not assume the existence of any Killing vector beside the asymptotically time like one required by definition for stationarity.

We explicitly construct all stationary, non-static, extremal near horizon geometries in D dimensions that satisfy the vacuum Einstein equations, and that have D-3 commuting rotational symmetries. Our work generalizes [arXiv:0806.2051] by Kunduri and Lucietti, where such a classification had been given in D = 4,5. But our method is different from theirs and relies on a matrix formulation of the Einstein equations. Unlike their method, this matrix formulation works for any dimension. The metrics that we find come in three families, with horizon topology S (2) x T (D-4), or S (3) x T (D-5), or quotients thereof. Our metrics depend on two discrete parameters specifying the topology type, as well as (D - 2)(D - 3)/2 continuous parameters. Not all of our metrics in D a parts per thousand yen 6 seem to arise as the near-horizon limits of known black hole solutions.

All known stationary black hole solutions in higher dimensions possess additional rotational symmetries in addition to the stationary Killing field. Also, for all known stationary solutions, the event horizon is a Killing horizon, and the surface gravity is constant. In the case of non-degenerate horizons (non-extremal black holes), a general theorem was previously established [24] proving that these statements are in fact generally true under the assumption that the spacetime is analytic, and that the metric satisfies Einstein's equation. Here, we extend the analysis to the case of degenerate (extremal) black holes. It is shown that the theorem still holds true if the vector of angular velocities of the horizon satisfies a certain "diophantine condition," which holds except for a set of measure zero.

We discuss spherically symmetric black holes in the modified self-dual theory of gravity recently studied by Krasnov, obtained by adding a Weyl curvature-dependent 'cosmological term' to the Plebanski lagrangian for general relativity. This type of modified gravity admits two different types of singularities: one is a true singularity for the theory where the fundamental fields of the theory, as well as the (auxiliary) spacetime metric, become singular, and the other one is a milder 'non-metric singularity' where the metric description of the spacetime breaks down but the fundamental fields themselves are regular. We first generalize this modified self-dual gravity to include Maxwell's field and then study the basic features of spherically symmetric, charged black holes, with particular focus on whether these two types of singularities are hidden or naked. We restrict our attention to minimal forms of the modification, and find that the theory exhibits 'screening' effects of the electric charge (or 'anti-screening', depending upon the sign of the modification term), in the sense that it leads to the possibility of charging the black hole more (or less) than it would be possible in general relativity without exposing a naked singularity. We also find that for any (even arbitrarily large) value of charge, true singularities of the theory appear to be either achronal (non-timelike) covered by the hypersurface of a harmless non-metric singularity or simply hidden inside at least one Killing horizon.

A higher (even spacetime) dimensional generalization of the Bondi energy has recently been proposed (Hollands and Ishibashi 2005 J. Math. Phys. 46 022503) within the framework of conformal infinity and Hamiltonian formalism. The gauge condition employed in Hollands and Ishibashi to derive the Bondi-energy expression is, however, peculiar in the sense that cross sections of null infinity specified by that gauge are anisotropic and in fact non-compact. For this reason, that gauge is difficult to use for explicit computation of the Bondi energy in general, asymptotically flat radiative spacetimes. Also it is not clear, under that gauge condition, whether an apparent difference between the expressions of higher dimensional Bondi energy and the four-dimensional one is due to the choice of gauges or a qualitatively different nature of higher dimensional gravity from four-dimensional gravity. In this paper, we consider instead, the Gaussian null conformal gauge as one of the more natural gauge conditions that admit a global specification of background structure with compact, spherical cross sections of null infinity. Accordingly, we modify the previous definition of higher dimensional news tensor so that it becomes well defined in the Gaussian null conformal gauge and derive, for vacuum solutions, an expression for the Bondi energy-momentum in the new gauge choice, which takes a universal form in arbitrary (even spacetime) dimensions greater than or equal to 4.

We discuss symmetry properties of black holes in general relativity-known as black hole rigidity of which basic assertion is that the event horizon of an asymptotically flat, stationary black hole with certain matter fields must be a Killing horizon and is rephrased (combined together with staticity results) that such a black hole must be either static, or axisymmetric. A precise formulation of the rigidity theorem for black holes with non-degenerate event horizon in arbitrary spacetime dimensions has been recently made by Hollands, Wald and the present author. [Hollands, S., Ishibashi, A. and Wald, R. M., Commun. Math. Phys. 271 (2007), 699.] In our formulation, no assumptions concerning the topology of cross-sections of event horizon (other than the compactness) are made. Therefore, different from Hawking's original proof given in 4-dimensions, our proof applies also to non-spherical black holes, which are known to occur in higher dimensions but not in 4-dimensions.

