Horizons and Correlation Functions in 2D Schwarzschild-de Sitter Spacetime

Anderson, Paul A.; Traschen, Jennie

doi:10.48550/arxiv.2012.08494

Cited by 4 publications

(8 citation statements)

References 30 publications

(52 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…1 For a detailed review of coordinate systems in dS, see [56]. so that the static patch metric is In either of the static patches, I or I I , the metric of the Schwarzschild de Sitter spacetime is [57].…”

Section: Preliminariesmentioning

confidence: 99%

See 1 more Smart Citation

Spacetime entanglement entropy: covariance and discreteness

2022

View full text Add to dashboard Cite

We review some recent results on Sorkin's spacetime formulation of the entanglement entropy (SSEE) for a free quantum scalar field both in the continuum and in manifold-like causal sets. The SSEE for a causal diamond in a 2d cylinder spacetime has been shown to have a Calabrese-Cardy form, while for de Sitter and Schwarzschild de Sitter horizons in dimensions d > 2, it matches the mode-wise von-Neumann entropy. In these continuum examples the SSEE is regulated by imposing a UV cut-off. Manifold-like causal sets come with a natural covariant spacetime cut-off and thus provide an arena to study regulated QFT. However, the SSEE for different manifold-like causal sets in d = 2 and d = 4 has been shown to exhibit a volume rather than an area law. The area law is recovered only when an additional UV cut-off is implemented in the scaling regime of the spectrum which mimics the continuum behaviour. We discuss the implications of these results and suggest that a volume-law may be a manifestation of the fundamental non-locality of causal sets and a sign of new UV physics.

show abstract

Section: Preliminariesmentioning

confidence: 99%

“…where κ b and κ c are the surface gravity of the black hole and the cosmological horizon respectively [57]…”

Section: Preliminariesmentioning

confidence: 99%

Spacetime entanglement entropy: covariance and discreteness

2022

View full text Add to dashboard Cite

show abstract

“…u, v ∈ (−∞, ∞) are the light-cone coordinates defined as u = t − r * and v = t + r * , where dr * = dr f (r) [14]. As in the Schwarzschild spacetime, there is a Kruskal extension beyond the black hole and the cosmological horizon, given respectively by…”

Section: Preliminariesmentioning

confidence: 99%

“…where κ b and κ c are the surface gravity of the black hole and the cosmological horizon respectively [14]…”

Section: Preliminariesmentioning

confidence: 99%

Spacetime Entanglement Entropy of de Sitter and Black Hole Horizons

Mathur,

Surya,

2021

Preprint

View full text Add to dashboard Cite

We calculate Sorkin's manifestly covariant entanglement entropy S 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 L 2 norm in the static patch implies that S is well defined for each mode. We find that S for this mixed state is independent of the effective mass of the scalar field, and matches that of [1], where, a spatial density matrix was used to calculate the horizon entanglement entropy. Using a cut-off in the angular modes we show that S ∝ Ac, where Ac is 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 L 2 norm in the static regions. Although the explicit form of the modes is not known in this case, we use the boundary conditions of [2] for a massless minimally coupled scalar field, to find the mode-wise S b,c , where b, c denote the black hole and de Sitter cosmological horizons, respectively. As in the de Sitter calculation we see that S b,c ∝ A b,c after taking a cut-off in the angular modes.

show abstract

“…This contribution is a demonstration and touchstone of the established program where the simplicity of analog gravitational systems in a flat spacetime with lower dimensions have shed light on the more complicated curved spacetime higher dimensional physics. This approach is expected to be tractable in part because in (1+1)-dimensional SdS spacetime one can analytically solve the wave equation [52,53], where there is no effective potential and so the effects of the causal structure on the initial waveforms are accentuated. Despite significant simplifications that take place in (1+1) dimensions, nontrivial quantum effects are present.…”

Section: Introductionmentioning

confidence: 99%

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

Fernández-Silvestre,

Foo,

Good

2021

Preprint

View full text Add to dashboard Cite

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.

show abstract

Horizons and Correlation Functions in 2D Schwarzschild-de Sitter Spacetime

Cited by 4 publications

References 30 publications

Spacetime entanglement entropy: covariance and discreteness

Spacetime entanglement entropy: covariance and discreteness

Spacetime Entanglement Entropy of de Sitter and Black Hole Horizons

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

Contact Info

Product

Resources

About