Abstract
In a quantum gravity theory, spacetime at mesoscopic scales can acquire a novel structure very different from the classical concept of general relativity. A way to effectively characterize the quantum nature of spacetime is through a momentum dependent space-time metric. There is a vast literature showing that this geometry is related to relativistic deformed kinematics, which is precisely a way to capture residual effects of a quantum gravity theory. In this work, we study the notion of surface gravity in a momentum dependent Schwarzschild black hole geometry. We show that using the two main notions of surface gravity in general relativity we obtain a momentum independent result. However, there are several definitions of surface gravity, all of them equivalent in general relativity when there is a Killing horizon. We show that in our scheme, despite the persistence of a Killing horizon, these alternative notions only agree in a very particular momentum basis, obtained in a previous work, so further supporting its physical relevance.
Highlights
It is common lore that the most daunting challenge of theoretical physics is nowadays the unification of General Relativity (GR) and Quantum Field Theory (QFT), or equivalently, the formulation of a Quantum Gravity Theory (QGT)
In this work we have studied different notions of surface gravity of a Schwarzschild black hole in a rainbow geometry in the deformed special relativity (DSR) scenario
This study differs from previous works in the literature because here we have taken into account that, in order describe the relativistic deformed kinematics of DSR, the momentum metric must be a maximally symmetric momentum space
Summary
It is common lore that the most daunting challenge of theoretical physics is nowadays the unification of General Relativity (GR) and Quantum Field Theory (QFT), or equivalently, the formulation of a Quantum Gravity Theory (QGT). LIV scenarios modify the kinematics of special relativity (SR) with the introduction of a preferred frame associated to some extra geometrical structure such as a fixed norm vector field Such framework allows to write for elementary particles a modified, no more Lorentz invariant, dispersion relation. In DSR theories the relativity principle is instead preserved, albeit at the cost of introducing a non-linear realization of the Lorentz group which allows for an invariant (observer independent) energy scale, leading to a relativistic deformed kinematics. In this case, this quantum gravity scale can be associated to a deformed dispersion relation, in this framework this is not fully capturing the new physics.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
