Extended Generalized Uncertainty Principle: Mathematical Framework for Astrophysical Applications

Authors

Abstract

We present a comprehensive mathematical framework for extended Generalized Uncertainty Principle (GUP) formulations and their systematic application to astrophysical systems. Through rigorous dimensional analysis and comparative evaluation of competing theoretical models, we establish a unified approach for incorporating quantum gravity effects into macroscopic astronomical observations. Our analysis reveals fundamental scaling relationships between microscopic quantum gravity parameters and observable astrophysical phenomena, providing the theoretical foundation for observational constraints on minimal length scales. The framework developed here offers a systematic methodology for translating Planck-scale physics into testable predictions for neutron star structure, black hole thermodynamics, and gravitational wave signatures. We demonstrate that while individual quantum gravity corrections appear negligible, their cumulative effects in extreme astrophysical environments can potentially reach observational thresholds, particularly in gravitational wave observations of binary neutron star mergers, where tidal deformability measurements offer unprecedented sensitivity to the underlying equation of state modifications.

Dimensions

Abbott, B. P., et al. (2017). GW170817: Observation of gravitational waves from a binary neutron star inspiral. Physical Review Letters, 119(16), 161101. https://doi.org/10.1103/PhysRevLett.119.161101 DOI: https://doi.org/10.1103/PhysRevLett.119.161101

Ali, A. F., & Wojnar, A. (2024). A covariant tapestry of linear GUP, metric-affine gravity, their Poincar´e algebra and entropy bound. Classical and Quantum Gravity, 41(10), 105001. DOI: https://doi.org/10.1088/1361-6382/ad3ac7

Amati, D., Ciafaloni, M., & Veneziano, G. (1989). Can spacetime be probed below the string size? Physics Letters B, 216(1-2), 41-47. https://doi.org/10.1016/0370-2693(89)91366-X DOI: https://doi.org/10.1016/0370-2693(89)91366-X

Ashtekar, A., & Lewandowski, J. (2004). Background independent quantum gravity: A status report. Classical and Quantum Gravity, 21(15), R53-R152. https://doi.org/10.1088/0264-9381/21/15/R01 DOI: https://doi.org/10.1088/0264-9381/21/15/R01

Battista, E., Capozziello, S., & Errehymy, A. (2024). Generalized uncertainty principle corrections in Rastall–Rainbow Casimir wormholes. European Physical Journal C, 84, 1314. https://doi.org/10.1140/epjc/s10052-024-13273-7 DOI: https://doi.org/10.1140/epjc/s10052-024-13656-y

Bernaldez, J. P. R., Abac, A. G., & Otadoy, R. E. S. (2023). Radial oscillations and dynamical instability analysis for linear-quadratic GUP-modified white dwarfs. International Journal of Modern Physics D, 32(14), 2350095. https://doi.org/10.1142/S0218271823500955 DOI: https://doi.org/10.2139/ssrn.4434868

Bizet, N. C., Obreg´on, O., & Yupanqui, W. (2023). Modified entropies as the origin of generalized uncertainty principles. Physics Letters B, 836, 137636. https://doi.org/10.1016/j.physletb.2022.137636 DOI: https://doi.org/10.1016/j.physletb.2022.137636

Brown, S. M. (2022). Tidal deformability of neutron stars in scalar-tensor theories of gravity. Physical Review D, 108, 124032. https://doi.org/10.1103/PhysRevD.108.124032 DOI: https://doi.org/10.1103/PhysRevD.108.124073

Casadio, R., Giugno, A., Giusti, A., & Faizal, M. (2014). Quantum corrections to the thermodynamics of black holes. Classical and Quantum Gravity, 31, 045016. https://doi.org/10.1088/0264-9381/31/4/045016 DOI: https://doi.org/10.1088/0264-9381/31/4/045016

