Eur. Phys. J. C (2016) 76: 264
https://doi.org/10.1140/epjc/s10052-016-4124-7

Regular Article - Theoretical Physics

Branes in Gravity’s Rainbow

¹ Mathematics Department, Faculty of Science, Damascus University, Damascus, Syria
² Department of Physics and Astronomy, University of Lethbridge, Lethbridge, AB, T1K3M4, Canada
³ Department of Physics, Faculty of Science, Benha University, Benha, 13518, Egypt
⁴ Physics Department & STAR Research Cluster, Bishop’s University, 2600 College Street, Sherbrooke, QC, J1M 1Z7, Canada
⁵ Physics Department, Champlain College-Lennoxville, Sherbrooke, QC, J1M 0C8, Canada

^* e-mail: ahmed.ali@fsc.bu.edu.eg

Received: 23 February 2016
Accepted: 29 April 2016
Published online: 11 May 2016

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 -Minkowski non-commutative 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.