Local free-fall Temperature of modified Schwarzschild black hole in rainbow spacetime

We obtain a (5+1)-dimensional global flat embedding of modified Schwarzschild black hole in rainbow gravity. We show that local free-fall temperature in rainbow gravity, which depends on different energy $ω$ of a test particle, is finite at the event horizon for a freely falling observer, while local temperature is divergent at the event horizon for a fiducial observer. Moreover, these temperatures in rainbow gravity satisfy similar relations to those of the Schwarzschild black hole except overall factor $g(ω)$, which plays a key role of rainbow functions in this embedding approach.

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