Scalar Field Static Spherically Symmetric Solutions in Teleparallel <i>F</i>(<i>T</i>) Gravity
We investigate in this paper the static radial coordinate-dependent spherically symmetric spacetime in teleparallel <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>F</mi><mo>(</mo&...
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| description | We investigate in this paper the static radial coordinate-dependent spherically symmetric spacetime in 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 for a scalar field source. We begin by setting the static field equations (FEs) to be solved and solve the conservation laws for scalar field potential solutions. We simplify the FEs and then find a general formula for computing the 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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>V</mi><mo>(</mo><mi>T</mi><mo>)</mo></mrow></semantics></math></inline-formula> and coframe ansatz. We compute 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 a power-law coframe ansatz for each scalar potential case arising from the conservation laws. We apply this formula to find new exact 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 cases of coframe ansatz parameter. The 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 will be relevant for studying the models close to Born–Infeld and/or scalarized Black Hole (BH) solutions inside the dark energy (DE) described by a fundamental scalar field such as quintessence, phantom energy or quintom system, to name only those types. |
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| spelling | doaj-art-a6debb7f9a104c6b954dfd8d586ef7462025-08-20T01:49:04ZengMDPI AGMathematics2227-73902025-03-01136100310.3390/math13061003Scalar Field Static Spherically Symmetric Solutions in Teleparallel <i>F</i>(<i>T</i>) GravityAlexandre Landry0Department of Mathematics and Statistics, Dalhousie University, Halifax, NS B3H 3J5, CanadaWe investigate in this paper the static radial coordinate-dependent spherically symmetric spacetime in 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 for a scalar field source. We begin by setting the static field equations (FEs) to be solved and solve the conservation laws for scalar field potential solutions. We simplify the FEs and then find a general formula for computing the 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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>V</mi><mo>(</mo><mi>T</mi><mo>)</mo></mrow></semantics></math></inline-formula> and coframe ansatz. We compute 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 a power-law coframe ansatz for each scalar potential case arising from the conservation laws. We apply this formula to find new exact 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 cases of coframe ansatz parameter. The 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 will be relevant for studying the models close to Born–Infeld and/or scalarized Black Hole (BH) solutions inside the dark energy (DE) described by a fundamental scalar field such as quintessence, phantom energy or quintom system, to name only those types.https://www.mdpi.com/2227-7390/13/6/1003teleparallel F(T) gravitystaticscalar field sourcesscalar field sourcesstatic spherically symmetric teleparallel spacetimesdark energy sourcesastrophysical systems in dark energy |
| spellingShingle | Alexandre Landry Scalar Field Static Spherically Symmetric Solutions in Teleparallel <i>F</i>(<i>T</i>) Gravity Mathematics teleparallel F(T) gravity staticscalar field sources scalar field sources static spherically symmetric teleparallel spacetimes dark energy sources astrophysical systems in dark energy |
| title | Scalar Field Static Spherically Symmetric Solutions in Teleparallel <i>F</i>(<i>T</i>) Gravity |
| title_full | Scalar Field Static Spherically Symmetric Solutions in Teleparallel <i>F</i>(<i>T</i>) Gravity |
| title_fullStr | Scalar Field Static Spherically Symmetric Solutions in Teleparallel <i>F</i>(<i>T</i>) Gravity |
| title_full_unstemmed | Scalar Field Static Spherically Symmetric Solutions in Teleparallel <i>F</i>(<i>T</i>) Gravity |
| title_short | Scalar Field Static Spherically Symmetric Solutions in Teleparallel <i>F</i>(<i>T</i>) Gravity |
| title_sort | scalar field static spherically symmetric solutions in teleparallel i f i i t i gravity |
| topic | teleparallel F(T) gravity staticscalar field sources scalar field sources static spherically symmetric teleparallel spacetimes dark energy sources astrophysical systems in dark energy |
| url | https://www.mdpi.com/2227-7390/13/6/1003 |
| work_keys_str_mv | AT alexandrelandry scalarfieldstaticsphericallysymmetricsolutionsinteleparallelifiitigravity |