# Gravitational Redshift in Kerr-Newman Geometry Using Gravity's Rainbow

## TL;DR

This paper derives an energy-dependent gravitational redshift formula in Kerr-Newman spacetime within gravity's rainbow framework, showing that high-energy photons can significantly alter redshift measurements and potentially reveal new physics scales.

## Contribution

It introduces a novel energy-dependent gravitational redshift expression for Kerr-Newman geometry incorporating gravity's rainbow effects, extending previous static and non-rotating models.

## Key findings

- Gravitational redshift depends on the energy of the emitted photon.
- High-energy photons cause greater corrections to redshift values.
- Potential to set bounds on rainbow function parameters using astrophysical data.

## Abstract

Gravitational redshift is generally reported by most of the authors without considering the influence of the energy of the test particle using various spacetime geometries such as Schwarzschild, Reissner-Nordstrom, Kerr and Kerr-Newman geometries for static, charged static, rotating and charged rotating objects respectively. In the present work, the general expression for the energy dependent gravitational redshift is derived for charged rotating body using the Kerr-Newman geometry along with the energy dependent gravity's rainbow function. It is found that the gravitational redshift is influenced by the energy of the source or emitter. One may obtain greater correction in the value of gravitational redshift, using the high energy photons. Knowing the value of gravitational redshift from a high energy sources such as Gamma-ray Bursters (GRB), one may obtain the idea of upper bounds on the dimensionless rainbow function parameter ($\xi$). Also there may be a possibility to introduce a new physical scale of the order of $\frac{\xi}{E_{Pl}}$.