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PreprintCC BY 4.0arXiv

Holographic zeros and poles from apparent singularities

  • Edwan Préau
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Abstract

We study general holographic fluctuation equations with apparent singularities, and the associated spectral functions. We consider the regime where an apparent singularity approaches the boundary, for which the near-boundary behavior of solutions can be determined via an inner/outer matching type of calculation. Depending on properties of the equation, we find that the merging of an apparent singularity with the boundary may generate either a zero or a pole for the corresponding spectral function. Our results also indicate that the recently introduced holographic product formula still applies in the presence of apparent singularities.

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Cite

BibTeXRIS
BibTeX
@misc{preau2026holographic,
  title = {{Holographic zeros and poles from apparent singularities}},
  author = {Edwan Préau},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.03023},
  eprint = {2609.03023},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.03023},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Holographic zeros and poles from apparent singularities
AU  - Edwan Préau
PY  - 2026
DA  - 2026/09/02
PB  - arXiv
DO  - 10.48550/arxiv.2609.03023
UR  - https://arxiv.org/abs/2609.03023
AB  - We study general holographic fluctuation equations with apparent singularities, and the associated spectral functions. We consider the regime where an apparent singularity approaches the boundary, for which the near-boundary behavior of solutions can be determined via an inner/outer matching type of calculation. Depending on properties of the equation, we find that the merging of an apparent singularity with the boundary may generate either a zero or a pole for the corresponding spectral function. Our results also indicate that the recently introduced holographic product formula still applies in the presence of apparent singularities.
ER  -