2020
DOI: 10.48550/arxiv.2012.08494
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Horizons and Correlation Functions in 2D Schwarzschild-de Sitter Spacetime

Abstract: The two-point correlation function, and the two point function for the field velocities, are computed for a massless minimally coupled scalar field in 2D Schwarzschild-de Sitter spacetime when the field is in the Unruh state. It is found that the field correlations grow linearly in terms of a particular time coordinate that is good throughout the spacetime, and that the rate of growth is equal to the sum of the black hole plus cosmological surface gravities. This time dependence of the two-point function resul… Show more

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Cited by 4 publications
(8 citation statements)
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References 30 publications
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“…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
“…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%
“…where κ b and κ c are the surface gravity of the black hole and the cosmological horizon respectively [57]…”
Section: Preliminariesmentioning
confidence: 99%
“…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%
“…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%