scholarly journals Blow-up of solutions of semilinear wave equations in accelerated expanding Friedmann–Lemaître–Robertson–Walker spacetime

2021 ◽  
Author(s):  
Kimitoshi Tsutaya ◽  
Yuta Wakasugi
Keyword(s):  
Wave Equation ◽  
Scalar Field ◽  
Wave Equations ◽  
Blow Up ◽  
Minkowski Spacetime ◽  
Upper Bounds ◽  
Accelerated Expansion ◽  
Massless Scalar ◽  
Massless Scalar Field ◽  
Arbitrary Power

Consider a nonlinear wave equation for a massless scalar field with self-interaction in the spatially flat Friedmann–Lemaître–Robertson–Walker spacetimes. For the case of accelerated expansion, we show that the blow-up in a finite time occurs for the equation with arbitrary power nonlinearity as well as upper bounds of the lifespan of blow-up solutions. Comparing to the case of the Minkowski spacetime, we discuss how the scale factor affects the lifespan of blow-up solutions of the equation.

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.

HIDDEN CONFORMAL SYMMETRY OF ROTATING NS5-BRANES IN EXTREMAL LIMIT

2011 ◽  
Vol 26 (13) ◽  
pp. 2233-2241 ◽  
Author(s):  
M. R. SETARE ◽  
V. KAMALI
Keyword(s):  
Correlation Function ◽  
Wave Equation ◽  
Scalar Field ◽  
Conformal Symmetry ◽  
Massless Scalar ◽  
Massless Scalar Field ◽  
Perfect Agreement ◽  
Extremal Limit

We show that extremal rotating NS5-branes space–times have a hidden conformal symmetry. In this regard, we consider the wave equation of a massless scalar field propagating in extremal NS5-branes space–times and find in the "near region," the wave equation in extremal limit can be written in terms of the SL (2, R) quadratic Casimir. Moreover, we obtain the microscopic entropy of the extremal NS5-branes space–times, also we calculate the correlation function of a near-region scalar field and find perfect agreement with the dual 2D CFT.

scholarly journals WAVE EQUATION OF THE SCALAR FIELD AND SUPERFLUIDS

2009 ◽  
Vol 24 (40) ◽  
pp. 3249-3256 ◽  
Author(s):  
A. NADDEO ◽  
G. SCELZA
Keyword(s):  
General Relativity ◽  
Wave Equation ◽  
Scalar Field ◽  
Dimensional Space ◽  
Massless Scalar ◽  
Back Reaction ◽  
Massless Scalar Field ◽  
Sound Waves ◽  
Hydrodynamical Equation ◽  
Common Features

The new formal analogy between superfluid systems and cosmology, which emerges by taking into account the back-reaction of the vacuum to the quanta of sound waves,1 enables us to put forward some common features between these two different areas of physics. We find the condition that allows us to justify a General Relativity (GR) derivation of the hydrodynamical equation for the superfluid in a four-dimensional space whose metric is the Unruh one.2 Furthermore, we show how, in the particular case taken into account, our hydrodynamical equation can be deduced within a four-dimensional space from the wave equation of a massless scalar field.

scholarly journals Vacuum Polarization in a Zero-Width Potential: Self-Adjoint Extension

Universe ◽  
2021 ◽  
Vol 7 (5) ◽  
pp. 127
Author(s):  
Yuri V. Grats ◽  
Pavel Spirin
Keyword(s):  
Scalar Field ◽  
Vacuum Polarization ◽  
Dimensional Regularization ◽  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
Field Approximation ◽  
Dimensional Euclidean Space ◽  
Massless Scalar ◽  
Massless Scalar Field ◽  
Adjoint Extension

The effects of vacuum polarization associated with a massless scalar field near pointlike source with a zero-range potential in three spatial dimensions are analyzed. The “physical” approach consists in the usage of direct delta-potential as a model of pointlike interaction. We use the Perturbation theory in the Fourier space with dimensional regularization of the momentum integrals. In the weak-field approximation, we compute the effects of interest. The “mathematical” approach implies the self-adjoint extension technique. In the Quantum-Field-Theory framework we consider the massless scalar field in a 3-dimensional Euclidean space with an extracted point. With appropriate boundary conditions it is considered an adequate mathematical model for the description of a pointlike source. We compute the renormalized vacuum expectation value ⟨ϕ2(x)⟩ren of the field square and the renormalized vacuum averaged of the scalar-field’s energy-momentum tensor ⟨Tμν(x)⟩ren. For the physical interpretation of the extension parameter we compare these results with those of perturbative computations. In addition, we present some general formulae for vacuum polarization effects at large distances in the presence of an abstract weak potential with finite-sized compact support.

scholarly journals THE EDGE STATES OF THE BF SYSTEM AND THE LONDON EQUATIONS

1993 ◽  
Vol 08 (04) ◽  
pp. 723-752 ◽  
Author(s):  
A.P. BALACHANDRAN ◽  
P. TEOTONIO-SOBRINHO
Keyword(s):  
Scalar Field ◽  
Scaling Limit ◽  
Quantum Hall ◽  
Simons Theory ◽  
Massless Scalar ◽  
Electromagnetic Current ◽  
Massless Scalar Field ◽  
Edge States ◽  
Chern Simons ◽  
London Equations

It is known that the 3D Chern–Simons interaction describes the scaling limit of a quantum Hall system and predicts edge currents in a sample with boundary, the currents generating a chiral U(1) Kac-Moody algebra. It is no doubt also recognized that, in a somewhat similar way, the 4D BF interaction (with B a two-form, dB the dual *j of the electromagnetic current, and F the electromagnetic field form) describes the scaling limit of a superconductor. We show in this paper that there are edge excitations in this model as well for manifolds with boundaries. They are the modes of a scalar field with invariance under the group of diffeomorphisms (diffeos) of the bounding spatial two-manifold. Not all diffeos of this group seem implementable by operators in quantum theory, the implementable group being a subgroup of volume-preserving diffeos. The BF system in this manner can lead to the w1+∞ algebra and its variants. Lagrangians for fields on the bounding manifold which account for the edge observables on quantization are also presented. They are the analogs of the (1+1)-dimensional massless scalar field Lagrangian describing the edge modes of an Abelian Chern-Simons theory with a disk as the spatial manifold. We argue that the addition of “Maxwell” terms constructed from F∧*F and dB∧*dB does not affect the edge states, and that the augmented Lagrangian has an infinite number of conserved charges—the aforementioned scalar field modes—localized at the edges. This Lagrangian is known to describe London equations and a massive vector field. A (3+1)-dimensional generalization of the Hall effect involving vortices coupled to B is also proposed.

scholarly journals COLLAPSING SCALAR FIELD WITH KINEMATIC SELF-SIMILARITY OF THE SECOND KIND IN (2+1) GRAVITY

2005 ◽  
Vol 14 (06) ◽  
pp. 1049-1061 ◽  
Author(s):  
R. CHAN ◽  
M. F. A. DA SILVA ◽  
J. F. VILLAS DA ROCHA ◽  
ANZHONG WANG
Keyword(s):  
Black Holes ◽  
Scalar Field ◽  
Gravitational Collapse ◽  
Massless Scalar ◽  
Massless Scalar Field ◽  
Field Equations ◽  
Self Similarity ◽  
Global Properties ◽  
Scalar Field Equations

All the (2+1)-dimensional circularly symmetric solutions with kinematic self-similarity of the second kind to the Einstein-massless-scalar field equations are found and their local and global properties are studied. It is found that some of them represent gravitational collapse of a massless scalar field, in which black holes are always formed.

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