Black Holes in Higher Dimensions: Final state of Gregory–Laflamme instability
Black Holes in Higher Dimensions: Final state of Gregory–Laflamme instability
复制标题
高维黑洞：格雷戈里-拉弗拉姆不稳定性的最终状态
DOI：
10.1017/cbo9781139004176.004
复制
发表时间：
2012
影响因子：
5.4
通讯作者：
F. Pretorius
中科院分区：
文献类型：
--
作者：
L. Lehner;F. Pretorius
3.2 BackgroundThe observation of Gregory and Laflamme that linearized perturbations of D-dimensional black strings (D≥ 5) are unstable for long wavelengths (see Chapter 2 or [1]) is in stark contrast with the known behavior of black holes in four dimentions [2]. On the basis of the nature of growing perturbations of black strings, together with entropy arguments, Gregory and Laflamme conjectured that black strings would bifurcate, thus inducing a topology change in the horizon to yield localized SD-2 black holes. However, black hole bifurcation necessarily implies, at the classical level, the formation of a naked singularity where the pinch-off occurs (see for example [3]). Assuming such behavior would be resolved by quantum gravity, the conjecture was taken as likely to be true for about a decade. In the early years after 2000, tension arose when Horowitz and Maeda proved that any bifurcation could only take place at infinite affine time along the generators of the horizon that cross the bifurcation point [4]. They dismissed this possibility as unlikely and conjectured the existence of stationary nonuniform black string solutions as the endpoint of the instability. Follow-up works presented approximate stationary solutions found perturbatively [5] or numerically [6–8](see Chapter 4), though these had less entropy than the uniform string and so could not be the end-point of the system. Regarding these developments, interesting observations were made as to a possible reversal of this behavior for D> Derit [9], where the critical dimension Derit depends on the boost of the black string [10](Derit= 13 for an unboosted black string and Derit= 0 for sufficiently large boosts). Furthermore, it was pointed out that electrically charged black strings are more unstable than magnetically charged ones [11], and arguments were presented for a conical structure in the black-string-black-hole transition [12, 13]. This flurry of activity not only hinted at the possibility of rich phenomenology awaiting in the dynamics of the system but also at the need for a full analysis to uncover it. A first attempt to do so was presented in [14]. This study revealed that the development of a black string perturbed by a long-wavelength periodic mode progressed to a structure that could be described as a sequence of S³ black holes joined by strings, though the final fate of the structure could not be uncovered since the code was unable to evolve the solution further. Detailed follow-up analysis of the results from this simulation showed that the affine time along the generators grew faster than a simple exponential in the asymptotic time [15], suggesting the consistency of a possible pinch-off with the theorem presented in [4]; see also [16]. Following these works, additional hints to the possible end state came from the analogy with fluid systems. The membrane paradigm [17] first suggested that event horizon dynamics could be described, to leading order, by the Navier-Stokes equations for a viscous fluid (albeit with some" unusual" properties, such as a
