Abstract:We investigate the variation of the charged anti-de Sitter black hole under charged particle absorption by considering thermodynamic volume. When the energy of the particle is considered to contribute to the internal energy of the black hole, the variation exactly corresponds to the prediction of the first law of thermodynamics. Nevertheless, we find the decrease of the Bekenstein-Hawking entropy for extremal and near-extremal black holes under the absorption, which is an irreversible process. This violation of the second law of thermodynamics is only found when considering thermodynamic volume. We test the weak cosmic censorship conjecture affected by the violation. Fortunately, the conjecture is still valid, but extremal and near-extremal black holes do not change their configurations when any particle enters the black hole. This result is quite different from the case in which thermodynamic volume is not considered.

We study the instability of charged anti-de Sitter black holes in four or higher-dimension under fragmentation. The instability of fragmentation breaks the black hole into two black holes. We have found that the region near extremal or massive black holes become unstable under fragmentation. These regions depend not only on the mass and charge of initial black hole but also those of the fragmented one. The instability in higher-dimension is qualitatively similar to that of four-dimension. The detailed instabilities are numerically investigated.

The validity of the cosmic censorship conjecture for the Kerr-Sen black hole, which is a solution to the lowenergy effective field theory for four-dimensional heterotic string theory, is investigated using charged particle absorption. When the black hole absorbs the particle, the charge on it changes owing to the conserved quantities of the particle. Changes in the black hole are constrained to the equation for the motion of the particle and are consistent with the laws of thermodynamics. Particle absorption increases the mass of the Kerr-Sen black hole to more than that of the absorbed charges such as angular momentum and electric charge; hence, the black hole cannot be overcharged. In the near-extremal black hole, we observe a violation of the cosmic censorship conjecture for the angular momentum in the first order of expansion and the electric charge in the second order.However, considering an adiabatic process carrying the conserved quantities as those of the black hole, we prove the stability of the black hole horizon. Thus, we resolve the violation. This is consistent with the third law of thermodynamics.

We investigate the weak cosmic censorship conjecture in Kerr-(anti-)de Sitter black holes under the scattering of a scalar field. We test the conjecture in terms of whether the black hole can exceed the extremal condition with respect to its change caused by the energy and angular momentum fluxes of the scalar field. Without imposing the laws of thermodynamics, we prove that the conjecture 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 the near-extremal black hole is different from the results of similar tests conducted by adding a particle because the fluxes represent the energy and angular momentum transferred to the black hole during the time interval not included in the tests involving the particle. Using the time interval, we show that the angular velocity of the black hole with the scalar field of a constant state takes a long time for saturation to the frequency of the scalar field. 1 rasenis@sejong.ac.krBlack holes, which are directly proven to exist through detection by the Laser Interferometer Gravitational-Wave Observatory (LIGO), are among the most interesting topics in gravity theories. Classically, in the black hole spacetime, there is an event horizon through which no matter can escape from the black hole; thus, no radiation from the black hole can reach an observer located outside this horizon. However, in quantum theory, black holes act as thermal systems that emit energy through Hawking radiation [1,2]. In Hawking radiation, the Hawking temperature is defined for a black hole. Furthermore, when a particle is added to the black hole, depending on the conserved quantities of the particle, the conserved quantities of the black hole, such as mass and angular momentum, can increase or decrease. However, an irreducible quantity exists during this process, which is known as the irreducible mass [3][4][5]. The irreducible mass is the energy distributed on the surface of the horizon of the black hole [6]. Owing to the similarity between the irreducible mass and the thermodynamic entropy, the Bekenstein-Hawking entropy is defined to be proportional to the surface area of the black hole, which is the square of its irreducible mass [7,8]. Accordingly, we can establish the laws of thermodynamics for black holes.

We investigate the weak cosmic censorship conjecture for Kerr-Sen black holes, which are solutions to the four-dimensional low-energy effective field theory for the heterotic string theory, based on the scattering of a charged scalar field. When the fluxes of the scalar field are assumed to transfer its conserved quantities to the black hole, extremal and near-extremal black holes cannot be over-spun and over-charged in their first-order variations, which is sufficient to conclude that the weak cosmic censorship conjecture is valid for Kerr-Sen black holes. We confirm our conclusion by relating it to the first, second, and third laws of thermodynamics. 1