Asymptotic Symmetry Near the Cosmological Horizon

Physics

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Recently, the local or quasi-local definitions have been given to the horizon, such as the trapping horizon1 and the isolated horizon2. Such analyses of the local behavior of the horizon may provide a new insight into black hole thermodynamics. Indeed, in the context of the isolated horizon, the Bekenstein-Hawking formula of the black hole entropy has been successfully reproduced in a microscopic manner based on the loop quantum gravity3, while the expression of the entropy includes a parameter of the theory which is still to be determined. In addition, due to its recent developments4,5,6, the string theory also has provided successful methods to count the microscopic states of the black hole and derive the Bekenstein-Hawking formula, by using the conformal field theory. However, we cannot apply these methods of the string theory to the generic black hole. Furthermore, it is not clear where those microscopic states of the black hole live. In order to resolve these issues, it will be important to understand whether the microscopic states of the arbitrary black hole can be described locally on the horizon by use of the conformal field theory ...

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