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A new class of solutions that are curved in 4D but flat in 5D

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Abstract

We present four new solutions of the vacuum field equations that are flat in five dimensions, but curved in four. Two are wave-like in three-dimensional space with a wavelength related to the cosmological constant. The other two are spherically symmetric in three-dimensional space and reduce to the standard Schwarzschild metric in appropriate limits. Solutions like these could be used to test for an extra dimension.

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Acknowledgements

We are grateful to Alex Silbergleit for his comments on an early draft of this work. This research was supported by the the Maryland Space Grant Consortium and the Fisher College of Science and Mathematics at Towson University.

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Authors and Affiliations

  1. Department of Physics, Astronomy and Geosciences, Towson University, Towson, MD, USA

    James Overduin, Jonathan Perry & Azriel Weinreb

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  1. James Overduin
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  2. Jonathan Perry
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  3. Azriel Weinreb
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Correspondence to James Overduin.

Additional information

The above results grew out of notes left behind by the late Paul S. Wesson, to whom we dedicate this paper.

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Overduin, J., Perry, J. & Weinreb, A. A new class of solutions that are curved in 4D but flat in 5D. Gen Relativ Gravit 54, 8 (2022). https://doi.org/10.1007/s10714-021-02892-2

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