arXiv subjects

Kentaro Tanabe

Publications and source records attributed to Kentaro Tanabe.

At least 19 recordsLinked to original sources

arXiv2018

Phases and Stability of Non-Uniform Black Strings

We construct solutions of non-uniform black strings in dimensions from $D \approx 9$ all the way up to $D = \infty$, and investigate their thermodynamics and dynamical stability. Our approach employs the large-$D$ perturbative expansion beyond the leading order, including corrections up to $1/D^4$. Combining both analytical techniques and relatively simple numerical solution of ODEs, we map out the ranges of parameters in which non-uniform black strings exist in each dimension and compute their thermodynamics and quasinormal modes with accuracy. We establish with very good precision the existence of Sorkin's critical dimension and we prove that not only the thermodynamic stability, but also the dynamic stability of the solutions changes at it.

hep-th↗

arXiv2017

Energy extraction from Kerr black holes by rigidly rotating strings

In this paper, we show that a rigidly rotating string can extract the rotational energy from a rotating black hole. We consider Nambu-Goto strings stationary with respect to a corotating Killing vector with an uniform angular velocity $ω$ in the Kerr spacetime. We show that a necessary condition of the energy-extraction process is that an effective horizon on the string world sheet, which corresponds to the inner light surface, is inside the ergosphere of the Kerr black hole and the angular velocity $ω$ is less than that of the black hole $Ω_\mathrm{h}$. Furthermore, we discuss global configurations of such strings in both of a slow-rotation limit and the extremal Kerr case.

gr-qc↗

arXiv2016

Charged rotating black holes at large D

We study odd dimensional charged equally rotating black holes in the Einstein-Maxwell theory with/without a cosmological constant by using the large D expansion method, where D is a spacetime dimension. Solving the Einstein-Maxwell equations in the 1/D expansion we obtain the large D effective equations for charged equally rotating black holes. The effective equations describe the nonlinear dynamics of charged equally rotating black holes. Especially the perturbation analysis of the effective equations gives analytic formula for quasinormal mode frequencies, and we can show charged equally rotating black holes have instabilities. As one interesting feature of instabilities, we observe that the ultraspinning instability of neutral equally rotating black holes in de Sitter is connected with the instability of de Sitter Reissner-Nordstrom black hole in a rotation-charge plane of the solution parameter space. So these instabilities have same origin as dynamical properties of charged rotating black holes. We also give perturbation analysis by a small charge for even dimensional equally rotating black holes.

hep-th↗

arXiv2016

Elastic instability of black rings at large D

Using the inverse dimensional expansion method we study the elastic instability of black rings found recently in numerical analysis of fully nonlinear dynamical evolutions. In our analysis we should perform 1/D^1/2 expansions, not usual 1/D expansions, of the Einstein equations to capture this elastic instability of D dimensional black rings. By solving the Einstein equations at large D we obtain the effective equations for black rings, and the perturbation analysis of the large D effective equations with 1/D^1/2 expansions yields the formula for quasinormal mode frequencies. From this formula, we find that black rings actually suffer from both elastic and Gregory-Laflamme like instabilities. These instabilities are coupled and appear at the same time as observed in numerical analysis. The elastic instability does disappear at the infinite limit of a ring radius, which implies that the (boosted) black string is stable to elastic perturbations. Furthermore we observe that the Gregory-Laflamme like instability becomes more efficient than the elastic instability even for certain thin black rings in enough higher dimensions.

hep-th↗

arXiv2016

Instability of de Sitter Reissner-Nordstrom black hole in the 1/D expansion

We study large D effective theory for D dimensional charged (Anti) de Sitter black holes. Then we show that de Sitter Reissner-Nordstrom black hole becomes unstable against gravitational perturbations at larger charge than certain critical value in higher dimension. Furthermore we find that there is a non-trivial zero-mode static perturbation at the critical charge. The existence of static perturbations suggests the appearance of non-spherical symmetric solution branches of static charged de Sitter black hole. This expectation is confirmed by constructing the non-spherical symmetric static solutions of large D effective equations.

hep-th↗

arXiv2016

Non-uniform black strings and the critical dimension in the $1/D$ expansion

Non-uniform black strings (NUBS) are studied by the large $D$ effective theory approach. By solving the near-horizon geometry in the $1/D$ expansion, we obtain the effective equation for the deformed horizon up to the next-to-next-to-leading order (NNLO) in $1/D$. We also solve the far-zone geometry by the Newtonian approximation. Matching the near and far zones, the thermodynamic variables are computed in the $1/D$ expansion. As the result, the large $D$ analysis gives a critical dimension $D_*\simeq13.5$ at which the translation-symmetry-breaking phase transition changes between first and second order. This value of $D_*$ agrees perfectly, within the precision of the $1/D$ expansion, with the result previously obtained by E. Sorkin through the numerical resolution. We also compare our NNLO results for the thermodynamics of NUBS to earlier numerical calculations, and find good agreement within the expected precision.