Chatziioannou, K., Haster, C. J., & Zimmerman, A. (2018). Measuring the neutron star tidal deformability with equation-of-state-independent relations and gravitational waves. Physical Review D, 97(10), 104036. https://doi.org/10.1103/PhysRevD.97.104036 DOI: https://doi.org/10.1103/PhysRevD.97.104036

Feng, Z. W., Yang, S. Z., Li, H. L., & Zu, X. T. (2016). Quantum corrections to the thermodynamics of Schwarzschild-Tangherlini black hole and the generalized uncertainty principle. European Physical Journal C, 76, 212. https://doi.org/10.1140/epjc/s10052-016-4057-1 DOI: https://doi.org/10.1140/epjc/s10052-016-4057-1

Gross, D. J., & Mende, P. F. (1988). String theory beyond the Planck scale. Nuclear Physics B, 303(3), 407-454. https://doi.org/10.1016/0550-3213(88)90390-2 DOI: https://doi.org/10.1016/0550-3213(88)90390-2

Hossenfelder, S. (2013). Minimal length scale scenarios for quantum gravity. Living Reviews in Relativity, 16(1), 2. https://doi.org/10.12942/lrr-2013-2 DOI: https://doi.org/10.12942/lrr-2013-2

Jizba, P., Lambiase, G., Luciano, G. G., & Petruzziello, L. (2023). Coherent states for generalized uncertainty relations as Tsallis probability amplitudes: New route to nonextensive thermostatistics. Physical Review D, 108(6), 066005. DOI: https://doi.org/10.1103/PhysRevD.108.064024

https://doi.org/10.1103/PhysRevD.108.066005 DOI: https://doi.org/10.1103/PhysRevD.108.066005

Kempf, A., Mangano, G., & Mann, R. B. (1995). Hilbert space representation of the minimal length uncertainty relation. Physical Review D, 52(2), 1108-1118. https://doi.org/10.1103/PhysRevD.52.1108 DOI: https://doi.org/10.1103/PhysRevD.52.1108

Kim, Y. M., Kwak, K., Hyun, C. H., et al. (2020). Neutron star equation of state and tidal deformability with nuclear energy density functionals. European Physical Journal A, 56, 157. https://doi.org/10.1140/epja/s10050-020-00166-6 DOI: https://doi.org/10.1140/epja/s10050-020-00164-2

Leung, K. L., Chu, M. C., & Lin, L. M. (2022). Tidal deformability of dark matter admixed neutron stars. Physical Review D, 105, 123010. https://doi.org/10.1103/PhysRevD.105.123010 DOI: https://doi.org/10.1103/PhysRevD.105.123010

L´opez-Aguayo, O., & Sabido, M. (2023). On the generalized uncertainty principle and cosmology. Physical Review D, 107, 064010. https://doi.org/10.1103/PhysRevD.107.064010 DOI: https://doi.org/10.1103/PhysRevD.107.064010

Maggiore, M. (1993). A generalized uncertainty principle in quantum gravity. Physics Letters B, 304(1-2), 65-69. https://doi.org/10.1016/0370-2693(93)91401-8 DOI: https://doi.org/10.1016/0370-2693(93)91401-8

Moussa, M. (2015). Effect of generalized uncertainty principle on main-sequence stars and white dwarfs. Advances in High Energy Physics, 2015, 343284. https://doi.org/10.1155/2015/343284 DOI: https://doi.org/10.1155/2015/343284

Pacho l, A. (2024). Generalized extended uncertainty principles, Liouville theorem and density of states: Snyder-de Sitter and Yang models. Nuclear Physics B, 1006, 116771. https://doi.org/10.1016/j.nuclphysb.2024.116771 DOI: https://doi.org/10.1016/j.nuclphysb.2024.116771

Pantig, R. C., Lambiase, G., ¨Ovg¨un, A., & Lobos, N. J. L. S. (2025). Spacetime- Curvature induced uncertainty principle: Linking the large-structure global effects to the local black hole physics. Physics of the Dark Universe, 47, 101489. https://doi.org/10.1016/j.dark.2024.101489 DOI: https://doi.org/10.1016/j.dark.2025.101817

Parsamehr, S. (2025). Research Paper: The effect of the generalized uncertainty principle with maximum length on the size of white dwarfs. Iranian Journal of Applied Physics, 15(1), 35-50.

