Abstract
In the string theory, all particles are tiny vibrating strings and each type of vibration corresponds to a different particle. From the divergence theorem on a geodesic surface, we obtain some relations between the length and the speed of a free falling closed string in a warped product space. In particular, we show that if the intrinsic length of the string is constant, then the speed of the corresponding particle should be smaller than 0.6, where the speed of light is 1. Also, we can find a condition for a timelike geodesic surface to be incomplete even if the space expands infinitely.
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Acknowledgements
This paper was written as part of Konkuk University’s research support program for its faculty on sabbatical leave in 2021 and was submitted during a sabbatical visit to KIAS. This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government(MSIT) (No. 2019R1F1A1042490).
Funding
This was supported by Basic Research Program in Science and Engineering through the National Research Foundation of Korea (NRF) funded by MSIT (NRF-2019R1F1A1042490).
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Paeng, SH. Length and speed of a string in a geodesic surface. Gen Relativ Gravit 54, 118 (2022). https://doi.org/10.1007/s10714-022-03005-3
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DOI: https://doi.org/10.1007/s10714-022-03005-3