Schwarzschild-dS solution in modified teleparallel gravity theories

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A tetrad field, having one unknown function of radial coordinate r and an angle Φ which is a function of the azimuthal angle Φ, is applied to the field equation of modified teleparallel theory of gravity with cosmological constant. Exact vacuum solution is derived whose scalar torsion, T = Tα uv Suv α , (where Tα uv is the torsion tensor and Suv α is a tensor defined in terms of the contortion and torsion tensors), is vanishing. When the angle φ coincides with the polar angle (-φ), another solution is derived whose scalar torsion is constant. The space-time of the derived solutions is rewritten as a multiplication of two matrices: The first matrix is a special case of Euler's angle "so(3)" while the second matrix represents the square root of the spherically-symmetric-dS metric. © 2014 The Physical Society of Japan.

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