Pourhassan, B., Faizal, M., & Capozziello, S. (2017). Quantum loop corrections of a charged de Sitter black hole. Annals of Physics, 377, 108-116. https://doi.org/10.1016/j.aop.2016.11.014 DOI: https://doi.org/10.1016/j.aop.2016.11.014

Raithel, C., ¨Ozel, F., & Psaltis, D. (2018). Tidal deformability from GW170817 as a direct probe of the neutron star radius. Astrophysical Journal Letters, 857(2), L23. https://doi.org/10.3847/2041-8213/aabcbf DOI: https://doi.org/10.3847/2041-8213/aabcbf

Scardigli, F. (1999). Generalized uncertainty principle in quantum gravity from micro-black hole gedanken experiment. Physics Letters B, 452(1-2), 39-44. https://doi.org/10.1016/S0370-2693(99)00167-7 DOI: https://doi.org/10.1016/S0370-2693(99)00167-7

Song, J. J., & Liu, C. Z. (2024). Thermodynamics in a quantum corrected Reiss-ner–Nordstr¨om–AdS black hole and its GUP-corrections. Chinese Physics C, 48(7), 075101. https://doi.org/10.1088/1674-1137/ad4267 DOI: https://doi.org/10.1088/1674-1137/ad4267

Tang, M. (2024). Weak cosmic censorship conjecture and black hole shadow for black hole with generalized uncertainty principle. European Physical Journal C, 84(4), 396. https://doi.org/10.1140/epjc/s10052-024-12761-0 DOI: https://doi.org/10.1140/epjc/s10052-024-12641-9

Tawfik, A. N., & Diab, A. M. (2015). Review on generalized uncertainty principle. Reports on Progress in Physics, 78(12), 126001. https://doi.org/10.1088/0034-4885/78/12/126001 DOI: https://doi.org/10.1088/0034-4885/78/12/126001

Wagner, F., Var˜ao, G., Lobo, I. P., & Bezerra, V. B. (2023). Quantum-spacetime effects on nonrelativistic Schr¨odinger evolution. Physical Review D, 108(6), 066002. https://doi.org/10.1103/PhysRevD.108.066002 DOI: https://doi.org/10.1103/PhysRevD.108.066008

Wani, S. S., Al-Kuwari, S., Shi, X., Chen, Y., & Naqash, A. A. (2024). Unveiling phase space modifications: A clash of modified gravity and the generalized uncertainty principle. Europhysics Letters, 144(6), 69001. https://doi.org/10.1209/0295-5075/ad8a0a

Zhang, X. (2023). Loop quantum black hole. Universe, 9(7), 313. https://doi.org/10.3390/universe9070313 DOI: https://doi.org/10.3390/universe9070313

Published

2025-06-30

How to Cite

Extended Generalized Uncertainty Principle: Mathematical Framework for Astrophysical Applications. (2025). Nigerian Journal of Theoretical and Environmental Physics, 3(2), 95-103. https://doi.org/10.62292/njtep.v3i2.2025.88

Issue

Vol. 3 No. 2 (2025): Nigerian Journal of Theoretical and Environmental Physics - Vol. 3 No. 2

Section

Articles
Copyright & Licensing

How to Cite

Extended Generalized Uncertainty Principle: Mathematical Framework for Astrophysical Applications. (2025). Nigerian Journal of Theoretical and Environmental Physics, 3(2), 95-103. https://doi.org/10.62292/njtep.v3i2.2025.88

Most read articles by the same author(s)