scholarly journals Five-Dimensional Warped Product Space-Time with Time-Dependent Warp Factor and Cosmology of the Four-Dimensional Universe

2011 ◽  
Vol 51 (1) ◽  
pp. 55-68 ◽  
Author(s):  
Sarbari Guha ◽  
Subenoy Chakraborty
Keyword(s):  
Product Space ◽  
Warped Product ◽  
Space Time ◽  
Time Dependent ◽  
Warp Factor

scholarly journals The W2-curvature tensor on warped product manifolds and applications

2016 ◽  
Vol 13 (07) ◽  
pp. 1650099 ◽  
Author(s):  
Sameh Shenawy ◽  
Bülent Ünal
Keyword(s):  
Curvature Tensor ◽  
Product Space ◽  
Warped Product ◽  
Space Time ◽  
Product Manifold ◽  
Warped Product Manifold ◽  
Static Space

The purpose of this paper is to study the [Formula: see text]-curvature tensor on (singly) warped product manifolds as well as on generalized Robertson–Walker and standard static space-times. Some different expressions of the [Formula: see text]-curvature tensor on a warped product manifold in terms of its relation with [Formula: see text]-curvature tensor on the base and fiber manifolds are obtained. Furthermore, we investigate [Formula: see text]-curvature flat warped product manifolds. Many interesting results describing the geometry of the base and fiber manifolds of a [Formula: see text]-curvature flat warped product manifold are derived. Finally, we study the [Formula: see text]-curvature tensor on generalized Robertson–Walker and standard static space-times; we explore the geometry of the fiber of these warped product space-time models that are [Formula: see text]-curvature flat.

Compact Einstein multiply warped product space with nonpositive scalar curvature

2019 ◽  
Vol 16 (10) ◽  
pp. 1950162 ◽  
Author(s):  
Buddhadev Pal ◽  
Pankaj Kumar
Keyword(s):  
Riemannian Manifold ◽  
Scalar Curvature ◽  
Product Space ◽  
Warped Product ◽  
Space Time ◽  
Product Spaces ◽  
Warped Product Spaces ◽  
Friedmann Robertson Walker

In this paper, we characterize the Einstein multiply warped product space with nonpositive scalar curvature. As a result, it is shown that, if [Formula: see text] is Einstein multiple-warped product spaces with compact base and nonpositive scalar curvature, then [Formula: see text] is simply a Riemannian manifold. Next, we apply our result on Generalized Robertson–Walker space-time and Generalized Friedmann–Robertson–Walker space-time.

scholarly journals Classification of Einstein equations with cosmological constant in warped product space-time

2018 ◽  
Vol 15 (03) ◽  
pp. 1850041 ◽  
Author(s):  
F. Gholami ◽  
A. Haji-Badali ◽  
F. Darabi
Keyword(s):  
Cosmological Constant ◽  
Product Space ◽  
Warped Product ◽  
Space Time ◽  
Einstein Equations ◽  
Twisted Product ◽  
Product Structures ◽  
Static Space

We classify all warped product space-times in three categories as (i) generalized twisted product structures, (ii) base conformal warped product structures and (iii) generalized static space-times and then we obtain the Einstein equations with the corresponding cosmological constant by which we can determine uniquely the warp functions in these warped product space-times.

scholarly journals Global existence and decay estimates for nonlinear wave equations with space-time dependent dissipative term

2015 ◽  
Vol 12 (02) ◽  
pp. 249-276
Author(s):  
Tomonari Watanabe
Keyword(s):  
Global Existence ◽  
Nonlinear Wave ◽  
Wave Equations ◽  
Space Time ◽  
Time Dependent ◽  
Nonlinear Wave Equations ◽  
Energy Estimates ◽  
Space Region ◽  
Decay Estimates ◽  
Dissipative Term

We study the global existence and the derivation of decay estimates for nonlinear wave equations with a space-time dependent dissipative term posed in an exterior domain. The linear dissipative effect may vanish in a compact space region and, moreover, the nonlinear terms need not be in a divergence form. In order to establish higher-order energy estimates, we introduce an argument based on a suitable rescaling. The proposed method is useful to control certain derivatives of the dissipation coefficient.

scholarly journals Evolution of a domain wall in expanding universe: inflation and after it

2018 ◽  
Vol 191 ◽  
pp. 08004
Author(s):  
A.D. Dolgov ◽  
S.I. Godunov ◽  
A.S. Rudenko
Keyword(s):  
Domain Wall ◽  
Hubble Parameter ◽  
Domain Walls ◽  
Flat Space ◽  
Space Time ◽  
Time Dependent ◽  
Expanding Universe ◽  
Large Size ◽  
Dependent Parameter ◽  
Thick Domain Walls

We study the evolution of thick domain walls in the expanding universe. We have found that the domain wall evolution crucially depends on the time-dependent parameter C(t) = 1/(H(t)δ0)2, where H(t) is the Hubble parameter and δ0 is the width of the wall in flat space-time. For C(t) > 2 the physical width of the wall, a(t)δ(t), tends with time to constant value δ0, which is microscopically small. Otherwise, when C(t) ≤ 2, the wall steadily expands and can grow up to a cosmologically large size.

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