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Thermodynamics of Evolving Lorentzian Wormhole at Apparent and Event Horizons

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Abstract

We have investigated the non-static Lorentzian Wormhole model in presence of anisotropic pressure. We have presented some exact solutions of Einstein equations for anisotropic pressure case. Introducing two EoS parameters we have shown that these solutions give very rich dynamics of the universe yielding to the different expansion history of it in the r - direction and in the T - direction. The corresponding explicit forms of the shape function b(r) is presented.We have shown that the Einstein’s field equations and unified first law are equivalent for the dynamical wormhole model. The first law of thermodynamics has been derived by using the Unified first law. The physical quantities including surface gravity and the temperature are derived for the wormhole. Here we have obtained all the results without any choice of the shape function. The validity of generalized second law (GSL) of thermodynamics has been examined at apparent and event horizons for the evolving Lorentzian wormhole.

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Acknowledgments

One of the author (UD) is thankful to IUCAA, Pune, India for warm hospitality where part of the work was carried out. M. Jamil would like to thank the Abdus Salam International Center for Theoretical Physics (ICTP) for its kind hospitality during which part of this work was completed.

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Authors and Affiliations

  1. Department of Mathematics, Bengal Engineering and Science University, Shibpur, Howrah, 711 103, India

    Ujjal Debnath

  2. Center for Advanced Mathematics and Physics, National University of Sciences and Technology, Islamabad, Pakistan

    Mubasher Jamil & M. Akbar

  3. Eurasian International Center for Theoretical Physics, Eurasian National University, Astana, 010008, Kazakhstan

    Mubasher Jamil & Ratbay Myrzakulov

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  1. Ujjal Debnath
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  2. Mubasher Jamil
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  3. Ratbay Myrzakulov
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  4. M. Akbar
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Correspondence to Ujjal Debnath.

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Debnath, U., Jamil, M., Myrzakulov, R. et al. Thermodynamics of Evolving Lorentzian Wormhole at Apparent and Event Horizons. Int J Theor Phys 53, 4083–4094 (2014). https://doi.org/10.1007/s10773-014-2159-9

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