In this thesis, we study the energy extraction from rotating black holes in anti-de Sitter (AdS) spacetime (Kerr-AdS black holes), via the Blandford-Znajek (BZ) process. The motivation is the anti-de Sitter/conformal field theory (AdS/CFT) correspondence which provides a duality between gravitational physics in asymptotically AdS spacetimes and lower dimensional boundary field theories. The BZ process operates via a force-free magnetosphere around black holes and the rotational energy of the black hole is extracted electromagnetically in the form of Poynting flux. The major part of the thesis is devoted to obtaining force-free solutions in the Kerr-AdS background, which generalize traditional BZ solutions in the asymptotically flat Kerr background. Given the solutions, we use the AdS/CFT to infer dual descriptions in terms of the boundary field theory, which hopefully will lead to a better understanding of the energy extraction for rotating black holes. / Graduate

As an operational approach to the Bekenstein-Hawking formula S_{BH}=A/4l_{Pl}^{2} for the black hole entropy, we consider the reversible contraction of a spinning thin shell to its event horizon and find that its thermodynamic entropy approaches $S_{\mathrm{BH}}$. In this sense the shell, called a "black shell", imitates and is externally indistinguishable from a black hole. Our work is a generalization of the previous result [10] for the spherical case. We assume the exterior space-time of the shell is given by the Kerr metric and match it to two different interior metrics, a vacuum one and a non-vacuum one. We find the vacuum interior embedding breaks down for fast spinning shells. The mechanism is not clear and worth further exploring. We also examine the case of a Kerr-AdS exterior, without trying to find a detailed interior solution. We expect the same behavior of the shell when the horizon limit is approached.

As an operational approach to the Bekenstein-Hawking formula S_{BH}=A/4l_{Pl}^{2} for the black hole entropy, we consider the reversible contraction of a spinning thin shell to its event horizon and find that its thermodynamic entropy approaches $S_{\mathrm{BH}}$. In this sense the shell, called a "black shell", imitates and is externally indistinguishable from a black hole. Our work is a generalization of the previous result [10] for the spherical case. We assume the exterior space-time of the shell is given by the Kerr metric and match it to two different interior metrics, a vacuum one and a non-vacuum one. We find the vacuum interior embedding breaks down for fast spinning shells. The mechanism is not clear and worth further exploring. We also examine the case of a Kerr-AdS exterior, without trying to find a detailed interior solution. We expect the same behavior of the shell when the horizon limit is approached.