On the duality of Schwarzschild–de Sitter spacetime and moving mirror

Abstract

The Schwarzschild-de Sitter (SdS) metric is the simplest spacetime solution in general relativity with both a black hole event horizon and a cosmological event horizon. Since the Schwarzschild metric is the most simple solution of Einstein's equations with spherical symmetry and the de Sitter metric is the most simple solution of Einstein's equations with a positive cosmological constant, the combination in the SdS metric defines an appropriate background geometry for semi-classical investigation of Hawking radiation with respect to past and future horizons. Generally, the black hole temperature is larger than that of the cosmological horizon, so there is heat flow from the smaller black hole horizon to the larger cosmological horizon, despite questions concerning the definition of the relative temperature of the black hole without a measurement by an observer sitting in an asymptotically flat spacetime. Here we investigate the accelerating boundary correspondence (ABC) of the radiation in SdS spacetime without such a problem. We have solved for the boundary dynamics, energy flux and asymptotic particle spectrum. The distribution of particles is globally non-thermal while asymptotically the radiation reaches equilibrium.

Upon the horizon’s verge: Thermal particle creation between and approaching horizons

“…As we shall see, the non-equilibrium transition between thermal states is full of new information, as highlighted by the confluent hypergeometric function in equation (21). Likewise, spectral variations on the characteristic transition between thermal states will also be present between horizons, as illustrated in the following section.…”

“…Finally, we can extend the solution of ABC with Schwarzschild-de Sitter spacetime as given in [21] (which approximates by neglecting the third term) to include the full solution with all three terms present. The approximated Bogoliubov coefficient considering only two terms involves the confluent hypergeometric function of one variable.…”

“…which corresponds to the high frequency limit, as seen by an inertial observer at infinity. Let us now write the function that parameterizes the analog Schwarzschild-de Sitter mirror trajectory as [21] f…”

Möbius mirrors

“…Using this, we can explore the relation between mirrors, and hence spacetimes, with identical flux, such as thermal emission from de Sitter space [26,27] and the Carlitz-Willey (CW) [28] mirror, investigate cases with merely asymptotically identical flux, and probe the zero energy, but nonzero particle, production of uniformly accelerating motion, whose asymptotic dynamics corresponds to extremal black holes [6,[29][30][31][32].…”

Unruh quantum Otto engine in the presence of a reflecting boundary

“…Accelerating mirrors can be considered as an analogue of the dynamical Casimir effect in (1+1) dimensions [34,35], a prototype for black hole evaporation [36][37][38][39][40]. It has been observed that there is a strong connection between accelerating mirrors and black hole physics [41][42][43][44].…”