scholarly journals Harvesting correlations in Schwarzschild and collapsing shell spacetimes

2020 ◽  
Vol 2020 (8) ◽  
Author(s):  
Erickson Tjoa ◽  
Robert B. Mann
Keyword(s):  
Black Hole ◽  
Scalar Field ◽  
Proper Time ◽  
Time Derivative ◽  
Vacuum State ◽  
Massless Scalar ◽  
Late Time ◽  
Massless Scalar Field ◽  
Schwarzschild Black Hole ◽  
Black Hole Spacetime

Abstract We study the harvesting of correlations by two Unruh-DeWitt static detectors from the vacuum state of a massless scalar field in a background Vaidya spacetime consisting of a collapsing null shell that forms a Schwarzschild black hole (hereafter Vaidya spacetime for brevity), and we compare the results with those associated with the three preferred vacua (Boulware, Unruh, Hartle-Hawking-Israel vacua) of the eternal Schwarzschild black hole spacetime. To do this we make use of the explicit Wightman functions for a massless scalar field available in (1+1)-dimensional models of the collapsing spacetime and Schwarzschild spacetimes, and the detectors couple to the proper time derivative of the field. First we find that, with respect to the harvesting protocol, the Unruh vacuum agrees very well with the Vaidya vacuum near the horizon even for finite-time interactions. Second, all four vacua have different capacities for creating correlations between the detectors, with the Vaidya vacuum interpolating between the Unruh vacuum near the horizon and the Boulware vacuum far from the horizon. Third, we show that the black hole horizon inhibits any correlations, not just entanglement. Finally, we show that the efficiency of the harvesting protocol depend strongly on the signalling ability of the detectors, which is highly non-trivial in presence of curvature. We provide an asymptotic analysis of the Vaidya vacuum to clarify the relationship between the Boulware/Unruh interpolation and the near/far from horizon and early/late-time limits. We demonstrate a straightforward implementation of numerical contour integration to perform all the calculations.

scholarly journals Massive scalar field quasinormal modes of a Schwarzschild black hole surrounded by quintessence

Open Physics ◽  
2008 ◽  
Vol 6 (2) ◽  
Author(s):  
Chunrui Ma ◽  
Yuanxing Gui ◽  
Wei Wang ◽  
Fujun Wang
Keyword(s):  
Black Hole ◽  
Scalar Field ◽  
Quasinormal Modes ◽  
Massless Scalar ◽  
Massless Scalar Field ◽  
Massive Scalar ◽  
Schwarzschild Black Hole ◽  
Third Order ◽  
Massive Scalar Field ◽  
Absolute Value

AbstractWe present the quasinormal frequencies of the massive scalar field in the background of a Schwarzchild black hole surrounded by quintessence with the third-order WKB method. The mass of the scalar field u plays an important role in studying the quasinormal frequencies, the real part of the frequencies increases linearly as mass of the field u increases, while the imaginary part in absolute value decreases linearly which leads to damping more slowly than the massless scalar field. The frequencies have a limited value, so it is easier to detect the quasinormal modes. Moreover, owing to the presence of the quintessence, the massive scalar field damps more slowly.

scholarly journals LATE-TIME TAIL OF A COUPLED SCALAR FIELD IN THE BACKGROUND OF A BLACK HOLE WITH A GLOBAL MONOPOLE

2008 ◽  
Vol 23 (05) ◽  
pp. 359-369 ◽  
Author(s):  
SONGBAI CHEN ◽  
JILIANG JING
Keyword(s):  
Black Hole ◽  
Scalar Field ◽  
Scalar Fields ◽  
Massless Scalar ◽  
Late Time ◽  
Massless Scalar Field ◽  
Global Monopole ◽  
Massive Scalar Field ◽  
Gravitational Fields ◽  
Field Decay

Using the technique of spectral decomposition, we investigated the late-time tails of massless and massive coupled scalar fields in the background of a black hole with a global monopole. We found that due to the existence of the coupling between the scalar and gravitational fields, the massless scalar field decay faster at timelike infinity i+, and so does the massive one in the intermediate late time. But the asymptotically late-time tail for the massive scalar field is not affected and its decay rate is still t-5/6.

scholarly journals Distinguishing black holes through their ringing

SURG Journal ◽  
2010 ◽  
Vol 4 (1) ◽  
pp. 87-92
Author(s):  
Shannon Potter ◽  
Luis Lehner
Keyword(s):  
Black Hole ◽  
Gravitational Wave ◽  
Black Hole Solution ◽  
Alternative Explanation ◽  
Quasinormal Modes ◽  
Massless Scalar ◽  
Massless Scalar Field ◽  
Schwarzschild Black Hole ◽  
Black Hole Spacetime ◽  
Hole Model