A key result in the proof of black hole uniqueness in 4-dimensions is that a stationary black hole that is "rotating" - i.e., is such that the stationary Killing field is not everywhere normal to the horizon - must be axisymmetric. The proof of this result in 4-dimensions relies on the fact that the orbits of the stationary Killing field on the horizon have the property that they must return to the same null geodesic generator of the horizon after a certain period, P. This latter property follows, in turn, from the fact that the cross-sections of the horizon are two-dimensional spheres. However, in space-times of dimension greater than 4, it is no longer true that the orbits of the stationary Killing field on the horizon must return to the same null geodesic generator. In this paper, we prove that, nevertheless, a higher dimensional stationary black hole that is rotating must be axisymmetric. No assumptions are made concerning the topology of the horizon cross-sections other than that they are compact. However, we assume that the horizon is non-degenerate and, as in the 4-dimensional proof, that the spacetime is analytic.

We study the perturbative dynamics of an infinite gravitating Nambu-Goto
string within the general-relativistic perturbation framework. We develop the
gauge invariant metric perturbation on a spacetime containing a
self-gravitating straight string with a finite thickness and solve the
linearized Einstein equation. In the thin string case, we show that the string
does not emit gravitational waves by its free oscillation in the first order
with respect to its oscillation amplitude, nevertheless the string actually
bends when the incidental gravitational waves go through it.

The equation of motion for a domain wall coupled to the gravitational field is derived from the Nambu-Goto action. The domain wall is treated as a source of the gravitational field and the gravitational back reaction on the wall motion is taken into account. The perturbed equation is also obtained, and is expressed in terms of the gauge-invariant variables in a general spherically symmetric background case. © 1999 The American Physical Society.

We study a coupled system of gravitational waves and a domain wall which is
the boundary of a vacuum bubble in de Sitter spacetime. To treat the system, we
use the metric junction formalism of Israel. We show that the dynamical degree
of the bubble wall is lost and the bubble wall can oscillate only while the
gravitational waves go across it. It means that the gravitational backreaction
on the motion of the bubble wall can not be ignored.

量子情報をキーワードとして「極限宇宙の３問題」の解明を目的とする本領域が2021年9月に発足して以来、本総括班は、この研究プロジェクトを発展させるために、「領域運営」「分野融合」「若手育成」「国際活動」「広報」の各活動を開始し、以下に挙げるような実績を挙げてきた。まず、領域の運営方針を打ち合わせる「総括班会議」を総括班メンバー15名がオンライン会議を行う形式で9月以降毎月開催してきた。領域内の異分野融合を促進する目的で、複数の計画研究が主催し、その研究成果を報告・討論する「循環ミーティング」をオンライン会議の形で毎月開催し、毎回50名以上の出席者を得ている。特に、11月には、これを拡大して、本領域のキックオフミーティングとして、9つの計画研究が全て講演する形で2日間行った。また、国際的な視点から異分野融合の話題に触れる機会を領域メンバーやより広く領域外の研究者が得られるように、「領域オンラインコロキウム」を立ち上げ、毎月、国内外より著名な研究者をコロキウム講演に招へいしてきた。講演後もオンラインお茶会を開催し、講演者と若手研究者が交流し合う機会を提供した。さらに、米国のIt from Qubitサイモンズ共同研究と共催する形で、「領域国際会議」を12月に3日間オンラインで開催し、国際交流を促進した。また、2022年の3月には、領域メンバー全員が参加し、今年度の成果報告と来年度以降の研究計画の討論を行う「領域会議」を2日間、京都大学基礎物理学研究所にて対面とオンラインを併用して開催した。その直前には、若手育成を目的に「領域スクール」を開催し、量子情報、場の量子論、一般相対論の実践的な知識を異分野の若手が習得する良い機会となり、300名超の参加者を得た。また本総括班は、広報活動として、領域ホームページの作成・発信、領域ツイッターの作成・発信、ニュースレター発行を行った。

