Abstract
In this work, we investigate the thermodynamics of black $p$-branes (BB) in the context of Gravity's Rainbow. We investigate this using rainbow functions that have been motivated from loop quantum gravity and $\kappa$-Minkowski noncommutative spacetime. Then for the sake of comparison, we examine a couple of other rainbow functions that have also appeared in the literature. We show that, for consistency, Gravity's Rainbow imposes a constraint on the minimum mass of the BB, a constraint that we interpret here as implying the existence of a black $p$-brane remnant. This interpretation is supported by the computation of the black $p$-brane's heat capacity that shows that the latter vanishes when the Schwarzschild radius takes on a value that is bigger than its extremal limit. We found that the same conclusion is reached for the third version of rainbow functions treated here but not with the second one for which only standard black $p$-brane thermodynamics is recovered.
Highlights
One common feature among most of semi-classical approaches to quantum gravity is a Lorentz invariance violation due to a departure from the usual relativistic dispersion relation caused by a redefinition of the physical momentum and physical energy at the Planck scale
This means that, in contrast to what we found for the rainbow functions (9), the heat capacity does not vanish for any value of r0 for a p-brane obeying a modified dispersion relation based on the rainbow functions (19)
We have examined in this paper the effects of modified dispersion relations on the thermodynamics of p-branes
Summary
One common feature among most of semi-classical approaches to quantum gravity is a Lorentz invariance violation due to a departure from the usual relativistic dispersion relation caused by a redefinition of the physical momentum and physical energy at the Planck scale. A UV completion (by taking different Lifshitz scalings for space and time) has been studied in the context of type IIA string theory [30], type IIB string theory [31], the AdS/CFT correspondence [32,33,34,35], dilaton black branes [36,37], and dilaton black holes [38,39] It turns out, that there is another way to obtain a UV completion of General Relativity, and this approach is none other than the theory of Gravity’s Rainbow [13] we have discussed above. After this brief review of black pbranes thermodynamics, we shall examine how the latter is modified when Gravity’s Rainbow is taken into consideration
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