A perturbed black hole spacetime emits gravitational waves possessing quasinormal modes that are characteristic of the black hole itself. We use a massless scalar field as an analog to a gravitational wave to find the quasinormal modes emitted by both a Schwarzschild black hole and a new alternative black hole model which places the Schwarzschild black hole in an aether—a zero density, negative pressure perfect fluid. The later model was proposed as an alternative explanation for accelerated cosmic expansion [1]. We construct a computational code to study both systems numerically and obtain the corresponding quasinormal modes. We find that the quasinormal modes of a black hole in an aether are distinguishable from those of a Schwarzschild black hole and so, in principle, gravitational wave observations could be exploited to determine if either black hole solution represents those existing in our universe.

scholarly journals Notes on massless scalar field partition functions, modular invariance and Eisenstein series

2021 ◽  
Vol 2021 (12) ◽  
Author(s):  
Francesco Alessio ◽  
Glenn Barnich ◽  
Martin Bonte
Keyword(s):  
Scalar Field ◽  
Partition Function ◽  
Low Temperature ◽  
Eisenstein Series ◽  
Chemical Potential ◽  
Proper Time ◽  
Series Representation ◽  
Massless Scalar ◽  
Massless Scalar Field ◽  
Spacetime Manifold

Abstract The partition function of a massless scalar field on a Euclidean spacetime manifold ℝd−1 × 𝕋2 and with momentum operator in the compact spatial dimension coupled through a purely imaginary chemical potential is computed. It is modular covariant and admits a simple expression in terms of a real analytic SL(2, ℤ) Eisenstein series with s = (d + 1)/2. Different techniques for computing the partition function illustrate complementary aspects of the Eisenstein series: the functional approach gives its series representation, the operator approach yields its Fourier series, while the proper time/heat kernel/world-line approach shows that it is the Mellin transform of a Riemann theta function. High/low temperature duality is generalized to the case of a non-vanishing chemical potential. By clarifying the dependence of the partition function on the geometry of the torus, we discuss how modular covariance is a consequence of full SL(2, ℤ) invariance. When the spacetime manifold is ℝp × 𝕋q+1, the partition function is given in terms of a SL(q + 1, ℤ) Eisenstein series again with s = (d + 1)/2. In this case, we obtain the high/low temperature duality through a suitably adapted dual parametrization of the lattice defining the torus. On 𝕋d+1, the computation is more subtle. An additional divergence leads to an harmonic anomaly.

scholarly journals Quasi-normal modes and the area spectrum of a near extremal de Sitter black hole with conformally coupled scalar field

2015 ◽  
Vol 30 (11) ◽  
pp. 1550057 ◽  
Author(s):  
Sharmanthie Fernando
Keyword(s):  
Black Hole ◽  
Wave Equation ◽  
Scalar Field ◽  
Normal Modes ◽  
Type Equation ◽  
Area Spectrum ◽  
Massless Scalar ◽  
Massless Scalar Field ◽  
De Sitter ◽  
Quasi Normal Mode

In this paper, we have studied a black hole in de Sitter space which has a conformally coupled scalar field in the background. This black hole is also known as the MTZ black hole. We have obtained exact values for the quasi-normal mode (QNM) frequencies under massless scalar field perturbations. We have demonstrated that when the black hole is near-extremal, that the wave equation for the massless scalar field simplifies to a Schrödinger type equation with the well-known Pöschl–Teller potential. We have also used sixth-order WKB approximation to compute QNM frequencies to compare with exact values obtained via the Pöschl–Teller method for comparison. As an application, we have obtained the area spectrum using modified Hods approach and show that it is equally spaced.

scholarly journals THE REAL SCALAR FIELD EQUATION FOR NARIAI BLACK HOLE IN THE 5D SCHWARZSCHILD–DE SITTER BLACK STRING SPACE

2007 ◽  
Vol 22 (24) ◽  
pp. 4451-4465 ◽  
Author(s):  
MOLIN LIU ◽  
HONGYA LIU ◽  
CHUNXIAO WANG ◽  
YONGLI PING
Keyword(s):  
Black Hole ◽  
Field Equation ◽  
Scalar Field ◽  
Massless Scalar ◽  
Massless Scalar Field ◽  
De Sitter ◽  
Black String ◽  
Transmission Coefficients ◽  
Scalar Field Equation ◽  
Continuous Potential

The Nariai black hole, whose two horizons are lying close to each other, is an extreme and important case in the research of black hole. In this paper we study the evolution of a massless scalar field scattered around in 5D Schwarzschild–de Sitter black string space. Using the method shown by Brevik and Simonsen (2001) we solve the scalar field equation as a boundary value problem, where real boundary condition is employed. Then with convenient replacement of the 5D continuous potential by square barrier, the reflection and transmission coefficients (R, T) are obtained. At last, we also compare the coefficients with the usual 4D counterpart.

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