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Spherically symmetric teleparallel geometries.

A A Coley1, A Landry1, R J van den Hoogen2

  • 1Department of Mathematics and Statistics, Dalhousie University, Halifax, NS B3H 3J5 Canada.

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This study explores spherically symmetric geometries in F(T) teleparallel gravity, developing new solutions for vacuum spacetimes. The research analyzes field equations and symmetries to advance understanding of these important gravitational models.

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Area of Science:

  • Theoretical Physics
  • Cosmology
  • Gravitational Theory

Background:

  • F(T) teleparallel gravity offers an alternative to general relativity for describing gravity.
  • Spherically symmetric spacetimes are crucial for modeling astrophysical objects and cosmological scenarios.
  • Understanding the mathematical framework of these geometries is essential for theoretical advancements.

Purpose of the Study:

  • To develop and analyze spherically symmetric geometries within F(T) teleparallel gravity.
  • To derive and solve the field equations for these geometries, including specific symmetry conditions.
  • To investigate new solutions, particularly in vacuum spacetimes.

Main Methods:

  • Expressing general forms for spherically symmetric frames and spin connections.
  • Analyzing antisymmetric and symmetric field equations in F(T) gravity.
  • Investigating specific subcases with additional affine symmetries, reducing equations to ordinary differential equations.
  • Solving field equations for static, Kantowski-Sachs, and similarity affine vector cases.

Main Results:

  • General forms for spherically symmetric frames and spin connections were derived.
  • Antisymmetric and symmetric field equations were analyzed, yielding new vacuum spacetime solutions.
  • Three subcases with enhanced symmetries were studied, simplifying the field equations.

Conclusions:

  • The study successfully developed and analyzed spherically symmetric geometries in F(T) teleparallel gravity.
  • New vacuum solutions were obtained, contributing to the understanding of gravitational models.
  • The application of affine symmetries provides a pathway to solvable models in teleparallel gravity.