Traversable wormholes in $$R+\alpha R^n$$ gravity
Nisha Godani, Gauranga C. Samanta
Abstract
Abstract In this work, the study of traversable wormholes in f ( R ) gravity with the function $$f(R)=R+\alpha R^n$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>f</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>R</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mi>R</mml:mi><mml:mo>+</mml:mo><mml:mi>α</mml:mi><mml:msup><mml:mi>R</mml:mi><mml:mi>n</mml:mi></mml:msup></mml:mrow></mml:math> , where $$\alpha $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>α</mml:mi></mml:math> and n are arbitrary constants, is taken into account. The shape function $$b(r)=\frac{r}{\exp (r-r_0)}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>b</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>r</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mfrac><mml:mi>r</mml:mi><mml:mrow><mml:mo>exp</mml:mo><mml:mo>(</mml:mo><mml:mi>r</mml:mi><mml:mo>-</mml:mo><mml:msub><mml:mi>r</mml:mi><mml:mn>0</mml:mn></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:mfrac></mml:mrow></mml:math> , proposed by Samanta et al. ( arXiv:1811.06834v1 [gr-qc], 2018), is considered. The energy conditions with respect to both constant and variable redshift functions are discussed and the existence of wormhole solutions without presence of exotic matter is investigated.