Mapping Hawking into Unruh thermal properties

By globally embedding curved spaces into higher dimensional flat ones, we show that Hawking thermal properties map into their Unruh equivalents: The relevant curved space detectors become Rindler ones, whose temperature and entropy reproduce the originals. Specific illustrations include Schwarzschild, Schwarzschild-(anti-)de Sitter, Reissner-Nordström, and Bañados-Teitelboim-Zanelli spaces.