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

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.

Late Time Acceleration of the Universe from Quantum Gravity

We show that the accelerating expansion phase of the universe can emerge from the group field theory formalism, a candidate theory of quantum gravity. The cosmological evolution can be extracted from condensate states using mean field approximation, in a form of modified FLRW equations. By introducing an effective equation of state w, we can reveal the relevant features of the evolution, and show that with proper choice of parameters, w will approach to −1, corresponds to the behaviour of cosmological constant, results in a late time acceleration and leads to de Sitter spacetime asymptotically.

Nonequilibrium Black Hole Thermodynamics in Anti-de Sitter Spacetime

This work discusses the black hole thermodynamics in a weak dynamical Anti-de Sitter spacetime, which should be described by the nonequilibrium thermodynamics, because the metric depends on the time coordinate. Taking the Vaidya-Anti-de Sitter black hole spacetime as an example, the local entropy balance equations and principle of minimum entropy generation are derived, and finally, some irreversible effects in nonequilibrium thermodynamics are studied by using the Onsager reciprocal relation.

Spacetime Entanglement Entropy of de Sitter and Black Hole Horizons

We calculate Sorkin's manifestly covariant, spacetime entanglement entropy (SSEE) for a massive and massless minimally coupled free Gaussian scalar field for the de Sitter horizon and Schwarzschild de Sitter horizons, respectively, in d > 2. In de Sitter spacetime we restrict the Bunch-Davies vacuum in the conformal patch to the static patch to obtain a mixed state. The finiteness of the spatial L2 norm in the static patch implies that the SSEE is well defined for each mode. We find that for this mixed state it is independent of the effective mass of the scalar field and matches results obtained by Higuchi and Yamamoto, where, a spatial density matrix was used to calculate the horizon entanglement entropy. Using a cut-off in the angular modes we show that the SSEE is proportional to the area of the de Sitter cosmological horizon. Our analysis can be carried over to the black hole and cosmological horizon in Schwarzschild de Sitter spacetime, which also has finite spatial L2 norm in the static regions. Although the explicit form of the modes is not known in this case, we use appropriate boundary conditions for a massless minimally coupled scalar field, to find the mode-wise SSEE for both the black hole and de Sitter cosmological horizons. As in the de Sitter calculation we see that SSEE is proportional to the horizon area in each case after taking a cut-off in the angular modes.

AdS one-loop partition functions from bulk and edge characters

We show that the one-loop partition function of any higher spin field in (d + 1)-dimensional Anti-de Sitter spacetime can be expressed as an integral transform of an SO(2, d) bulk character and an SO(2, d − 2) edge character. We apply this character integral formula to various higher-spin Vasiliev gravities and find miraculous (almost) cancellations between bulk and edge characters that lead to agreement with the predictions of HS/CFT holography. We also discuss the relation between the character integral representation and the Rindler-AdS thermal partition function.

Complexity of scalar collapse in anti-de Sitter spacetime

We calculate the volume and action forms of holographic complexity for the gravitational collapse of scalar field matter in asymptotically anti-de Sitter spacetime, using numerical methods to reproduce the geometry responding to the oscillating field over multiple crossing times. Like the scalar field pulse, the volume complexity oscillates quasiperiodically before horizon formation. It also shows a scaling symmetry with the amplitude of the scalar field. The action complexity is also quasiperiodic with spikes of increasing amplitude.

A classification of conformally flat generalized Ricci recurrent pseudo-Riemannian manifolds

Conformally flat pseudo-Riemannian manifolds with generalized Ricci recurrent, [Formula: see text] structure are completely classified in this short report. A conformally flat generalized Ricci recurrent pseudo-Riemannian manifold is shown to be an Einstein manifold. In particular, a conformally flat generalized Ricci recurrent spacetime must be either a de Sitter spacetime or an anti-de Sitter spacetime.