Stable, thin wall, negative mass bubbles in de Sitter space-time
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Stable, thin wall, negative mass bubbles in de Sitter space-time Matthew C. Johnson3,5 · M. B. Paranjape1,2,3 Natalia Tapia-Arellano1,4
· Antoine Savard1 ·
Received: 19 May 2020 / Accepted: 14 August 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
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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M. B. Paranjape [email protected]
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1 Introduction The Schwarzschild metric is a solution of the vacuum Einstein equations with one parameter, the mass. It is a solution of the Einstein equations for any value of the mass, including negative mass. However it is a singular solution, the singularity residing at the origin of the coordinate system. The singularity means that in some sense the solution actually contains a source, a singular source located at the position of the singularity. The positive mass singularity is hidden behind an event horizon while the negative mass singularity is naked. Smoothing out the singularity corresponds to adding an energy-momentum source to the space-time. The smo
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