Traversable Finslerian wormholes supported by phantom energy
Ksh. Newton Singh, Farook Rahaman, Debabrata Deb, S. K. Maurya
Abstract
This paper supplements the article (Eur. Phys. J. C 76: 246, 2016) by extending some more new wormhole solutions in the background of Finslerian geometry. Here, we present six more solutions by considering i) a linear equation of state (EoS) p r = ωρ and three different shape functions, ii) a linear relationship between radial and tangential pressure as p t = np r with two different redshift functions and iii) a specific density profile with a linear equation of state p r = ωρ . It is found that all these wormholes are violating null energy condition (NEC) signifying that the throats are opened by exotic matters. Since the equation of state parameters, ω or ω r = p r / ρ for all the solutions are <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m1"><mml:mo><</mml:mo><mml:mo>−</mml:mo><mml:mn>1</mml:mn></mml:math> , the corresponding exotic matter is none other than the phantom energy. Further, the two solutions in Case ii) are not asymptotically flat since <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m2"><mml:msub><mml:mrow><mml:mi>lim</mml:mi></mml:mrow><mml:mrow><mml:mi>r</mml:mi><mml:mo>→</mml:mo><mml:mi>∞</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo stretchy="false">[</mml:mo><mml:mrow><mml:mi>b</mml:mi><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mi>r</mml:mi></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:mrow><mml:mo>/</mml:mo><mml:mi>r</mml:mi></mml:mrow><mml:mo stretchy="false">]</mml:mo></mml:mrow><mml:mo>↛</mml:mo><mml:mn>0</mml:mn></mml:math> . To make it asymptotically flat we matched it with the Schwarzschild vacuum.