scholarly journals Reparameterization dependence is useful for holographic complexity

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Ayoub Mounim ◽  
Wolfgang Mück
Keyword(s):  
Black Hole ◽  
Critical Time ◽  
De Sitter Space ◽  
Time Interval ◽  
De Sitter ◽  
Schwarzschild Black Hole ◽  
Static Vacuum ◽  
Reparameterization Invariance ◽  
Negative Time

Abstract Holographic complexity in the “complexity equals action” approach is reconsidered relaxing the requirement of reparameterization invariance of the action with the prescription that the action vanish in any static, vacuum causal diamond. This implies that vacuum anti-de Sitter space plays the role of the reference state. Moreover, the complexity of an anti-de Sitter-Schwarzschild black hole becomes intrinsically finite and saturates Lloyd’s bound after a critical time. It is also argued that several artifacts, such as the unphysical negative-time interval, can be removed by truly considering the bulk dual of the thermofield double state.

scholarly journals The price of curiosity: information recovery in de Sitter space

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Lars Aalsma ◽  
Watse Sybesma
Keyword(s):  
Black Hole ◽  
Thermal Equilibrium ◽  
De Sitter Space ◽  
Cosmological Horizon ◽  
De Sitter ◽  
Information Recovery ◽  
Fine Grained ◽  
Black Hole Radiation ◽  
Entropy Of Black Hole

Abstract Recent works have revealed that quantum extremal islands can contribute to the fine-grained entropy of black hole radiation reproducing the unitary Page curve. In this paper, we use these results to assess if an observer in de Sitter space can decode information hidden behind their cosmological horizon. By computing the fine-grained entropy of the Gibbons-Hawking radiation in a region where gravity is weak we find that this is possible, but the observer’s curiosity comes at a price. At the same time the island appears, which happens much earlier than the Page time, a singularity forms which the observer will eventually hit. We arrive at this conclusion by studying de Sitter space in Jackiw-Teitelboim gravity. We emphasize the role of the observer collecting radiation, breaking the thermal equilibrium studied so far in the literature. By analytically solving for the backreacted geometry we show how an island appears in this out-of-equilibrium state.

GRAVITATIONAL THERMODYNAMICS AND THE WHEELER–DEWITT EQUATION

2011 ◽  
Vol 20 (01) ◽  
pp. 23-42 ◽  
Author(s):  
M. D. POLLOCK
Keyword(s):  
Black Hole ◽  
Wave Function ◽  
Boundary Conditions ◽  
Cosmological Constant ◽  
Apparent Horizon ◽  
De Sitter Space ◽  
Hawking Temperature ◽  
De Sitter ◽  
Schwarzschild Black Hole ◽  
Gravitational Thermodynamics

In a previous paper, we have derived the Hawking temperature T H = 1/8πM for a Schwarzschild black hole of mass M, starting from the Wheeler–DeWitt for the wave function Ψ on the apparent horizon, due to Tomimatsu. Here we discuss the derivation of this result in greater detail, with particular regard to the Euclideanization procedure involved and the boundary conditions on the horizon. Further, analysis of the de Sitter space-time generated by a cosmological constant Λ yields the temperature [Formula: see text] found by Gibbons and Hawking, which thus vindicates the method. The emission of radiation occurs with preservation of unitarity, and hence entropy, which is substantiated by a global thermodynamical argument in the case of the black hole.

Noncommutative scalar field in de Sitter space–time and pair creation process

2021 ◽  
Vol 36 (02) ◽  
pp. 2150011
Author(s):  
Nabil Mehdaoui ◽  
Lamine Khodja ◽  
Salah Haouat
Keyword(s):  
Scalar Field ◽  
Chemical Potential ◽  
De Sitter Space ◽  
Space Time ◽  
Pair Creation ◽  
De Sitter ◽  
Creation Process ◽  
Scalar Particles ◽  
Constant Electromagnetic Field

In this work, we address the process of pair creation of scalar particles in [Formula: see text] de Sitter space–time in presence of a constant electromagnetic field by applying the noncommutativity on the scalar field up to first-order in [Formula: see text]. We calculate the density of particles created in the vacuum by the mean of the Bogoliubov transformations. In contrast to a previous result, we show that noncommutativity contributes to the pair creation process. We find that the noncommutativity plays the same role of chemical potential and gives an important interest for studies at high energies.

