scholarly journals Spacetime Entanglement Entropy of de Sitter and Black Hole Horizons

2021 ◽  
Author(s):  
Abhishek Mathur ◽  
Sumati Surya ◽  
Nomaan X
Keyword(s):  
Black Hole ◽  
Scalar Field ◽  
Density Matrix ◽  
Mixed State ◽  
Entanglement Entropy ◽  
Spatial Density ◽  
De Sitter Spacetime ◽  
Cosmological Horizon ◽  
De Sitter ◽  
Sitter Spacetime

Abstract 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.

scholarly journals An exact black hole spacetime with scalar field and its shadow together with quasinormal modes

2020 ◽  
Vol 35 (31) ◽  
pp. 2050256 ◽  
Author(s):  
Shuang Yu ◽  
Changjun Gao
Keyword(s):  
Black Hole ◽  
Scalar Field ◽  
Black Hole Solution ◽  
Quasinormal Modes ◽  
The Other ◽  
De Sitter Spacetime ◽  
De Sitter ◽  
First Law Of Thermodynamics ◽  
Sitter Spacetime ◽  
Black Hole Spacetime

We find an exact black hole solution with a minimally coupled scalar field. The corresponding spacetime has two horizons and one of them is the black hole event horizon and the other is the cosmic horizon. In this sense, the solution is analogous to the Schwarzschild-de Sitter (or anti-de Sitter) spacetime. We investigate the thermodynamics and construct the first law of thermodynamics. At the same time, we make a study on the shadow and quasinormal modes of this black hole solution.

scholarly journals Wavefunctions in dS/CFT revisited: principal series and double-trace deformations

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Hiroshi Isono ◽  
Hoiki Madison Liu ◽  
Toshifumi Noumi
Keyword(s):  
Principal Series ◽  
Light Fields ◽  
Quadratic Term ◽  
De Sitter Spacetime ◽  
Cosmological Horizon ◽  
De Sitter ◽  
Complementary Series ◽  
Point Function ◽  
Sitter Spacetime ◽  
Simple Scaling

Abstract We study wavefunctions of heavy scalars on de Sitter spacetime and their implications to dS/CFT correspondence. In contrast to light fields in the complementary series, heavy fields in the principal series oscillate outside the cosmological horizon. As a consequence, the quadratic term in the wavefunction does not follow a simple scaling and so it is hard to identify it with a conformal two-point function. In this paper, we demonstrate that it should be interpreted as a two-point function on a cyclic RG flow which is obtained by double-trace deformations of the dual CFT. This is analogous to the situation in nonrelativistic AdS/CFT with a bulk scalar whose mass squared is below the Breitenlohner-Freedman (BF) bound. We also provide a new dS/CFT dictionary relating de Sitter two-point functions and conformal two-point functions in the would-be dual CFT.

scholarly journals Graviton two-point function in 3 + 1 static de Sitter spacetime

2016 ◽  
Vol 25 (09) ◽  
pp. 1641016 ◽  
Author(s):  
Rafael P. Bernar ◽  
Luís C. B. Crispino ◽  
Atsushi Higuchi
Keyword(s):  
Vacuum State ◽  
De Sitter Spacetime ◽  
Cosmological Horizon ◽  
De Sitter ◽  
Point Function ◽  
Gauge Invariant ◽  
Gravitational Perturbations ◽  
Time Translation ◽  
Sitter Spacetime ◽  
Arbitrary Dimensions

In [R. P. Bernar, L. C. B. Crispino and A. Higuchi, Phys. Rev. D 90 (2014) 024045.] we investigated gravitational perturbations in the background of de Sitter spacetime in arbitrary dimensions. More specifically, we used a gauge-invariant formalism to describe the perturbations inside the cosmological horizon, i.e. in the static patch of de Sitter spacetime. After a gauge-fixed quantization procedure, the two-point function in the Bunch–Davies-like vacuum state was shown to be infrared finite and invariant under time-translation. In this work, we give details of the calculations to obtain the graviton two-point function in 3 + 1 dimensions.

scholarly journals NONSTATIC CHARGED BTZ-LIKE BLACK HOLES IN N+1 DIMENSIONS

2012 ◽  
Vol 21 (03) ◽  
pp. 1250022 ◽  
Author(s):  
SUSHANT G. GHOSH
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Gravitational Collapse ◽  
Naked Singularity ◽  
De Sitter Spacetime ◽  
De Sitter ◽  
Btz Black Hole ◽  
Sitter Spacetime ◽  
Apparent Horizons ◽  
Sitter Background

We find an exact nonstatic charged BTZ-like solutions, in (N+1)-dimensional Einstein gravity in the presence of negative cosmological constant and a nonlinear Maxwell field defined by a power s of the Maxwell invariant, which describes the gravitational collapse of charged null fluid in an anti-de Sitter background. Considering the situation that a charged null fluid injects into the initially an anti-de Sitter spacetime, we show that a black hole form rather than a naked singularity, irrespective of spacetime dimensions, from gravitational collapse in accordance with cosmic censorship conjecture. The structure and locations of the apparent horizons of the black holes are also determined. It is interesting to see that, in the static limit and when N = 2, one can retrieve 2+1 BTZ black hole solutions.

scholarly journals SPECTRA OF BLACK HOLE IN DE SITTER SPACETIME WITH HIGHLY DAMPED QUASINORMAL MODES: HIGH OVERTONE CASE

2012 ◽  
Vol 27 (23) ◽  
pp. 1250123 ◽  
Author(s):  
MOLIN LIU ◽  
XUEHUI HU ◽  
JUNWANG LU ◽  
JIANBO LU
Keyword(s):  
Black Hole ◽  
Quasinormal Modes ◽  
De Sitter Spacetime ◽  
De Sitter ◽  
Flat Spacetime ◽  
Sitter Spacetime ◽  
Spacetime Structure ◽  
Electrically Charged ◽  
High Overtone ◽  
Charged Case

Motivated by recent physical interpretation on quasinormal modes presented by Maggiore [Phys. Rev. Lett. 100, 141301 (2008)], the adiabatic quantity method given by Kunstatter [Phys. Rev. Lett. 90, 161301 (2003)] is used to calculate the spectrums of a non-extremal Schwarzschild de Sitter black hole in this paper, as well as electrically charged case. According to highly damped Konoplya and Zhidenko's numerical observational results for high overtone modes [JHEP 06, 037 (2004)], we found that the asymptotic non-flat spacetime structure leads to two interesting facts: (i) near inner event horizon, the area and entropy spectrums, which are given by Aen= 8 n1πℏ, Sen= 2πn1ℏ, are equally spaced accurately. (ii) However, near outer cosmological horizon the spectrums, which are in the form of [Formula: see text], are not markedly equidistant. Finally, we also discuss the electrically charged case and find that the black holes in de Sitter spacetime have similar quantization behavior no matter with or without charge.

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