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The possibility of an alternative way to formulate the Hawking radiation in a static Schwarzschild spacetime has been explored. To calculate the Hawking radiation, there can be two possible choices of the spacetime wedge pairs in the Krucal-Szekeres coordinates. One is the wedge pair consists of exterior spacetime of a black hole and the exterior spacetime of a white hole, and the other is that of exterior and interior spacetimes of one black hole. The radiation from the former is the Hawking’s original one. Though the the latter has been often regarded as the same phenomena as the former, the result here suggests it is not; its radiation has a temperature twice as high as the Hawking temperature.

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