Abstract
We study the model of four-dimensional Einstein-Maxwell-Λ theory minimally coupled to a massive charged self-interacting scalar field, parameterized by the quartic and hexic couplings, labelled by λ and β, respectively. In the absence of scalar field, there is a class of counterexamples to cosmic censorship. Moreover, we investigate the full nonlinear solution with nonzero scalar field included, and argue that these counterexamples can be removed by assuming charged self-interacting scalar field with sufficiently large charge not lower than a certain bound. In particular, this bound on charge required to preserve cosmic censorship is no longer precisely the weak gravity bound for the free scalar theory. For the quartic coupling, for λ < 0 the bound is below the one for the free scalar fields, whereas for λ > 0 it is above. Meanwhile, for the hexic coupling the bound is always above the one for the free scalar fields, irrespective of the sign of β.
Highlights
It asserts that if the weak gravity conjecture holds, the weak cosmic censorship can be preserved
We study the model of four-dimensional Einstein-Maxwell-Λ theory minimally coupled to a massive charged self-interacting scalar field, parameterized by the quartic and hexic couplings, labelled by λ and β, respectively
These results are completely the same as those for λ = β = 0. Above this zero-mode curve, the original Einstein-Maxwell solutions will become unstable to condense charged scalar field, and settle down to new stationary hairy solutions. To see whether these counterexamples to weak cosmic censorship can be removed with charged self-interacting scalar field, we investigate the full nonlinear solutions derived from eqs. (2.2) for the quartic coupling λ = 0 and the hexic coupling β = 0, respectively
Summary
To remove the counterexamples proposed in [33], we add massive charged self-interacting scalar field Φ into the original Einstein-Maxwell gravity. Before this we need a set of appropriate ansatz and boundary conditions for full nonlinear solutions with charged scalar. In the absence of scalar field, in [57] the authors showed that for different asymptotic profiles of vector potential, the solutions of the Einstein-Maxwell theory in AdS always appear to be singular as long as these profiles fall off faster than 1/r at large r. This result does not depend on a quite artificial model. Given ansatz and boundary conditions, we could search for the full nonlinear solutions to eqs. (2.2) numerically and further investigate their properties, as we will discuss below
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