We analyze black hole thermodynamics in a generalized theory of gravity whose Lagrangian is an arbitrary function of the metric, the Ricci tensor and a scalar field. We can convert the theory into the Einstein frame via a "Legendre" transformation or a conformal transformation. We calculate thermodynamical variables both in the original frame and in the Einstein frame, following the Iyer-Wald definition which satisfies the first law of thermodynamics. We show that all thermodynamical variables defined in the original frame are the same as those in the Einstein frame, if the spacetimes in both frames are asymptotically flat, regular and possess event horizons with non-zero temperatures. This result may be useful to study whether the second law is still valid in the generalized theory of gravity.

We consider entanglement extraction into two two-level Unruh-DeWitt detectors from a vacuum of a neutral massless quantum scalar field in a four-dimensional spacetime, where the general monopole coupling to the scalar field is assumed. Based on the reduced density matrix of the two detectors derived within the perturbation theory, we show that the single copy of the entangled pair of the detectors can be utilized in quantum teleportation even when the detectors are separated acausally, while we observe no violation of the Bell-CHSH inequality. In the case of the Minkowski vacuum, in particular, we find that entanglement usable in quantum teleportation is extracted due to the special relativistic effect when the detectors are in a relative inertial motion, while it is not when they are comoving inertially and the switching of the detectors is executed adiabatically at infinite past and future. * Electronic address: koga@waseda.jp † Electronic address: gen@shibaura-it.ac.jp

We study both spherically symmetric and rotating black holes with dilaton coupling and discuss the evaporation of these black holes via Hawking's quantum radiation and their fates. We find that the dilaton coupling constant a drastically affects the emission rates, and therefore the fates of the black holes. When the charge is conserved, the emission rate from the nonrotating hole is drastically changed beyond a = 1 (a superstring theory) and diverges in the extreme limit. In the rotating cases we analyze the slowly rotating black hole solution with arbitrary a as well as three exact solutions:the Kerr-Newman ( a = 0), Kaluza-Klein ( a = f i ) , and Sen black hole (a = 1 and with axion field).Beyond the same critical value of a N 1, the emission rate becomes very large near the maximally charged limit, while for a < 1 it remains finite. The black hole with a: > 1 may evolve into a naked singularity due to its large emission rate. We also consider the effects of a discharge process by investigating superradiance for the nonrotating dilatonic black hole.

We investigate an anisotropic model of superconductors in the Einstein-Maxwell-dilaton theory with a charged scalar field. It is found that the critical temperature decreases as the anisotropy becomes large. We then estimate the energy gap of the superconductor, and find that the ratio of the energy gap to the critical temperature increases as the anisotropy increases and so it is larger than that in the isotropic case. We also find that peudogap appears due to the anisotropy.