Thermodynamics and Luminosities of Rainbow Black Holes

Abstract

Doubly special relativity (DSR) is an effective model for encoding quantum gravity in flat spacetime. As a result of the nonlinearity of the Lorentz transformation, the energy-momentum dispersion relation is modified. One simple way to import DSR to curved spacetime is \textquotedblleft Gravity's rainbow", where the spacetime background felt by a test particle would depend on its energy. Focusing on the \textquotedblleft Amelino-Camelia dispersion relation" which is $E^2=m^2+p^2\left[1-\eta {\left(E/m_p\right)}^n\right]$ with $n>0$, we investigate the thermodynamical properties of a Schwarzschild black hole and a static uncharged black string for all possible values of $\eta$ and $n$ in the framework of rainbow gravity. It shows that there are non-vanishing minimum masses for these two black holes in the cases with $\eta <0$ and $n\ge 2$. Considering effects of rainbow gravity on both the Hawking temperature and radius of the event horizon, we use the geometric optics approximation to compute luminosities of a 2D black hole, a Schwarzschild one and a static uncharged black string. It is found that the luminosities can be significantly suppressed or boosted depending on the values of $\eta$ and $n$.

32 pages, 12 figures

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• Rainbow gravity corrections to the information flux of a black hole and the sparsity of Hawking radiation
• Parameter splitting in dark energy: is dark energy the same in the background and in the cosmic structures?
• Simulating cosmologies beyond $\Lambda$CDM with PINOCCHIO
• Thermodynamics and remnants of Kiselev black holes in Rainbow gravity
• Free-fall Frame Black Hole in Gravity's Rainbow
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• Exploring black hole mechanics in cotangent bundle geometries
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