Kappa vacua: enhancing the Unruh temperature

Abstract

We provide further elaboration on kappa mode, which is a mode constructed by the linear combination of Rindler modes in the right and the left Rindler wedges, exhibiting norms with opposite signs. We establish a relation among different kappa vacua, resembling the thermofield double state. However, the energy of a kappa photon no longer exhibits a linear dependence on its frequency, unless the limit of κ → 0 (the Rindler vacuum) is taken into account. In other words, a kappa vacuum can be expressed in terms of the Rindler vacuum as the conventional thermofield double state, with the usual energy for a photon. However, it features a modified Unruh temperature given by $$ {T}_{\kappa }=\frac{\mathit{\hslash a}}{2\pi c{k}_B}\kappa $$ T κ = ℏa 2 πc k B κ . Consequently, when a uniformly accelerated observer with an acceleration a is immersed in a κ-vacuum, they perceive a thermal bath. However, the temperature experienced by the observer is a modified Unruh temperature denoted as Tκ. Remarkably, the Unruh temperature can be enhanced by an arbitrary factor of κ.