Cosmic censorship and Weak Gravity Conjecture in the Einstein–Maxwell-dilaton theory

Abstract

We explore the cosmic censorship in the Einstein-Maxwell-dilaton theory following Wald's thought experiment to destroy a black hole by throwing in a test particle. We discover that at probe limit the extremal charged dilaton black hole could be destroyed by a test particle with specific energy.Nevertheless the censorship is well protected if backreaction or self-force is included. At the end, we discuss an interesting connection between Hoop Conjecture and Weak Gravity Conjecture. *

Static charged dilaton black hole cannot be overcharged by gedanken experiments

“…It is shown in [32] that the old version of the gedanken experiment can destroy the static dilaton black holes in Einstein-Maxwell-dilaton theory if the backreaction or self-energy is ignored. However, in this paper, we following a similar consideration in [27], we showed that after the second-order perturbation inequality are taken into account, the charged static dilaton black hole cannot be overcharged.…”

“…Since all of the charge added to the spacetime falls through the horizon, this flux is just equal to the total perturbed charge of the black hole, δ Q flux = δ Q. Combining these observations yields the following formula relating the perturbed parameters of the black hole spacetime: (32) where˜ is the corresponding volume element on the horizon, which is defined by ε ebcd = −4k [eεbcd] with the future-directed normal vector k a ∝ ξ a on the horizon. Then, according to the null energy condition δ T ab k a k b ≥ 0, (32) yields the inequality…”

Examining the weak cosmic censorship conjecture by gedanken experiments for Kerr-Sen black holes

“…With a similar consideration to [27], here we also assume the Kerr-Sen black hole is linearly stable to perturbations. That is to say, any source-free solution to the linearized equation of motion (35) will approach a perturbation towards another Kerr-Sen black hole at sufficiently late times. According to the above setup, it is not difficult to see that T ab (λ) and j a (λ) are vanishing except in a compact region of the future horizon.…”

“…First, we would like to analyze the result found in [35] for the old version of gedanken experiments. In that scene, we would like to neglect the O(λ 2 ) term.…”

Overspinning Kerr-MOG black holes by test fields and the third law of black hole dynamics

“…There it was shown that test particles cannot overcharge or overspin an extremal Kerr-Newman black hole into a naked singularity. Following Wald many similar tests of Wccc were applied to black holes in vacuum and Einstein-Maxwell theory involving test particles [4][5][6][7][8][9][10][11][12][13], and fields [14][15][16][17][18][19][20][21][22][23][24]. The stability of event horizons in the asymptotically anti-de Sitter case was also evaluated by perturbing the black holes with test particles and fields [25][26][27][28][29][30].…”