scholarly journals Scalar field equation in the presence of signature change

1993 ◽  
Vol 48 (6) ◽  
pp. 2587-2590 ◽  
Author(s):  
Tevian Dray ◽  
Corinne A. Manogue ◽  
Robin W. Tucker
Keyword(s):  
Field Equation ◽  
Scalar Field ◽  
Scalar Field Equation ◽  
Signature Change

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.

scholarly journals Anti-screening of the Galileon force around a disk center hole

2019 ◽  
Vol 34 (02) ◽  
pp. 1950013 ◽  
Author(s):  
Hiromu Ogawa ◽  
Takashi Hiramatsu ◽  
Tsutomu Kobayashi
Keyword(s):  
Field Equation ◽  
Scalar Field ◽  
Modified Gravity ◽  
Disk Center ◽  
Academic Interest ◽  
Screening Effect ◽  
Matter Source ◽  
Fifth Force ◽  
Scalar Field Equation

The Vainshtein mechanism is known as an efficient way of screening the fifth force around a matter source in modified gravity. This has been verified mainly in highly symmetric matter configurations. To study how the Vainshtein mechanism works in a less symmetric setup, we numerically solve the scalar field equation around a disk with a hole at its center in the cubic Galileon theory. We find, surprisingly, that the Galileon force is enhanced, rather than suppressed, in the vicinity of the hole. This anti-screening effect is larger for a thinner, less massive disk with a smaller hole. At this stage, our setup is only of academic interest and its astrophysical consequences are unclear, but this result implies that the Vainshtein screening mechanism around less symmetric matter configurations are quite nontrivial.

Least energy solution for a scalar field equation with a singular nonlinearity

2020 ◽  
pp. 1-17
Author(s):  
Jaeyoung Byeon ◽  
Sun-Ho Choi ◽  
Yeonho Kim ◽  
Sang-Hyuck Moon
Keyword(s):  
Field Equation ◽  
Scalar Field ◽  
Existence Result ◽  
Nonnegative Solution ◽  
Energy Solution ◽  
Existence Of A Solution ◽  
Singular Nonlinearity ◽  
Scalar Field Equation ◽  
Least Energy Solution ◽  
Least Energy

Abstract We are concerned with a nonnegative solution to the scalar field equation $$\Delta u + f(u) = 0{\rm in }{\open R}^N,\quad \mathop {\lim }\limits_{|x|\to \infty } u(x) = 0.$$ A classical existence result by Berestycki and Lions [3] considers only the case when f is continuous. In this paper, we are interested in the existence of a solution when f is singular. For a singular nonlinearity f, Gazzola, Serrin and Tang [8] proved an existence result when $f \in L^1_{loc}(\mathbb {R}) \cap \mathrm {Lip}_{loc}(0,\infty )$ with $\int _0^u f(s)\,{\rm d}s < 0$ for small $u>0.$ Since they use a shooting argument for their proof, they require the property that $f \in \mathrm {Lip}_{loc}(0,\infty ).$ In this paper, using a purely variational method, we extend the previous existence results for $f \in L^1_{loc}(\mathbb {R}) \cap C(0,\infty )$ . We show that a solution obtained through minimization has the least energy among all radially symmetric weak solutions. Moreover, we describe a general condition under which a least energy solution has compact support.

scholarly journals DILATON COUPLED QUINTESSENCE MODEL IN THE ω - ω′ PLANE

2007 ◽  
Vol 16 (07) ◽  
pp. 1109-1117 ◽  
Author(s):  
Z. G. HUANG ◽  
H. Q. LU ◽  
W. FANG
Keyword(s):  
Dark Energy ◽  
Field Equation ◽  
Scalar Field ◽  
Equation Of State ◽  
State Parameter ◽  
Equation Of Motion ◽  
Gravitational Theory ◽  
Scalar Field Equation ◽  
Equation Of State Parameter ◽  
Quintessence Model

In this paper, we regard the dilaton in Weyl-scaled induced gravitational theory as a coupled quintessence. Based on this consideration, we investigate the dilaton coupled quintessence (DCQ) model in the ω - ω′ plane, which is defined by the equation of state parameter for the dark energy and its derivative with respect to N (the logarithm of the scale factor a). We find the scalar field equation of motion in the ω - ω′ plane, and show mathematically the properties of attractor solutions which correspond to ωσ ~ -1, ωσ = 1. Finally, we find that our model is a tracking one which belongs to "freezing" type models classified in the ω - ω′ plane.

Hawking radiation is probably a type of superradiation

2021 ◽  
Author(s):  
Wen-Xiang Chen
Keyword(s):  
Field Equation ◽  
Scalar Field ◽  
Boundary Conditions ◽  
Effective Action ◽  
Hawking Radiation ◽  
Scalar Field Equation

In this article, it mainly discusses that when the scalar field equation presets boundary conditions, the effective action form of Hawking radiation is consistent with the effective action form of superradiation. From this I conclude that Hawking radiation may be a form of superradiation.

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