Maximal acceleration in Rainbow gravity

TL;DR

This paper derives the maximal acceleration in Rainbow gravity, explores its bounds, and examines implications for Unruh temperature and Newtonian limits, highlighting dependence on Rainbow function choices.

Contribution

It introduces a method to calculate maximal acceleration in Rainbow gravity and analyzes bounds on the Rainbow parameter based on physical conditions.

Findings

Upper bounds on Rainbow parameter for positrons and black holes.

Modified Unruh temperature expressions in Rainbow gravity.

Dependence of maximum acceleration and Newtonian limits on Rainbow functions.

Abstract

In this paper, we derive maximal acceleration of a massive particle in Rainbow gravity. Using eight-dimensional phase-space metric compatible with Rainbow gravity, we obtain the maximal acceleration, valid up to first order in the Rainbow gravity parameter $\eta$. Using the positivity condition on maximal acceleration, we find the upper bound on the Rainbow gravity parameter is of the order of $~10^{22}$ for positron and $10^{-44}$ for a black hole. After obtaining the expression for maximal acceleration for different choices of Rainbow functions, we derive corresponding modifications to Unruh temperature. Comparing with the observational value of the Unruh temperature, we find the upper bound on $\eta$ as $~10^{32}$ for positron radiation. %and of the order of $10^{-100}$ for radiation from a black hole. We then derive geodesic equations for different choices of Rainbow functions and also obtain Newtonian limit of these geodesic equations. We find that the changes in the value of maximum acceleration, maximum temperature and Newtonian force equation are dependent on the choices of Rainbow functions.