Kantowski-Sachs Cosmology, Weyl Geometry and Asymptotic Safety in Quantum Gravity

2020 ◽  
Author(s):  
Carlos Castro Perelman
Keyword(s):  
Black Hole ◽  
Planck Scale ◽  
Dilaton Gravity ◽  
De Sitter ◽  
Schwarzschild Black Hole ◽  
Exterior Region ◽  
Asymptotic Safety ◽  
Sign Change ◽  
Average Action ◽  
Black Hole Interior

A brief review of the essentials of Asymptotic Safety and the Renormalization Group (RG) improvement of the Schwarzschild Black Hole that removes the r = 0 singularity is presented. It is followed with a RG-improvement of the Kantowski-Sachs metric associated with a Schwarzschild black hole interior and such that there is no singularity at t = 0 due to the running Newtonian coupling G(t) (vanishing at t = 0). Two temporal horizons at t _- \simeq t_P and t_+ \simeq t_H are found. For times below the Planck scale t < t_P, and above the Hubble time t > t_H, the components of the Kantowski-Sachs metric exhibit a key sign change, so the roles of the spatial z and temporal t coordinates are exchanged, and one recovers a repulsive inflationary de Sitter-like core around z = 0, and a Schwarzschild-like metric in the exterior region z > R_H = 2G_o M. The inclusion of a running cosmological constant \Lambda (t) follows. We proceed with the study of a dilaton-gravity (scalar-tensor theory) system within the context of Weyl's geometry that permits to single out the expression for the classical potential V (\phi ) = \kappa\phi^4, instead of being introduced by hand, and find a family of metric solutions which are conformally equivalent to the (Anti) de Sitter metric. To conclude, an ansatz for the truncated effective average action of ordinary dilaton-gravity in Riemannian geometry is introduced, and a RG-improved Cosmology based on the Friedmann-Lemaitre-Robertson-Walker (FLRW) metric is explored.

scholarly journals QUASI-NORMAL MODES OF SCHWARZSCHILD–ANTI-DE SITTER BLACK HOLES: ELECTROMAGNETIC AND GRAVITATIONAL PERTURBATIONS

2002 ◽  
Vol 17 (20) ◽  
pp. 2752-2752
Author(s):  
VITOR CARDOSO ◽  
JOSÉ P. S. LEMOS
Keyword(s):  
Black Hole ◽  
Imaginary Part ◽  
Normal Modes ◽  
De Sitter ◽  
Schwarzschild Black Hole ◽  
Small Black Hole ◽  
Conformal Field ◽  
Gravitational Perturbations ◽  
Ads Spacetime ◽  
Electromagnetic Perturbation

We studied the quasi-normal modes (QNM) of electromagnetic and gravitational perturbations of a Schwarzschild black hole in an asymptotically anti-de Sitter (AdS) spacetime, extending previous works1,2 on the subject. Some of the electromagnetic modes do not oscillate, they only decay, since they have pure imaginary frequencies. The gravitational modes show peculiar features: the odd and even gravitational perturbations no longer have the same characteristic quasinormal frequencies. There is a special mode for odd perturbations whose behavior differs completely from the usual one in scalar1 and electromagnetic perturbation in an AdS spacetime, but has a similar behavior to the Schwarzschild black hole3 in an asymptotically flat spacetime: the imaginary part of the frequency goes as [Formula: see text], where r+ is the horizon radius. We also investigated the small black hole limit showing that the imaginary part of the frequency goes as [Formula: see text]. These results are important to the AdS/CFT4 conjecture since according to it the QNMs describe the approach to equilibrium in the conformal field theory. For other geometries see5,6.

scholarly journals VOROS PRODUCT AND NONCOMMUTATIVE INSPIRED BLACK HOLES

2013 ◽  
Vol 28 (09) ◽  
pp. 1350030
Author(s):  
SUNANDAN GANGOPADHYAY
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Extremal Point ◽  
De Sitter ◽  
Schwarzschild Black Hole ◽  
Standard Identity ◽  
Schwarzschild Geometry ◽  
Area Law

We emphasize the importance of the Voros product in defining the noncommutative (NC) inspired black holes. The computation of entropy for both the noncommutative inspired Schwarzschild and Reissner–Nordström (RN) black holes show that the area law holds up to order [Formula: see text]. The leading correction to the entropy (computed in the tunneling formalism) is shown to be logarithmic. The Komar energy E for these black holes is then obtained and a deviation from the standard identity E = 2STH is found at the order [Formula: see text]. This deviation leads to a nonvanishing Komar energy at the extremal point TH = 0 of these black holes. The Smarr formula is finally worked out for the NC Schwarzschild black hole. Similar features also exist for a de Sitter–Schwarzschild geometry.

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