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Search Results (5)

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Keywords = Kantowski–Sachs spacetimes

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52 pages, 652 KB  
Article
Scalar Field Kantowski–Sachs Solutions in Teleparallel F(T) Gravity
by Alexandre Landry
Universe 2025, 11(1), 26; https://doi.org/10.3390/universe11010026 - 16 Jan 2025
Cited by 3 | Viewed by 963
Abstract
In this paper, we investigate time-dependent Kantowski–Sachs spherically symmetric teleparallel F(T) gravity with a scalar field source. We begin by setting the exact field equations to be solved and solve conservation laws for possible scalar field potential, Vϕ, [...] Read more.
In this paper, we investigate time-dependent Kantowski–Sachs spherically symmetric teleparallel F(T) gravity with a scalar field source. We begin by setting the exact field equations to be solved and solve conservation laws for possible scalar field potential, Vϕ, solutions. Then, we find new non-trivial teleparallel F(T) solutions by using power-law and exponential ansatz for each potential case arising from conservation laws, such as linear, quadratic, or logarithmic, to name a few. We find a general formula allowing us to compute all possible new teleparallel F(T) solutions applicable for any scalar field potential and ansatz. Then, we apply this formula and find a large number of exact and approximate new teleparallel F(T) solutions for several types of cases. Some new F(T) solution classes may be relevant for future cosmological applications, especially concerning dark matter, dark energy quintessence, phantom energy leading to the Big Rip event, and quintom models of physical processes. Full article
(This article belongs to the Special Issue Dark Energy and Dark Matter)
31 pages, 455 KB  
Article
Kantowski–Sachs Spherically Symmetric Solutions in Teleparallel F(T) Gravity
by Alexandre Landry
Symmetry 2024, 16(8), 953; https://doi.org/10.3390/sym16080953 - 25 Jul 2024
Cited by 7 | Viewed by 1683
Abstract
In this paper, we investigate time-dependent Kantowski–Sachs spherically symmetric teleparallel F(T) gravity in vacuum and in a perfect isotropic fluid. We begin by finding the field equations and solve for new teleparallel F(T) solutions. With a power-law [...] Read more.
In this paper, we investigate time-dependent Kantowski–Sachs spherically symmetric teleparallel F(T) gravity in vacuum and in a perfect isotropic fluid. We begin by finding the field equations and solve for new teleparallel F(T) solutions. With a power-law ansatz for the co-frame functions, we find new non-trivial teleparallel F(T) vacuum solutions. We then proceed to find new non-trivial teleparallel F(T) solutions in a perfect isotropic fluid with both linear and non-linear equations of state. We find a great number of new exact and approximated teleparallel F(T) solutions. These classes of new solutions are relevant for future cosmological applications. Full article
(This article belongs to the Special Issue Symmetry and Applications of Differential Geometry to the Differential Equations of Mathematical Physics)
16 pages, 324 KB  
Article
Fock Quantization of a Klein–Gordon Field in the Interior Geometry of a Nonrotating Black Hole
by Jerónimo Cortez, Beatriz Elizaga Navascués, Guillermo A. Mena Marugán, Álvaro Torres-Caballeros and José Velhinho
Mathematics 2023, 11(18), 3922; https://doi.org/10.3390/math11183922 - 15 Sep 2023
Cited by 4 | Viewed by 1057
Abstract
We study the canonical quantization of a scalar field in Kantowski–Sachs spacetime. For simplicity, we consider compactified spatial sections, since this does not affect the ultraviolet behavior. A time-dependent canonical transformation is performed prior to quantization. As in previously studied cases, the purpose [...] Read more.
We study the canonical quantization of a scalar field in Kantowski–Sachs spacetime. For simplicity, we consider compactified spatial sections, since this does not affect the ultraviolet behavior. A time-dependent canonical transformation is performed prior to quantization. As in previously studied cases, the purpose of this canonical transformation is to identify and extract the background contribution to the field evolution which is obstructing a unitary implementation of the field dynamics at the quantum level. This splitting of the time dependence into a background piece and the part to be seen as true quantum evolution is, to a large extent, determined by the unitarity requirement itself. The quantization is performed in the usual setup of Fock representations, demanding the preservation of the spatial symmetries. Under the joint requirements of quantum unitary dynamics and compatibility with those classical symmetries, the quantization is shown to be unique, in the sense that any two representations with these properties are unitarily equivalent. This confirms the validity of our conditions as criteria to discriminate among possibly inequivalent quantum descriptions. The interest of this analysis goes beyond cosmological applications since the interior of a nonrotating black hole has a geometry of the Kantowski–Sachs type. Full article
(This article belongs to the Section E4: Mathematical Physics)
8 pages, 310 KB  
Communication
New Anisotropic Exact Solution in Multifield Cosmology
by Andronikos Paliathanasis
Universe 2021, 7(9), 323; https://doi.org/10.3390/universe7090323 - 30 Aug 2021
Cited by 7 | Viewed by 1766
Abstract
In the case of two-scalar field cosmology, and specifically for the Chiral model, we determine an exact solution for the field equations with an anisotropic background space. The exact solution can describe anisotropic inflation with a Kantowski–Sachs geometry and can be seen as [...] Read more.
In the case of two-scalar field cosmology, and specifically for the Chiral model, we determine an exact solution for the field equations with an anisotropic background space. The exact solution can describe anisotropic inflation with a Kantowski–Sachs geometry and can be seen as the anisotropic analogue of the hyperbolic inflation. Finally, we investigate the stability conditions for the exact solution. Full article
(This article belongs to the Special Issue Modified Theories of Gravity and Cosmological Applications)
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12 pages, 781 KB  
Article
Positive Energy Condition and Conservation Laws in Kantowski-Sachs Spacetime via Noether Symmetries
by Sumaira Saleem Akhtar, Tahir Hussain and Ashfaque H. Bokhari
Symmetry 2018, 10(12), 712; https://doi.org/10.3390/sym10120712 - 4 Dec 2018
Cited by 6 | Viewed by 2822
Abstract
In this paper, we have investigated Noether symmetries of the Lagrangian of Kantowski–Sachs spacetime. The associated Lagrangian of the Kantowski–Sachs metric is used to derive the set of determining equations. Solving the determining equations for several values of the metric functions, it is [...] Read more.
In this paper, we have investigated Noether symmetries of the Lagrangian of Kantowski–Sachs spacetime. The associated Lagrangian of the Kantowski–Sachs metric is used to derive the set of determining equations. Solving the determining equations for several values of the metric functions, it is observed that the Kantowski–Sachs spacetime admits the Noether algebra of dimensions 5, 6, 7, 8, 9, and 11. A comparison of the obtained Noether symmetries with Killing and homothetic vectors is also presented. With the help of Noether’s theorem, we have presented the expressions for conservation laws corresponding to all Noether symmetries. It is observed that the positive energy condition is satisfied for most of the obtained metrics. Full article
(This article belongs to the Special Issue Noether's Theorem and Symmetry)
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