Relativistic quantum information as radiation reaction: entanglement entropy and self-force of a moving mirror analog to the CGHS black hole

Abstract

The CGHS black hole has a spectrum and temperature that corresponds to an accelerated reflecting boundary condition in flat spacetime. The beta coefficients are identical to a moving mirror model where the acceleration is exponential in laboratory time. The center and the event horizon of the black hole are at the same location modeled by the perfectly reflecting regularity condition that red-shifts the field modes. In addition to computing the energy flux, we find the corresponding parameter associated with the black hole mass and the cosmological constant in the gravitational analog system. Generalized to any mirror trajectory we derive the self-force (Lorentz-Abraham-Dirac) and express it and the power (Larmor) in connection with entanglement entropy, inviting an interpretation of acceleration radiation in terms of information flow. The mirror self-force and radiative power are applied to the particular CGHS black hole analog moving mirror which reveals the physics of information at the horizon during asymptotic approach to thermal equilibrium.

Light and Airy: a simple solution for relativistic quantum acceleration radiation

“…Interestingly, a divergent information measure like entanglement entropy is, at first glance, seemingly at odds with the obvious unitarity of the dynamics as seen in the Penrose diagram. However, the entanglement-rapidity formula has a subtle caveat in that it was carefully derived [17,[37][38][39][40] assuming unitarity a priori only in the cases where entropy (rapidity) achieves a constant noninfinite value in the far future. Since this is not the case for an asymptotic light speed moving mirror, the entropy as rapidity interpretation is not a good measure of unitarity [39] for such cases.…”

“…36), and time evolution of energy quanta, Eq. (37). Here κ = 1 (though Nu/κ and Eu/κ 2 have invariant forms as a function of κu).…”

“…The continuous time evolution of particle creation, Eq. (36), and time evolution of energy quanta, Eq (37)…”

Möbius Mirrors

“…We then break the invariance by referencing a static mirror on one side of the system, which amounts to a choice of a reference frame for the observer, deriving the relationship to the rapidity of the mirror (see e.g. [26,[50][51][52]).…”

Tests For Maximum Force and Maximum Power

“…Also the emission of radiation by an accelerated mirror can be investigated [69][70][71]. Inserting the limit on acceleration derived above into the expression for the emitted power P = a 2 /6πc 2 yields a value that never larger than the maximum power divided by 6π.…”