Initial data of black hole localized on karch-randall brane

Based on the conjectured duality in the Karch-Randall braneworld models, it is suggested that a static brane-localized black hole larger than bulk curvature length does exist in this model. It is also suggested that the Hawking-Page transition of the fourdimensional black hole may be reproduced as a change in the shape of five-dimensional black hole in the bulk. In order to test these suggestions, we try to construct timesymmetric initial data of brane-localized black hole in the Karch-Randall braneworld model and study its properties. I will explain the method of the analysis and illustrate expected results.