Instability spectrum of gaussian potential wells: a toy model for scalar-tensor gravity

R. Ibadov, Sh. Najibullokhon

Samarqand davlat universiteti ilmiy tadqiqotlar axborotnomasi · 2025-yil

Annotatsiya

The stability analysis of solutions in alternative theories of gravity, such as scalar-tensor theories (STT), often leads to a Schrödinger-like equation governed by a complex effective potential. The properties of this potential's negative well are crucial for determining the existence and nature of instabilities. This paper presents a systematic methodological study of the instabilities driven by a simple, analytically manageable potential, using a Gaussian well as a "toy model". We specifically consider the context of two prominent STT models: the Brans-Dicke theory, characterized by a coupling f(ϕ) = ϕ, and a non-minimally coupled model with f(ϕ) = 1 – ξ ϕ2. We numerically solve the master equation for the Gaussian potential to explore how the instability spectrum (the eigenvalues Ω2 < 0) is fundamentally influenced by the geometric properties of the well, namely its depth, width, and asymmetry. We investigate the behavior of the leading unstable mode, the instability growth rates, and the emergence of a spectrum of higher, less unstable modes. While not tied to a specific physical solution, this detailed analysis of a toy model provides a robust qualitative framework and valuable physical intuition for understanding the complex stability properties of more realistic, numerically challenging systems in STT and other modified theories of gravity.

Maqola ma’lumotlari
MualliflarR. Ibadov, Sh. Najibullokhon
JurnalSamarqand davlat universiteti ilmiy tadqiqotlar axborotnomasi
NashriyotСамарқанд давлат университети
ISSN2091-5446, 2181-1296
Nashr sanasi2025-06-01
Jild5
Son1
Betlar33-45
TilIngliz
DOI10.59251/2181-3973.2025.v1.138.1.3576
Indeksga qo‘shilgan2026-09-02

DOI: 10.59251/2181-3973.2025.v1.138.1.3576 · Maqolaning asl sahifasi

Iqtibos keltirish

APAR. Ibadov, & Sh. Najibullokhon (2025). INSTABILITY SPECTRUM OF GAUSSIAN POTENTIAL WELLS: A TOY MODEL FOR SCALAR-TENSOR GRAVITY. Samarqand davlat universiteti ilmiy tadqiqotlar axborotnomasi, 5(1), 33-45. https://doi.org/10.59251/2181-3973.2025.v1.138.1.3576
GOST (OAK)R. Ibadov, Sh. Najibullokhon INSTABILITY SPECTRUM OF GAUSSIAN POTENTIAL WELLS: A TOY MODEL FOR SCALAR-TENSOR GRAVITY // Samarqand davlat universiteti ilmiy tadqiqotlar axborotnomasi. – 2025. – T. 5, № 1. – P. 33-45. – DOI: 10.59251/2181-3973.2025.v1.138.1.3576.
MLAR. Ibadov, and Sh. Najibullokhon. “INSTABILITY SPECTRUM OF GAUSSIAN POTENTIAL WELLS: A TOY MODEL FOR SCALAR-TENSOR GRAVITY.” Samarqand davlat universiteti ilmiy tadqiqotlar axborotnomasi, 5(1), 33-45, 2025. https://doi.org/10.59251/2181-3973.2025.v1.138.1.3576
ChicagoR. Ibadov, and Sh. Najibullokhon. “INSTABILITY SPECTRUM OF GAUSSIAN POTENTIAL WELLS: A TOY MODEL FOR SCALAR-TENSOR GRAVITY.” Samarqand davlat universiteti ilmiy tadqiqotlar axborotnomasi, 5(1), 33-45 (2025). https://doi.org/10.59251/2181-3973.2025.v1.138.1.3576
HarvardR. Ibadov, and Sh. Najibullokhon (2025) ‘INSTABILITY SPECTRUM OF GAUSSIAN POTENTIAL WELLS: A TOY MODEL FOR SCALAR-TENSOR GRAVITY’, Samarqand davlat universiteti ilmiy tadqiqotlar axborotnomasi, 5(1), 33-45. https://doi.org/10.59251/2181-3973.2025.v1.138.1.3576
BibTeX
@article{ribadov2025,
  title = {INSTABILITY SPECTRUM OF GAUSSIAN POTENTIAL WELLS: A TOY MODEL FOR SCALAR-TENSOR GRAVITY},
  author = {R. Ibadov and Sh. Najibullokhon},
  journal = {Samarqand davlat universiteti ilmiy tadqiqotlar axborotnomasi},
  year = {2025},
  volume = {5},
  number = {1},
  pages = {33-45},
  doi = {10.59251/2181-3973.2025.v1.138.1.3576},
  url = {https://doi.org/10.59251/2181-3973.2025.v1.138.1.3576}
}

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