Vacuum for a massless scalar field outside a collapsing body in de Sitter spacetime

Abstract We derive the response function for a comoving, pointlike Unruh-DeWitt particle detector coupled to a complex scalar field ϕ, in the (3 + 1)-dimensional cosmological de Sitter spacetime. The field-detector coupling is taken to be proportional to ϕ†ϕ. We address both conformally invariant and massless minimally coupled scalar field theories, respectively in the conformal and the Bunch-Davies vacuum. The response function integral for the massless minimal complex scalar, not surprisingly, shows divergences and accordingly we use suitable regularisation scheme to find out well behaved results. The regularised result also contains a de Sitter symmetry breaking logarithm, growing with the cosmological time. Possibility of extension of these results with the so called de Sitter α-vacua is discussed. While we find no apparent problem in computing the response function for a real scalar in these vacua, a complex scalar field is shown to contain some possible ambiguities in the detector response. The case of the minimal and nearly massless scalar field theory is also briefly discussed.

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

Modern Physics Letters A ◽

10.1142/s0217732315500571 ◽

2015 ◽

Vol 30 (11) ◽

pp. 1550057 ◽

Cited By ~ 4

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.

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

International Journal of Modern Physics A ◽

10.1142/s0217751x07037044 ◽

2007 ◽

Vol 22 (24) ◽

pp. 4451-4465 ◽

Cited By ~ 7

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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