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Lovelock gravity from entropic force

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Abstract

In this paper, we first generalize the formulation of entropic gravity to (\(n+1\))-dimensional spacetime and derive Newton’s law of gravity and Friedmann equation in arbitrary dimensions. Then, we extend the discussion to higher order gravity theories and propose an entropic origin for Gauss–Bonnet gravity and more general Lovelock gravity in arbitrary dimensions. As a result, we are able to derive Newton’s law of gravitation as well as the corresponding Friedmann equations in these gravity theories. This procedure naturally leads to a derivation of the higher dimensional gravitational coupling constant of Friedmann/Einstein equation which is in complete agreement with the results obtained by comparing the weak field limit of Einstein equation with Poisson equation in higher dimensions. Our strategy is to start from first principles and assuming the entropy associated with the apparent horizon given by the expression previously known via black hole thermodynamics, but replacing the horizon radius \(r_+\) with the apparent horizon radius \(R\). Our study shows that the approach presented here is powerful enough to derive the gravitational field equations in any gravity theory and further supports the viability of Verlinde’s proposal.

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Acknowledgments

We are grateful to the referees for very constructive comments which helped us to improve the paper significantly. We also acknowledge the Research Council of Shiraz University. The work of A Sheykhi has been financially supported by the Research Institute for Astronomy and Astrophysics of Maragha (RIAAM), Iran.

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Authors and Affiliations

  1. Physics Department and Biruni Observatory, College of Sciences, Shiraz University, 71454, Shiraz, Iran

    A. Sheykhi & H. Moradpour

  2. Physics Department, Shahid Beheshti University, 19839, Tehran, Evin, Iran

    N. Riazi

  3. Research Institute for Astronomy and Astrophysics of Maragha (RIAAM), P. O. Box 55134-441, Maragha, Iran

    A. Sheykhi

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  1. A. Sheykhi
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Correspondence to A. Sheykhi.

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Sheykhi, A., Moradpour, H. & Riazi, N. Lovelock gravity from entropic force. Gen Relativ Gravit 45, 1033–1049 (2013). https://doi.org/10.1007/s10714-013-1509-x

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