Rainbow Rindler metric and Unruh effect

Abstract

The energy of a particle moving on a spacetime, in principle, can affect the background metric. The modifications to it depend on the ratio of energy of the particle and the Planck energy, known as rainbow gravity. Here we find the explicit expressions for the coordinate transformations from rainbow Minkowski spacetime to accelerated frame. The corresponding metric is also obtained which we call as rainbow-Rindler metric. So far we are aware of, no body has done it in a concrete manner. Here this is found from the first principle and hence all the parameters are properly identified. The advantage of this is that the calculated Unruh temperature is compatible with the Hawking temperature of the rainbow black hole horizon, obtained earlier. Since the accelerated frame has several importance in revealing various properties of gravity, we believe that the present result will not only fill that gap, but also help to explore different aspects of rainbow gravity paradigm.

Modified version, to appear in Int.J.Mod.Phys. A

References in corpus (10)

• Remnant for all Black Objects due to Gravity's Rainbow
• Absence of an Effective Horizon for Black Holes in Gravity's Rainbow
• Remnants of Black Rings from Gravity's Rainbow
• Geodesic Structure of the Schwarzschild Black Hole in Rainbow Gravity
• Thermodynamic instability of nonlinearly charged black holes in gravity's rainbow
• Thermodynamic phase transition in the rainbow Schwarzschild black hole
• Thermodynamic stability of modified Schwarzschild-AdS black hole in rainbow gravity
• Gravitational Collapse in Gravity's Rainbow
• Black Hole Complementarity in Gravity's Rainbow
• The kinematics of particles moving in rainbow spacetime

Cited by in corpus (2)

• Rainbow gravity corrections to the information flux of a black hole and the sparsity of Hawking radiation
• Effect of Snyder-de Sitter model on the Black hole thermodynamics in the context of rainbow gravity