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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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2025-01-01
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| Series: | Universe |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2218-1997/11/1/26 |
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| Summary: | 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. |
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| ISSN: | 2218-1997 |