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Stable, thin wall, negative mass bubbles in de Sitter space-time

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Abstract

Negative mass makes perfect physical sense as long as the dominant energy condition is satisfied by the corresponding energy-momentum tensor. Heretofore, only configurations of negative mass had been found (Belletête and Paranjape in Int J Mod Phys D 22:1341017, 2013; Mbarek and Paranjape in Phys Rev D 90:101502, 2014), the analysis did not address stability or dynamics. In this paper, we analyze both of these criteria. We demonstrate the existence of stable, static, negative mass bubbles in an asymptotically de Sitter space-time. The bubbles are solutions of the Einstein equations and correspond to an interior region of space-time containing a specific mass distribution, separated by a thin wall from the exact, negative mass Schwarzschild-de Sitter space-time in the exterior. We apply the Israel junction conditions at the wall. For the case of an interior corresponding simply to de Sitter space-time with a different cosmological constant from the outside space-time, separated by a thin wall with energy density that is independent of the radius, we find static but unstable solutions which satisfy the dominant energy condition everywhere. The bubbles can collapse through spherically symmetric configurations to the exact, singular, negative mass Schwarzschild-de Sitter solution. Interestingly, this provides a counter-example of the cosmic censorship hypothesis. Alternatively, the junction conditions can be used to give rise to an interior mass distribution that depends on the potential for the radius of the wall. We show that for no choice of the potential, for positive energy density on the wall that is independent of the radius, can we get a solution that is non-singular at the origin. However, if we allow the energy density on the wall to depend on the radius of the bubble, we can find stable, static, non-singular solutions of negative mass which everywhere satisfy the dominant energy condition.

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Notes

  1. This is a novel property of negative mass Schwarzschild-de Sitter, implying that the entropy associated with the cosmological horizon can grow without bound. This can be contrasted with positive mass Schwarzschild-de Sitter, where the total entropy associated with the cosmological and black hole horizons is bounded by the magnitude of \(\Lambda \).

  2. We thank E. Wilson-Ewing for pointing this out to us.

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Acknowledgements

We thank Emil Mottola and Edward Wilson-Ewing for useful discussions. We thank NSERC of Canada for financial support and The Perimeter Institute for Theoretical Physics for hospitality. N. T. thanks to the Conicyt scholarship 21160064 and the University of Santiago de Chile. Research at Perimeter Institute is supported by the Government of Canada through the Department of Innovation, Science and Economic Development Canada and by the Province of Ontario through the Ministry of Research, Innovation and Science.

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Authors and Affiliations

  1. Groupe de physique des particules, Département de physique, Université de Montréal, C.P. 6128, succ. centre-ville, Montreal, QC, H3C 3J7, Canada

    M. B. Paranjape, Antoine Savard & Natalia Tapia-Arellano

  2. Centre de recherche mathématiques, Université de Montréal, Montreal, QC, Canada

    M. B. Paranjape

  3. Perimeter Institute for Theoretical Physics, 31 Caroline Street North, Waterloo, ON, N2L 2Y5, Canada

    Matthew C. Johnson & M. B. Paranjape

  4. Departamento de Fí sica, Universidad de Santiago de Chile, Avenida Ecuador 3493, Estaci-n Central, 9170124, Santiago, Chile

    Natalia Tapia-Arellano

  5. Department of Physics and Astronomy, 128 Petrie Science and Engineering Building, York University, 4700 Keele Street, Toronto, ON, M3J 1P3, Canada

    Matthew C. Johnson

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  1. Matthew C. Johnson
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Correspondence to M. B. Paranjape.

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Johnson, M.C., Paranjape, M.B., Savard, A. et al. Stable, thin wall, negative mass bubbles in de Sitter space-time. Gen Relativ Gravit 52, 80 (2020). https://doi.org/10.1007/s10714-020-02732-9

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