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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Main Author: Alexandre Landry
Format: Article
Language:English
Published: MDPI AG 2025-03-01
Series:Mathematics
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Online Access:https://www.mdpi.com/2227-7390/13/6/1003
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author Alexandre Landry
author_facet Alexandre Landry
author_sort Alexandre Landry
collection DOAJ
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