Harmonic functions and gravity localization

G. Luca (Stanford Institute for Theoretical Physics, Stanford University, 382 Via Pueblo Mall, Stanford, CA, 94305, USA) ; Nicolò Ponti (Dipartimento di Matematica e Applicazioni, Università di Milano-Bicocca, Via Cozzi 55, Milano, 20126, Italy) ; Andrea Mondino (Mathematical Institute, University of Oxford, Andrew-Wiles Building, Woodstock Road, Oxford, OX2 6GG, UK) ; Alessandro Tomasiello (Dipartimento di Matematica e Applicazioni, Università di Milano-Bicocca, Via Cozzi 55, Milano, 20126, Italy; INFN, Sezione di Milano-Bicocca, Piazza della Scienza 3, Milano, 20126, Italia)

In models with extra dimensions, matter particles can be easily localized to a ‘brane world’, but gravitational attraction tends to spread out in the extra dimensions unless they are small. Strong warping gradients can help localize gravity closer to the brane. In this note we give a mathematically rigorous proof that the internal wave-function of the massless graviton is constant as an eigenfunction of the weighted Laplacian, and hence is a power of the warping as a bound state in an analogue Schrödinger potential. This holds even in presence of singularities induced by thin branes.

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      "value": "In models with extra dimensions, matter particles can be easily localized to a \u2018brane world\u2019, but gravitational attraction tends to spread out in the extra dimensions unless they are small. Strong warping gradients can help localize gravity closer to the brane. In this note we give a mathematically rigorous proof that the internal wave-function of the massless graviton is constant as an eigenfunction of the weighted Laplacian, and hence is a power of the warping as a bound state in an analogue Schr\u00f6dinger potential. This holds even in presence of singularities induced by thin branes."
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Published on:
20 September 2023
Publisher:
Springer
Published in:
Journal of High Energy Physics , Volume 2023 (2023)
Issue 9
Pages 1-41
DOI:
https://doi.org/10.1007/JHEP09(2023)127
arXiv:
2306.05456
Copyrights:
The Author(s)
Licence:
CC-BY-4.0

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