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We investigate the weak cosmic censorship conjecture in Kerr-(anti-)de Sitterblack holes under the scattering of a scalar field. We test the conjecture interms of whether the black hole can exceed the extremal condition with respectto its change caused by the energy and angular momentum fluxes of the scalarfield. Without imposing the laws of thermodynamics, we prove that theconjecture is valid in all the initial states of the black hole (non-extremal,near-extremal, and extremal black holes). The validity in the case of thenear-extremal black hole is different from the results of similar testsconducted by adding a particle because the fluxes represent the energy andangular momentum transferred to the black hole during the time interval notincluded in the tests involving the particle. Using the time interval, we showthat the angular velocity of the black hole with the scalar field of a constantstate takes a long time for saturation to the frequency of the scalar field.

Weak Cosmic Censorship Conjecture in Kerr-(Anti-)de Sitter Black Hole with Scalar Field