今年度は、引き続き背景時空が局所的に反ドジッター（AdS）時空となる、いわゆるトポロジカル・ブラックホールおよびその特別な場合について、様々なボソン場の線形摂動のマスター方程式の大域解の構成と安定性解析を行った。すでに様々な有質量および零質量線形摂動場に対して、一部の力学自由度に関しては、各自由度を表す力学変数が独立した形式のマスター方程式は得られており、その一般解も超幾何関数を用いて具体的に求めることに成功している。本年度は、それらの一般解から、適切な境界条件を満たす大域解を構成する際に、境界条件と波動（特に不安定モード）の関係を精密かつ網羅的に決定することを行った。また、厳密繰り込み群的手法に基づく量子補正したブラックホール時空の構成を、静的荷電ブラックホールの場合に試みた。そして、重力相互作用と電磁気相互作用の両方の結合定数の量子補正により、古典的な時空の大域構造がどのように変更されるかを詳細に調べた。特に、古典的時空の中心にある曲率特異点が、量子補正によりドジッターや反ドジッターなどの正則な時空領域となる場合、あるいは弱い特異点が発生する場合があり得ることを示した。このような量子補正ブラックホールや、それらと類似の古典論における正則ブラックホールは、ブラックホール表面である事象の地平面の他に、内部に別の地平面（コーシー地平面）を持つ。この様なコーシー地平面の存在は、一般相対論・重力理論における未解決問題である宇宙検閲官仮説に反する。そこで、正則ブラックホール内部のコーシー地平面の安定性解析を目的として、正則ブラックホールを模倣する時空を、ドジッターや反ドジッター時空領域と古典的荷電ブラックホール解との時空接続により構成することを試みた。以上は、申請者の指導する大学院学生とともに遂行した。

今年度は、AdS/CFT双対性を用いて、ブラックホールが存在する背景時空において、強結合な場の理論におけるエネルギー条件及びエンタングルメントエントロピーの熱力学的性質について解析を行った。近年、ブラックホールは情報喪失問題という観点から再び注目を集めており、ブラックホール時空上での場の理論の基本的性質を調べることが急務となっている。その一つにエンタングルメントエントロピーの性質がある。劉-高柳公式によって、部分空間のエンタングルメントエントロピーは、その部分空間の境界を端点とするバルク時空での閉曲面の最小面積で与えられ、ブラックホールがない平坦時空では、熱力学第一法則が成立することが知られていた。今回の研究では、ワルドのネーターの定理を応用し、ブラックホールが存在する奇数次元の漸近的AdS背景時空において、熱力学第一法則が成立することを示した。この成立条件として、AdS時空の境界でノイマン条件が必要であることがわかった。この条件の下では、AdS時空の境界を通じてエネルギーの出入りがないので、自然な境界条件と考えられる。次に、時間依存するブラックホールのエネルギー条件について解析を行った。ブラックホールはホーキング輻射によって蒸発していく過程で、光的エネルギー条件が破れていることが知られている。一方で、このような時空でも、ブラックホール外部に放出されたエントロピーとブラックホールによる重力エントロピーの和は減らないとする一般化された熱力学第二法則が成立することが予想されており、この法則とエネルギー条件との整合性がどの様になっているのかわかっていなかった。そこで、本研究では、背景時空としてブラックホールが重力崩壊で形成された後、蒸発して消滅する時空を用意し、このブラックホール上のヌル測地線に沿って、重み付き平均の光的エネルギー条件が常に成立していることがわかった。

曲がった時空での強結合な場の理論の基礎的性質を調べるため、本研究では、微分展開法や空間次元Dが大きいときに適用される1/D展開法をAdSブラックホール時空に応用する。微分展開法を用いた回転ブラックドロップレット解の解析では、コーシーホライズンが量子的に不安定であることを発見した。1/D展開法を用いた偏極AdSブラックホール解の解析では、そのホライズンのダイナミックスを記述する有効方程式を導き、解が安定であることを示した。また、空間的にコンパクトな宇宙や蒸発するブラックホール時空などの曲がった時空において、強結合な場の理論では、大域的に平均化された光的エネルギーは負にならないことを示した。

究極理論への新たな実験観測ウインドウの開拓を目指して，宇宙物理現象論と超弦理論・超重力理論の双方からアクシオンについて組織的な研究を行い，200編を超える論文を発表した．主な成果は，回転ブラックホールの引き起こすアクシオンボーズノバ現象の数値シミュレーションによる実証とその重力波による観測可能性の発見，高エネルギーガンマ線観測と赤外線放射観測の矛盾をアクシオンにより解消するパラメータの導出，重いモジュライの崩壊により生成されたアクシオンの宇宙背景放射への影響の評価とそれによる余剰空間コンパクト化への制限，アクシオン起源の等曲率ゆらぎや位相的励起生成に基づく素粒子模型への制限の導出などである．