scholarly journals Correlation functions in finite temperature CFT and black hole singularities

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
D. Rodriguez-Gomez ◽  
J.G. Russo
Keyword(s):  
Black Hole ◽  
Event Horizon ◽  
Correlation Functions ◽  
Finite Temperature ◽  
Proper Time ◽  
Black Brane ◽  
Point Function ◽  
Black Hole Singularity ◽  
Point Correlation ◽  
Scaling Dimension

Abstract We compute thermal 2-point correlation functions in the black brane AdS5 background dual to 4d CFT’s at finite temperature for operators of large scaling dimension. We find a formula that matches the expected structure of the OPE. It exhibits an exponentiation property, whose origin we explain. We also compute the first correction to the two-point function due to graviton emission, which encodes the proper time from the event horizon to the black hole singularity.

scholarly journals Proper time to the black hole singularity from thermal one-point functions

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Matan Grinberg ◽  
Juan Maldacena
Keyword(s):  
Black Hole ◽  
Event Horizon ◽  
Proper Time ◽  
Expectation Values ◽  
Black Hole Singularity

Abstract We argue that the proper time from the event horizon to the black hole singularity can be extracted from the thermal expectation values of certain operators outside the horizon. This works for fields which couple to higher-curvature terms, so that they can decay into two gravitons. To extract this proper time, it is necessary to vary the mass of the field.

scholarly journals Thermal correlation functions in CFT and factorization

2021 ◽  
Vol 2021 (11) ◽  
Author(s):  
D. Rodriguez-Gomez ◽  
J. G. Russo
Keyword(s):  
Free Energy ◽  
Correlation Functions ◽  
Finite Temperature ◽  
Analytic Formula ◽  
Black Brane ◽  
Factorization Property ◽  
Point Function ◽  
Universal Formula ◽  
Thermal Correlation ◽  
Semiclassical Regime

Abstract We study 2-point and 3-point functions in CFT at finite temperature for large dimension operators using holography. The 2-point function leads to a universal formula for the holographic free energy in d dimensions in terms of the c-anomaly coefficient. By including α′ corrections to the black brane background, we reproduce the leading correction at strong coupling. In turn, 3-point functions have a very intricate structure, exhibiting a number of interesting properties. In simple cases, we find an analytic formula. When the dimensions satisfy ∆i = ∆j + ∆k, the thermal 3-point function satisfies a factorization property. We argue that in d > 2 factorization is a reflection of the semiclassical regime.

scholarly journals Holographic thermal correlators revisited

2021 ◽  
Vol 2021 (11) ◽  
Author(s):  
Hare Krishna ◽  
D. Rodriguez-Gomez
Keyword(s):  
Black Hole ◽  
Leading Order ◽  
Point Function ◽  
Position Space ◽  
Conformal Dimension ◽  
General Contraction ◽  
Neutral Operator ◽  
Point Correlation ◽  
Leading Term ◽  
Geodesic Approximation

Abstract We study 2-point correlation functions for scalar operators in position space through holography including bulk cubic couplings as well as higher curvature couplings to the square of the Weyl tensor. We focus on scalar operators with large conformal dimensions. This allows us to use the geodesic approximation for propagators. In addition to the leading order contribution, captured by geodesics anchored at the insertion points of the operators on the boundary and probing the bulk geometry thoroughly studied in the literature, the first correction is given by a Witten diagram involving both the bulk cubic coupling and the higher curvature couplings. As a result, this correction is proportional to the VEV of a neutral operator Ok and thus probes the interior of the black hole exactly as in the case studied by Grinberg and Maldacena [13]. The form of the correction matches the general expectations in CFT and allows to identify the contributions of TnOk (being Tn the general contraction of n energy-momentum tensors) to the 2-point function. This correction is actually the leading term for off-diagonal correlators (i.e. correlators for operators of different conformal dimension), which can then be computed holographically in this way.

scholarly journals Effective GUP-modified Raychaudhuri equation and black hole singularity: four models

2021 ◽  
Vol 2021 (9) ◽  
Author(s):  
Keagan Blanchette ◽  
Saurya Das ◽  
Saeed Rastgoo
Keyword(s):  
Black Hole ◽  
Proper Time ◽  
Generalized Uncertainty Principle ◽  
Rate Of Change ◽  
Conjugate Points ◽  
Raychaudhuri Equation ◽  
Schwarzschild Black Hole ◽  
Effective Dynamics ◽  
Singularity Theorems ◽  
Black Hole Singularity

Abstract The classical Raychaudhuri equation predicts the formation of conjugate points for a congruence of geodesics, in a finite proper time. This in conjunction with the Hawking-Penrose singularity theorems predicts the incompleteness of geodesics and thereby the singular nature of practically all spacetimes. We compute the generic corrections to the Raychaudhuri equation in the interior of a Schwarzschild black hole, arising from modifications to the algebra inspired by the generalized uncertainty principle (GUP) theories. Then we study four specific models of GUP, compute their effective dynamics as well as their expansion and its rate of change using the Raychaudhuri equation. We show that the modification from GUP in two of these models, where such modifications are dependent of the configuration variables, lead to finite Kretchmann scalar, expansion and its rate, hence implying the resolution of the singularity. However, the other two models for which the modifications depend on the momenta still retain their singularities even in the effective regime.

scholarly journals SCHRÖDINGER INVARIANCE IN DISCRETE STOCHASTIC SYSTEMS

1994 ◽  
Vol 08 (25n26) ◽  
pp. 3487-3499 ◽  
Author(s):  
MALTE HENKEL ◽  
GUNTER SCHÜTZ
Keyword(s):  
Stationary State ◽  
Stochastic Models ◽  
Correlation Functions ◽  
Scale Invariance ◽  
Stochastic Systems ◽  
Lattice Models ◽  
Local Scale ◽  
Point Function ◽  
Point Correlation ◽  
Schrödinger Algebra

Local scale invariance for lattice models is studied using new realizations of the Schrödinger algebra. The two-point function is calculated and it turns out that the result can be reproduced from exact two-point correlation functions evaluated in the stationary state of several simple stochastic models.