hep-th↗

arXiv2016

Black rings at large D

We study the effective theory of slowly rotating black holes at the infinite limit of the spacetime dimension D. This large D effective theory is obtained by integrating the Einstein equation with respect to the radial direction. The effective theory gives equations for non-linear dynamical deformations of the slowly rotating black hole as effective equations. The effective equations contain the slowly rotating Myers-Perry black hole, slowly boosted black string, non-uniform black string and black ring as stationary solutions. We obtain an analytic solution of the black ring by solving the effective equations. Furthermore, by perturbation analysis of the effective equations, we find a quasinormal mode condition of the black ring in analytic way. As a result we confirm that thin black ring is unstable against non-axisymmetric perturbations. We also include 1/D corrections to the effective equations and discuss the effects by 1/D corrections.

hep-th↗

arXiv2016

Hydro-elastic Complementarity in Black Branes at large D

We obtain the effective theory for the non-linear dynamics of black branes---both neutral and charged, in asymptotically flat or Anti-deSitter spacetimes---to leading order in the inverse-dimensional expansion. We find that black branes evolve as viscous fluids, but when they settle down they are more naturally viewed as solutions of an elastic soap-bubble theory. The two views are complementary: the same variable is regarded in one case as the energy density of the fluid, in the other as the deformation of the elastic membrane. The large-D theory captures finite-wavelength phenomena beyond the conventional reach of hydrodynamics. For asymptotically flat charged black branes (either Reissner-Nordstrom or p-brane-charged black branes) it yields the non-linear evolution of the Gregory-Laflamme instability at large D and its endpoint at stable non-uniform black branes. For Reissner-Nordstrom AdS black branes we find that sound perturbations do not propagate (have purely imaginary frequency) when their wavelength is below a certain charge-dependent value. We also study the polarization of black branes induced by an external electric field.

hep-th↗

arXiv2015

Stationary black holes: Large $D$ analysis

We consider the effective theory of the large D stationary black hole. By solving Einstein equation with a cosmological constant using the 1/D expansion in near zone of a black hole we obtain the effective equation for the stationary black hole. The effective equation describes the Myers-Perry black hole, bumpy black holes and, possibly, the black ring solution as its solutions. In this effective theory the black hole is represented as the embedded membrane in the background, i.e., Minkowski or Anti-de Sitter spacetime and its mean curvature is given by the redshifted surface gravity by the background geometry and the local Lorentz boost. The local Lorentz boost property of the effective equation is observed also in the metric. In fact we show that the leading order metric of the Einstein equation in the 1/D expansion is generically regarded as the Lorentz boosted Schwarzschild black hole. We apply this Lorentz boost property of the stationary black hole solution to solve the perturbation equation. As a result we obtain the analytic formula for the quasinormal mode of the singly rotating Myers-Perry black hole in the 1/D expansion.

hep-th↗

arXiv2015

Evolution and endpoint of the black string instability: Large D solution

We derive a simple set of non-linear, (1+1)-dimensional partial differential equations that describe the dynamical evolution of black strings and branes to leading order in the expansion in the inverse of the number of dimensions D. These equations are easily solved numerically. Their solution shows that thin enough black strings are unstable to developing inhomogeneities along their length, and at late times they asymptote to stable non-uniform black strings. This proves an earlier conjecture about the endpoint of the instability of black strings in a large enough number of dimensions. If the initial black string is very thin, the final configuration is highly non-uniform and resembles a periodic array of localized black holes joined by short necks. We also present the equations that describe the non-linear dynamics of Anti-deSitter black branes at large D.

hep-th↗

arXiv2015

Effective theory of Black Holes in the 1/D expansion

The gravitational field of a black hole is strongly localized near its horizon when the number of dimensions D is very large. In this limit, we can effectively replace the black hole with a surface in a background geometry (eg Minkowski or Anti-deSitter space). The Einstein equations determine the effective equations that this 'black hole surface' (or membrane) must satisfy. We obtain them up to next-to-leading order in 1/D for static black holes of the Einstein-(A)dS theory. To leading order, and also to next order in Minkowski backgrounds, the equations of the effective theory are the same as soap-film equations, possibly up to a redshift factor. In particular, the Schwarzschild black hole is recovered as a spherical soap bubble. Less trivially, we find solutions for 'black droplets', ie black holes localized at the boundary of AdS, and for non-uniform black strings.

