Horizons and correlation functions in 2D Schwarzschild-de Sitter spacetime

Anderson, Paul R.; Traschen, Jennie

doi:10.1007/jhep01(2022)192

“…In [9], it was shown that for a massless minimally coupled scalar field in a 2D spacetime with a static patch and one or two horizons, the symmetric two-point function grows linearly in time at late times when the time points are equal and the space points are separated and held fixed. We have shown that this occurs only for the first formulation of the Unruh state (3.2), where the p b ω modes are directly used to compute the two-point function.…”

Section: Discussionmentioning

confidence: 99%

“…It is useful to compute the surface gravities at each of these zeros of f . If we define them to be positive definite then the results are [9]…”

Section: 42)mentioning

confidence: 99%

“…In [9] it was shown that for a massless minimally coupled scalar field in a 2D spacetime with a static region and either a black hole horizon, a cosmological horizon, or both, then there is linear growth in G (1) (x, x ) in terms of a time coordinate T that is well-behaved on the future horizon(s) if the field is in the Unruh vacuum state and the points are split in the radial direction. In this section we first review that work and then show that the result implies that, in this case, the two formulations of the Unruh state given in [1] (see also [10])…”

Section: Two-point Functionmentioning

confidence: 99%

“…For a massless minimally coupled scalar field in a static 2D black hole spacetime, it was shown in [9] that the symmetric two-point function grows linearly in time when the points are split in the radial direction for a time coordinate that is regular on the future horizon and is regular on future null infinity for an asymptotically flat spacetime or the future cosmological horizon for SdS. In [1], two different formulations of the Unruh state were given along with the statement that the vacuum states for the two formulations are equivalent (see also [10]).…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Infrared Effects and the Unruh State

Anderson¹,

Siahmazgi²,

Scofield³

2022

Preprint

0

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Detailed behaviors of the modes of quantized scalar fields in the Unruh state for various eternal black holes in two dimensions are investigated. It is shown that the late time behaviors of some of the modes of the quantum fields and of the symmetric two-point function are determined by infrared effects. The nature of these effects depends upon whether there is an effective potential in the mode equation and what form this potential takes. Here, three cases are considered, one with no potential and two with potentials that are nonnegative everywhere and are zero on the event horizon of the black hole and zero at either infinity or the cosmological horizon. Specifically, the potentials are a delta function potential and the potential that occurs for a massive scalar field in Schwarzschild-de Sitter spacetime. In both cases, scattering effects remove infrared divergences in the mode functions that would otherwise arise from the normalization process. When such infrared divergences are removed, it is found that the modes that are positive frequency with respect to the Kruskal time on the past black hole horizon approach zero in the limit that the radial coordinate is fixed and the time coordinate goes to infinity. In contrast, when there is no potential and thus infrared divergences occur, the same modes approach nonzero constant values in the late time limit when the radial coordinate is held fixed. The behavior of the symmetric two-point function when the field is in the Unruh state is investigated for the case of a delta function potential in certain asymptotically flat black hole spacetimes in two dimensions. The removal of the infrared divergences in the mode functions results in the elimination of terms that grow linearly in time.

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“…For a massless minimally coupled scalar field in a spacetime with a 2D general static black hole metric, it was shown in [9] that the symmetric two-point function grows linearly in time when the points are split in the radial direction for a time coordinate that is regular on the future horizon and is regular on future null infinity for an asymptotically flat spacetime or the future cosmological horizon for SdS. In [4], two different formulations of the Unruh state were given along with the statement that the vacuum states for the two formulations are equivalent (see also [10]).…”

Section: Introductionmentioning

confidence: 99%

Infrared effects and the Unruh state

Anderson

¹

,

Siahmazgi

²

,

Scofield

³

2023

Class. Quantum Grav.

0

View full text Add to dashboard Cite

Detailed behaviors of the modes of quantized scalar fields in the Unruh state for various eternal black holes in two dimensions are investigated. It is shown that the late time behaviors of some of the modes of the quantum fields and of the symmetric two-point function are determined by infrared effects. The nature of these effects depends upon whether there is an effective potential in the mode equation and what form this potential takes. Here, three cases are considered, one with no potential and two with potentials that are nonnegative everywhere and are zero on the event horizon of the black hole and zero at either infinity or the cosmological horizon. Specifically, the potentials are a delta function potential and the potential that occurs for a massive scalar field in Schwarzschild-de Sitter spacetime. In both cases, scattering effects remove infrared divergences in the mode functions that would otherwise arise from the normalization process. When such infrared divergences are removed, it is found that the modes that are positive frequency with respect to the Kruskal time on the past black hole horizon approach zero in the limit that the radial coordinate is fixed and the time coordinate goes to infinity. In contrast, when there is no potential and thus infrared divergences occur, the same modes approach nonzero constant values in the late time limit when the radial coordinate is held fixed. The behavior of the symmetric two-point function when the field is in the Unruh state is investigated for the case of a delta function potential in certain asymptotically flat black hole spacetimes in two dimensions. The removal of the infrared divergences in the mode functions results in the elimination of terms that grow linearly in time.

show abstract

Black hole evaporation in de Sitter space

Gregory

¹

,

Moss

²

,

Oshita

³

et al. 2021

Class. Quantum Grav.

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We investigate the evaporation process of a Kerr–de Sitter black hole with the Unruh–Hawking-like vacuum state, which is a realistic vacuum state modelling the evaporation process of a black hole originating from gravitational collapse. We also compute the greybody factors for gravitons, photons, and conformal-coupling massless scalar particles by using the analytic solutions of the Teukolsky equation in the Kerr–de Sitter background. It turns out that the cosmological constant quenches the amplification factor and it approaches to zero towards the critical point where the Nariai and extremal limits merge together. We confirm that even near the critical point, the superradiance of gravitons is more significant than that of photons and scalar particles. Angular momentum is carried out by particles several times faster than the mass energy decreases. This means that a Kerr–de Sitter black hole rapidly spins down to a nearly Schwarzschild–de Sitter black hole before it completely evaporates. We also compute the time evolution of the Bekenstein–Hawking entropy. The total entropy of the Kerr–de Sitter black hole and cosmological horizon increases with time, which is consistent with the generalized second law of thermodynamics.

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Horizons and correlation functions in 2D Schwarzschild-de Sitter spacetime

Cited by 6 publications

References 33 publications

Infrared Effects and the Unruh State

Infrared Effects and the Unruh State

Infrared effects and the Unruh state

Black hole evaporation in de Sitter space

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