Testing the weak cosmic censorship conjecture for extremal magnetized Kerr-Newman black holes

We test the weak cosmic censorship conjecture for magnetized Kerr-Newman spacetime via the method of injecting a test particle. Hence, we need to know how the black hole's parameters change when a test particle enters the horizon. This was an unresolved issue for non-asymptotically flat spacetimes since there are ambiguities on the energies of black holes and particles. We find a novel approach to solve the problem. We start with the "physical process version" of the first law, which relates the particle's parameters with the change in the area of the black hole. By comparing this first law with the usual first law of black hole thermodynamics, we redefine the particle's energy such that the energy can match the mass parameter of the black hole. Then, we show that the horizon of the extremal magnetized Kerr-Newman black hole could be destroyed after a charged test particle falls in, which leads to a possible violation of the weak cosmic censorship conjecture. We also find that the allowed parameter range for this process is very small, which indicates that after the self-force and radiation effects are taken into account, the weak cosmic censorship conjecture could still be valid. In contrast to the case where the magnetic field is absent, the particle cannot be released at infinity to destroy the horizon. And in the case of a weak magnetic field, the releasing point becomes closer to the horizon as the magnetic field increases. This indicates that the magnetic field makes the violation of the cosmic censorship more difficult. Finally, by applying our new method to Kerr-Newman-dS (AdS) black holes, which are well-known non-asymptotically flat spacetimes, we obtain the expression of the particle's energy which matches the black hole's mass parameter.