We numerically investigate the formation of D-dimensional black holes in high-energy particle collision with the impact parameter and evaluate the total cross section of the black hole production. We find that the formation of an apparent horizon occurs when the distance between the colliding particles is less than 1.5 times the effective gravitational radius of each particles. Our numerical result indicates that although both the one-dimensional hoop and the (D-3)-dimensional volume corresponding to the typical scale of the system give a fairly good condition for the horizon formation in the higher-dimensional gravity, the (D-3)-dimensional volume provide a better condition to judge the existence of the horizon.Comment: 13 pages, 6 figure

Motivated by possible existence of stringy axions with ultralight mass, we study the behavior of an axion field around a rapidly rotating black hole (BH) obeying the sine-Gordon equation by numerical simulations. Due to superradiant instability, the axion field extracts the rotational energy of the BH and the nonlinear self-interaction becomes important as the field grows larger. We present clear numerical evidences that the nonlinear effect leads to a collapse of the axion cloud and a subsequent explosive phenomena, which is analogous to the "bosenova" observed in experiments of Bose-Einstein condensate. The criterion for the onset of the bosenova collapse is given. We also discuss the reason why the bosenova happens by constructing an effective theory of a wavepacket model under the nonrelativistic approximation.

Suppose one of the string axions has mass µ ∼ 10 −10 eV. The Compton wavelength 1/µ is comparable to the radius of a BH with solar mass M ∼ M ⊙ (Throughout this paper, we use the units c = G = = 1). Then, around a rotating solar-mass BH, there appears an unstable quasibound-state mode whose amplitude grows exponentially through the extraction of the BH rotation energy. This instability is called superradiant instability. Due to this instability, an axion cloud is formed around the BH from quantum zero-point oscillations even if we start from vacuum. The growth rate has been calculated by approximate methods [4,5] and by numerical methods [6][7][8] by solving the frequency-domain eigenvalue problem. 1 The maximum growth rate has been found to be M ω I ∼ 10 −7 , and the corresponding time scale to be around 10 7 M , which is much longer than M (see Fig. 1). But this time scale is about 1 minute for M = M ⊙ . Even for M ω I ∼ 10 −12 , the time scale is about 1 day. Therefore, for a wide range of parameters, the time scale of the superradiant instability is much shorter than the observation period of the ground-based GW detectors.The axion cloud becomes denser and denser as the superradiant instability proceeds, and two effects gradually become important. One is nonlinear self-interaction, and the other is the GW emission. Here, the nonlinear self-interaction comes from the potential of the axion field Φ, which is assumed to have the standard form V = f 2 a µ 2 [1 − cos(Φ/f a )] in the present paper where f a is the axion decay constant. In our previous paper [9], we numerically simulated the time evolution of an axion field obeying the sine-Gordon equation in the Kerr background spacetime. The result is that the nonlinear self-interaction leads to "axion bosenova," which shares some features with the bosenova observed in experiments [12] on Bose-Einstein condensates. The bosenova is characterized by the termination of superradiant instability and the gradual infall of positive energy from the axion cloud into the BH. The bosenova happens when the energy E a of the axion cloud becomes E a /M ≈ 1600(f a /M p ) 2 , where M p is the Planck mass. If f a corresponds to the GUT scale, f a = 10 16 GeV, the bosenova happens when axion cloud acquires 0.16% energy of the BH mass.In the same paper [9], we also gave an order estimate of the amplitude of GWs emitted during the bosenova, and found a possibility to detect signals from the bosenova if it happens around a BH near the solar system (say, within 1 kpc). This motivates us to study GWs from the bosenova in more detail. However, before doing that, we have to study GW emission before the bosenova, i.e., in the superradiant phase. The reason is as follows. The axion cloud obtains energy by extraction of BH's rotation energy, while it loses energy by emission of GWs. The energy extraction rate dE a /dt is related to the superradiant growth rate asand therefore, it is proportional to (E a /M ). On the other hand, the energy loss rate by the GW emission (i.e., the radiation rat...

Numerical-relativity simulation is performed for rapidly spinning black holes (BHs) in a higherdimensional spacetime of special symmetries for the dimensionality 6 ≤ d ≤ 8. We find that higherdimensional BHs, spinning rapidly enough, are dynamically unstable against nonaxisymmetric barmode deformation and spontaneously emit gravitational waves, irrespective of d as in the case d = 5[1]. The critical values of a nondimensional spin parameter for the onset of the instability are q := a/µ 1/(d−3) ≈ 0.74 for d = 6, ≈ 0.73 for d = 7, and ≈ 0.77 for d = 8 where µ and a are mass and spin parameters. Black holes with a spin smaller than these critical values (qcrit) appear to be dynamically stable for any perturbation. Longterm simulations for the unstable BHs are also performed for d = 6 and 7. We find that they spin down as a result of gravitational-wave emission and subsequently settle to a stable stationary BH of a spin smaller than qcrit. For more rapidly spinning unstable BHs, the timescale, for which the new state is reached, is shorter and fraction of the spin-down is larger. Our findings imply that a highly rapidly spinning BH with q > qcrit cannot be a stationary product in the particle accelerators, even if it would be formed as a consequence of a TeV-gravity hypothesis. Its implications for the phenomenology of a mini BH are discussed.