hep-th↗

arXiv2015

Quasinormal modes of (Anti-)de Sitter black holes in the 1/D expansion

We use the inverse-dimensional expansion to compute analytically the frequencies of a set of quasinormal modes of static black holes of Einstein-(Anti-)de Sitter gravity, including the cases of spherical, planar or hyperbolic horizons. The modes we study are decoupled modes localized in the near-horizon region, which are the ones that capture physics peculiar to each black hole (such as their instabilities), and which in large black holes contain hydrodynamic behavior. Our results also give the unstable Gregory-Laflamme frequencies of Ricci-flat black branes to two orders higher in 1/D than previous calculations. We discuss the limits on the accuracy of these results due to the asymptotic but not convergent character of the 1/D expansion, which is due to the violation of the decoupling condition at finite D. Finally, we compare the frequencies for AdS black branes to calculations in the hydrodynamic expansion in powers of the momentum k. Our results extend up to k^9 for the sound mode and to k^8 for the shear mode.

hep-th↗

arXiv2014

Decoupling and non-decoupling dynamics of large D black holes

The limit of large number of dimensions localizes the gravitational field of a black hole in a well-defined region near the horizon. The perturbative dynamics of the black hole can then be characterized in terms of states in the near-horizon geometry. We investigate this by computing the spectrum of quasinormal modes of the Schwarzschild black hole in the 1/D expansion, which we find splits into two classes. Most modes are non-decoupled modes: non-normalizable states of the near-horizon geometry that straddle between the near-horizon zone and the asymptotic zone. They have frequency of order D/r_0 (with r_0 the horizon radius), and are also present in a large class of other black holes. There also exist a much smaller number of decoupled modes: normalizable states of the near-horizon geometry that are strongly suppressed in the asymptotic region. They have frequency of order 1/r_0, and are specific of each black hole. Our results for their frequencies are in excellent agreement with numerical calculations, in some cases even in D=4.

hep-th↗

arXiv2014

Instability of rotating black holes: large D analysis

We study the stability of odd-dimensional rotating black holes with equal angular momenta by performing an expansion in the inverse of the number of dimensions D. Universality at large $D$ allows us to calculate analytically the complex frequency of quasinormal modes to next-to-leading order in the expansion. We identify the onset of non-axisymmetric, bar-mode instabilities at a specific finite rotation, and axisymmetric instabilities at larger rotation. The former occur at the threshold where the modes become superradiant, and before the ultraspinning regime is reached. Our results fully confirm the picture found in numerical studies, with very good quantitative agreement. We extend the analysis to the same class of black holes in Anti-deSitter space, and find the same qualitative features. We also discuss the appearance at high frequencies of the universal set of (stable) quasinormal modes.

hep-th↗

arXiv2014

Universal quasinormal modes of large D black holes

We show that in the limit where the number of spacetime dimensions D grows to infinity a very large class of black holes (including non-extremal, static, asymptotically flat ones, with any number of gauge-field charges, possibly coupled to dilatons) possess a universal set of quasinormal modes whose complex frequencies depend only on the horizon radius and no other black hole parameters. The damping ratio of these modes vanishes like $D^{-2/3}$, so they are almost normal modes, or 'quasi-particle' excitations of the black hole. The structure responsible for the existence of these modes at large D is also present very generally in other black holes.

hep-th↗

arXiv2013

Holographic superconductivity in the large D expansion

We study holographic superconductivity by expanding the equations in the inverse of the number of spacetime dimensions D. We obtain an analytic expression for the critical temperature as a function of the conformal dimension of the condensate operator. Its accuracy for 3+1-dimensional superconductors is better than 15%. The analysis reveals a simple, and quantitative, explanation for the onset of the superconducting instability, as well as universal features of holographic superconductivity in the large D limit. In particular, this allows to easily compute the effects of backreaction on the critical temperature.

hep-th↗

arXiv2013

Quasi-local characteristics of dynamical extreme black holes

Introducing the concept of the extreme trapping horizon, we discuss geometric features of dynamical extreme black holes in four dimensions and then derive the integral identities which hold for the dynamical extreme black holes. We address the causal/geometrical features too.

gr-qc↗

arXiv2013

The large D limit of General Relativity

General Relativity simplifies dramatically in the limit that the number of spacetime dimensions D is infinite: it reduces to a theory of non-interacting particles, of finite radius but vanishingly small cross sections, which do not emit nor absorb radiation of any finite frequency. Non-trivial black hole dynamics occurs at length scales that are 1/D times smaller than the horizon radius, and at frequencies D times larger than the inverse of this radius. This separation of scales at large D, which is due to the large gradient of the gravitational potential near the horizon, allows an effective theory of black hole dynamics. We develop to leading order in 1/D this effective description for massless scalar fields and compute analytically the scalar absorption probability. We solve to next-to-next-to-leading order the black brane instability, with very accurate results that improve on previous approximations with other methods. These examples demonstrate that problems that can be formulated in an arbitrary number of dimensions may be tractable in analytic form, and very efficiently so, in the large D expansion.

hep-th↗