Naked singularity explosion in higher dimensions

Abstract

Motivated by the recent argument that in the TeV-scale gravity trans-Planckian domains of spacetime as effective naked singularities would be generated by high-energy particle (and black-hole) collisions, we investigate the quantum particle creation by nakedsingularity formation in general dimensions. Background spacetime is simply modeled by the self-similar Vaidya solution, describing the spherical collapse of a null dust fluid. In a generic case the emission power is found to be proportional to the quadratic inverse of the remaining time to a Cauchy horizon, as known in four dimensions. On the other hand, the power is proportional to the quartic inverse for a critical case in which the Cauchy horizon is 'degenerate'. According to these results, we argue that the backreaction of the particle creation to gravity will be important in particle collisions, in contrast to the gravitational collapse of massive stellar objects, since the bulk of energy is carried away by the quantum radiation even if a quantum gravitational effect cutoff the radiation just before the appearance of naked singularity.

Naked singularity explosion in higher-dimensional dust collapse

“…In the degenerate case, we have found that the power and energy diverge as the quartic and cubic inverse of the remaining time, respectively, and have shown that the power and energy depend on the total mass of dust fluid M phys despite the scale invariance of the central region. While a similar result has been obtained in the Vaidya case [19], it should be stressed that the behavior of the power and energy is different between the exactly degenerate case ζ = ζ c and the limit of ζ → ζ c .…”

“…(48). These features are similar to those in the higher-dimensional Vaidya (null dust) case [19]. Numerical values of (49) when the parameters are chosen as M P c 2 = 1 TeV and M phys c 2 = 5 TeV are given in Table 1.…”

“…An almost complete formulation was presented in Appendix B of Ref. [19], which is just a higher-dimensional generalization of the original formulation given by Ford and Parker [8]. Substituting Eqs.…”

“…This model, however, needed a fine-tuning to realize the background geometry. Therefore, we considered the more generic situation in the last paper [19], still adopting the Vaidya spacetime. In this paper, as the next step, we generalize the analysis in the last paper [19] to the Lemaître-Tolman-Bondi (LTB) spacetime, which describes the spherical collapse of an inhomogeneous dust fluid (i.e., pressureless timelike fluid).…”

Single shot amplitude and phase characterization of optical arbitrary waveforms

“…Recently there has been significant activity in optical arbitrary waveform generation (OAWG) in which the amplitude and phase of individual lines of relatively high repetition rate frequency combs are controlled [1][2][3][4][5][6]. In the time domain, this leads to generation of wide temporal window (up to 100% duty factor) waveforms repeating at the repetition rate of the comb.…”