Scalar Field Kantowski–Sachs Solutions in Teleparallel <i>F</i>(<i>T</i>) Gravity
In this paper, we investigate time-dependent Kantowski–Sachs spherically symmetric teleparallel <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>F</mi><mo>(</mo><mi>T</m...
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| author | Alexandre Landry |
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| description | In this paper, we investigate time-dependent Kantowski–Sachs spherically symmetric teleparallel <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>F</mi><mo>(</mo><mi>T</mi><mo>)</mo></mrow></semantics></math></inline-formula> 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, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>V</mi><mfenced open="(" close=")"><mi>ϕ</mi></mfenced></mrow></semantics></math></inline-formula>, solutions. Then, we find new non-trivial teleparallel <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>F</mi><mo>(</mo><mi>T</mi><mo>)</mo></mrow></semantics></math></inline-formula> 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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>F</mi><mo>(</mo><mi>T</mi><mo>)</mo></mrow></semantics></math></inline-formula> 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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>F</mi><mo>(</mo><mi>T</mi><mo>)</mo></mrow></semantics></math></inline-formula> solutions for several types of cases. Some new <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>F</mi><mo>(</mo><mi>T</mi><mo>)</mo></mrow></semantics></math></inline-formula> 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. |
| format | Article |
| id | doaj-art-66ca79e4bc0748fba0a2e804996a5852 |
| institution | Kabale University |
| issn | 2218-1997 |
| language | English |
| publishDate | 2025-01-01 |
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| spelling | doaj-art-66ca79e4bc0748fba0a2e804996a58522025-01-24T13:51:31ZengMDPI AGUniverse2218-19972025-01-011112610.3390/universe11010026Scalar Field Kantowski–Sachs Solutions in Teleparallel <i>F</i>(<i>T</i>) GravityAlexandre Landry0Department of Mathematics and Statistics, Dalhousie University, Halifax, NS B3H 3J5, CanadaIn this paper, we investigate time-dependent Kantowski–Sachs spherically symmetric teleparallel <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>F</mi><mo>(</mo><mi>T</mi><mo>)</mo></mrow></semantics></math></inline-formula> 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, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>V</mi><mfenced open="(" close=")"><mi>ϕ</mi></mfenced></mrow></semantics></math></inline-formula>, solutions. Then, we find new non-trivial teleparallel <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>F</mi><mo>(</mo><mi>T</mi><mo>)</mo></mrow></semantics></math></inline-formula> 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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>F</mi><mo>(</mo><mi>T</mi><mo>)</mo></mrow></semantics></math></inline-formula> 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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>F</mi><mo>(</mo><mi>T</mi><mo>)</mo></mrow></semantics></math></inline-formula> solutions for several types of cases. Some new <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>F</mi><mo>(</mo><mi>T</mi><mo>)</mo></mrow></semantics></math></inline-formula> 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.https://www.mdpi.com/2218-1997/11/1/26teleparallel gravityfield equationsKantowski–Sachs spacetimesscalar field source solutionsframe-based approachtime-dependent spacetimes |
| spellingShingle | Alexandre Landry Scalar Field Kantowski–Sachs Solutions in Teleparallel <i>F</i>(<i>T</i>) Gravity Universe teleparallel gravity field equations Kantowski–Sachs spacetimes scalar field source solutions frame-based approach time-dependent spacetimes |
| title | Scalar Field Kantowski–Sachs Solutions in Teleparallel <i>F</i>(<i>T</i>) Gravity |
| title_full | Scalar Field Kantowski–Sachs Solutions in Teleparallel <i>F</i>(<i>T</i>) Gravity |
| title_fullStr | Scalar Field Kantowski–Sachs Solutions in Teleparallel <i>F</i>(<i>T</i>) Gravity |
| title_full_unstemmed | Scalar Field Kantowski–Sachs Solutions in Teleparallel <i>F</i>(<i>T</i>) Gravity |
| title_short | Scalar Field Kantowski–Sachs Solutions in Teleparallel <i>F</i>(<i>T</i>) Gravity |
| title_sort | scalar field kantowski sachs solutions in teleparallel i f i i t i gravity |
| topic | teleparallel gravity field equations Kantowski–Sachs spacetimes scalar field source solutions frame-based approach time-dependent spacetimes |
| url | https://www.mdpi.com/2218-1997/11/1/26 |
| work_keys_str_mv | AT alexandrelandry scalarfieldkantowskisachssolutionsinteleparallelifiitigravity |