Wormhole solutions with a polynomial equation-of-state and minimal violation of the null energy condition

Abstract This paper discusses wormholes supported by general equation-of-state , resulting in a significant combination of the linear equation-of-state and some other models. Wormhole with a quadratic equation-of-state is studied as a particular example. It is shown that the violation of null energy condition is restricted to some regions in the vicinity of the throat. The combination of barotropic and polytropic equation-of-state has been studied. We consider fluid near the wormhole throat in an exotic regime which at some $$r=r_{1}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>r</mml:mi><mml:mo>=</mml:mo><mml:msub><mml:mi>r</mml:mi><mml:mn>1</mml:mn></mml:msub></mml:mrow></mml:math> , the exotic regime is connected to a distribution of asymptotically dark energy regime with $$-1&lt;\omega &lt;-1/3$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mo>-</mml:mo><mml:mn>1</mml:mn><mml:mo>&lt;</mml:mo><mml:mi>ω</mml:mi><mml:mo>&lt;</mml:mo><mml:mo>-</mml:mo><mml:mn>1</mml:mn><mml:mo>/</mml:mo><mml:mn>3</mml:mn></mml:mrow></mml:math> . We have presented wormhole solutions with small amount of exotic matter. We have shown that using different forms of equation-of-state has a considerable effect on the minimizing violation of the null energy condition. The effect of many parameters such as redshift as detected by a distant observer and energy density at the throat on the $$r_1$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>r</mml:mi><mml:mn>1</mml:mn></mml:msub></mml:math> is investigated. The solutions are asymptotically flat and compatible with presently available observational data at the large cosmic scale.

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