Can matter really cross a horizon?

2014 ◽  
Vol 23 (12) ◽  
pp. 1442021
Author(s):  
Huiquan Li
Keyword(s):  
Field Theory ◽  
Black Hole ◽  
Event Horizon ◽  
Test Particle ◽  
Tachyon Condensation ◽  
Proper Time ◽  
Free Particle ◽  
Condensation Process ◽  
Tachyon Field ◽  
Rindler Space

It has been taken as a truth that collapsing matter can eventually cross the horizon and enter into the interior of a black hole in a finite proper time. However, the Rindler/tachyon dual description we suggested recently implies that this should not be the case. A test particle falling towards the event horizon of a nonextreme black hole can actually be viewed as an unstable particle, whose dynamics is described by the tachyon field theory. This means that the collapsing process of a free particle in Rindler space is essentially a tachyon condensation process. In terms of the results in tachyon condensation, we learn that the infalling particle should strongly couple to bulk gravitational modes and should decay completely into something like gravitons before reaching the horizon. Hence, there should be no matter that can cross a horizon as still matter. The matter will get "dissolved" into spacetime when approaching the horizon.

Classical and quantum equations of motion of a 4-dimensional Schwarzschild–AdS and Reissner–Nordström–AdS black hole

2019 ◽  
Vol 28 (04) ◽  
pp. 1950061
Author(s):  
Eric Greenwood
Keyword(s):  
Black Hole ◽  
Wave Function ◽  
Domain Wall ◽  
Event Horizon ◽  
Particle Production ◽  
Proper Time ◽  
Oscillatory Solution ◽  
Finite Amount ◽  
Classical Singularity ◽  
Asymptotic Observer

We investigate the gravitational collapse of both a massive (Schwarzschild–AdS) and a massive-charged (Reissner–Nordström–AdS) 4-dimensional domain wall in AdS space. Here, we consider both the classical and quantum collapse, in the absence of quasi-particle production and backreaction. For the massive case, we show that, as far as the asymptotic observer is concerned, the collapse takes an infinite amount of time to occur in both the classical and quantum cases. Hence, quantizing the domain wall does not lead to the formation of the black hole in a finite amount of time. For the infalling observer, we find that the domain wall collapses to both the event horizon and the classical singularity in a finite amount of proper time. In the region of the classical singularity, however, the wave function exhibits both nonlocal and nonsingular effects. For the massive-charged case, we show that, as far as the asymptotic observer is concerned, the details of the collapse depend on the amount of charge present; that is, the extremal, nonextremal and overcharged cases. In the overcharged case, the collapse never fully occurs since the solution is an oscillatory solution which prevents the formation of a naked singularity. For the extremal and nonextremal cases, it takes an infinite amount of time for the outer horizon to form. For the infalling observer in the nonextremal case, we find that the domain wall collapses to both the event horizon and the classical singularity in a finite amount of proper time. In the region of the classical singularity, the wave function also exhibits both nonlocal and nonsingular effects. Furthermore, in the large energy density limit, the wave function vanishes as the domain wall approaches classical singularity implying that the quantization does not rid the black hole of its singular nature.

scholarly journals No Way Back: Maximizing Survival Time Below the Schwarzschild Event Horizon

2007 ◽  
Vol 24 (2) ◽  
pp. 46-52 ◽  
Author(s):  
Geraint F. Lewis ◽  
Juliana Kwan
Keyword(s):  
Black Holes ◽  
General Relativity ◽  
Black Hole ◽  
Survival Time ◽  
Event Horizon ◽  
Proper Time ◽  
Teaching Tool ◽  
Maximum Value ◽  
Central Singularity ◽  
Remaining Time

AbstractIt has long been known that once you cross the event horizon of a black hole, your destiny lies at the central singularity, irrespective of what you do. Furthermore, your demise will occur in a finite amount of proper time. In this paper, the use of rockets in extending the amount of time before the collision with the central singularity is examined. In general, the use of such rockets can increase your remaining time, but only up to a maximum value; this is at odds with the ‘more you struggle, the less time you have' statement that is sometimes discussed in relation to black holes. The derived equations are simple to solve numerically and the framework can be employed as a teaching tool for general relativity.

scholarly journals AdS3/CFT2 CORRESPONDENCE AT FINITE TEMPERATURE

1999 ◽  
Vol 14 (31) ◽  
pp. 2157-2168 ◽  
Author(s):  
L. CHEKHOV
Keyword(s):  
Black Hole ◽  
Correlation Functions ◽  
Finite Temperature ◽  
Solid Torus ◽  
Btz Black Hole ◽  
Black Hole Solutions

The AdS/CFT correspondence is established for the AdS3 space compactified on a solid torus with the CFT field on the boundary. Correlation functions that correspond to the bulk theory at finite temperature are obtained in the regularization a la Gubser, Klebanov, and Polyakov. The BTZ black hole solutions in AdS3 are T-dual to the solution in the AdS3 space without singularity.

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