Weak cosmic censorship with excited scalar fields and bound on charge-to-mass ratio
arxiv(2024)
Abstract
Recent study in [1] discovered that introducing a massive charged scalar
field and requiring the Weak Gravity Conjecture (WGC) to hold can eliminate a
class of Weak Cosmic Censorship Conjecture (WCCC) counterexamples in anti-de
Sitter spacetime, indicating a potential connection between WCCC and WGC. In
this paper, we extend the study to the case of excited-state scalar fields, and
numerically construct the static solutions of excited massive charged scalar
fields coupled to the Einstein-Maxwell field in four dimensional spacetime with
asymptotically anti-de Sitter boundary conditions. In the absence of scalar
field, there is a class of counterexamples to cosmic censorship. However, after
adding the scalar field with sufficiently large charge, the original
counterexamples can be removed and cosmic censorship is preserved. We find this
conclusion also applies to the excited-state of scalar field. There is a
minimum value q_c^bound. When the charge of the excited scalar field is
larger than this minimum value, for sufficiently large boundary electric
amplitude a, there will not appear a region with arbitrarily large curvature.
That means there exists lower bound on the charge for excited state fields
which protects cosmic censorship from being violated.
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