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The weak gravity conjecture, overcharged shells and gravitational traps
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DOI：10.1088/1361-6382/ad28f9.png)
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Abstract
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The Weak Gravity Conjecture (WGC) predicts that in quantum gravity there should exist overcharged states, that is states with charge larger than their mass. Extending this to large masses and charges, we are expecting similar overcharged classical solutions. This has been demonstrated in higher-derivative extensions of General Relativity. In this paper we investigate the existence of overcharged solutions in General Relativity. We study the dynamics of a thin shell of mass m and charge Q under the action of its own gravitational and U(1) fields. We show that shells with surface energy sigma and pressure P obeying P = w sigma with 0 <= w <= 1 are necessarily undercharged m >= vertical bar Q vertical bar and always collapse to form Reissner-Nordstrom black holes. Nevertheless, if -1 <= w < 0, we find that overcharged m <= vertical bar Q vertical bar shells exist, which however, are inevitably stabilized at finite radial distance. Therefore they never form naked singularities in accordance with cosmic censorship and the conjectured relation between cosmic censorship and the WGC. An intriguing consequence of the existence of such overcharged shells is that gravitational modes may form bound states due to the peculiar form of the Regge-Wheeler-Zerilli potential. This might lead to gravitational traps close the surface of near-overcharged shells.
Keywords:
weak gravity conjecture
quasinormal modes
gravitational modes
classical gravity
overcharged shells
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3.7
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1.3W
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3.0W
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