ISSN2320-2882
Impact Factor9.17
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ESTD2013
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Paper Title
Cauchy's Principle and the Relativistic Cauchy Problem: Mathematical Foundations, Physical Implications, and the Role of Determinism in Spacetime Theories
Authors
Dr. Noruddin Ansari
Keywords
Cauchy problem; relativity; hyperbolic partial differential equations; initial value formulation; ADM formalism; constraint equations; global hyperbolicity; Cauchy horizons; determinism; cosmic censorship
Abstract
This article provides a comprehensive examination of Cauchy's principle in the context of special and general relativity, tracing its origins from classical partial differential equations to its modern role in the formulation of deterministic spacetime evolution. We review the mathematical structure of the Cauchy problem, including PDE classification, constraint equations, and well-posedness criteria, before applying these concepts to relativistic field theories. In special relativity, the principle manifests in Lorentz-invariant hyperbolic systems, ensuring consistent propagation of initial data across inertial frames. In general relativity, the interplay between the Einstein field equations, foliation techniques, and gauge choices defines a more intricate Cauchy problem, where spacetime geometry itself is a dynamical variable. We analyze the ADM decomposition, constraint propagation, and the implications of local versus global hyperbolicity, emphasizing the physical significance of domains of dependence and Cauchy horizons. The discussion connects these mathematical results to the principles of relativity, determinism, and cosmic censorship, situating Cauchy's principle at the core of modern theoretical physics.
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IJCRT — journal style
"Cauchy's Principle and the Relativistic Cauchy Problem: Mathematical Foundations, Physical Implications, and the Role of Determinism in Spacetime Theories", IJCRT - International Journal of Creative Research Thoughts (www.ijcrt.org), ISSN:2320-2882, Vol.13, Issue 10, page no.c639-c649, October 2025, Available :https://ijcrt.org/papers/IJCRT2510314.pdf
APA — 7th edition
Ansari, N. (2025). Cauchy's Principle and the Relativistic Cauchy Problem: Mathematical Foundations, Physical Implications, and the Role of Determinism in Spacetime Theories. International Journal of Creative Research Thoughts, 13(10), c639-c649. https://ijcrt.org/viewpaperforall.php?paper=IJCRT2510314
MLA — 9th edition
Ansari, Noruddin. "Cauchy's Principle and the Relativistic Cauchy Problem: Mathematical Foundations, Physical Implications, and the Role of Determinism in Spacetime Theories." International Journal of Creative Research Thoughts, vol. 13, no. 10, 2025, pp. c639-c649, https://ijcrt.org/viewpaperforall.php?paper=IJCRT2510314.
Chicago — 17th, bibliography
Ansari, Noruddin. "Cauchy's Principle and the Relativistic Cauchy Problem: Mathematical Foundations, Physical Implications, and the Role of Determinism in Spacetime Theories." International Journal of Creative Research Thoughts 13, no. 10 (2025): c639-c649. https://ijcrt.org/viewpaperforall.php?paper=IJCRT2510314.
Harvard — author–date
Ansari, N. (2025) 'Cauchy's Principle and the Relativistic Cauchy Problem: Mathematical Foundations, Physical Implications, and the Role of Determinism in Spacetime Theories', International Journal of Creative Research Thoughts, 13(10), pp. c639-c649. Available at: https://ijcrt.org/viewpaperforall.php?paper=IJCRT2510314
IEEE — numbered reference
N. Ansari, "Cauchy's Principle and the Relativistic Cauchy Problem: Mathematical Foundations, Physical Implications, and the Role of Determinism in Spacetime Theories," IJCRT, vol. 13, no. 10, pp. c639-c649, Oct. 2025.
Vancouver — biomedical
Ansari N. Cauchy's Principle and the Relativistic Cauchy Problem: Mathematical Foundations, Physical Implications, and the Role of Determinism in Spacetime Theories. IJCRT. 2025 Oct;13(10):c639-c649.
AMA — 11th edition
Ansari N. Cauchy's Principle and the Relativistic Cauchy Problem: Mathematical Foundations, Physical Implications, and the Role of Determinism in Spacetime Theories. IJCRT. 2025;13(10):c639-c649. Accessed at https://ijcrt.org/viewpaperforall.php?paper=IJCRT2510314
BibTeX — Zotero, Mendeley, LaTeX
@article{IJCRT2510314,
author = {Noruddin Ansari},
title = {Cauchy's Principle and the Relativistic Cauchy Problem: Mathematical Foundations, Physical Implications, and the Role of Determinism in Spacetime Theories},
journal = {International Journal of Creative Research Thoughts},
volume = {13},
number = {10},
pages = {c639-c649},
year = {2025},
month = {October},
issn = {2320-2882},
url = {https://ijcrt.org/viewpaperforall.php?paper=IJCRT2510314}
}
RIS — EndNote, RefWorks
TY - JOUR
AU - Ansari, Noruddin
TI - Cauchy's Principle and the Relativistic Cauchy Problem: Mathematical Foundations, Physical Implications, and the Role of Determinism in Spacetime Theories
T2 - International Journal of Creative Research Thoughts
JA - IJCRT
VL - 13
IS - 10
PY - 2025
SN - 2320-2882
UR - https://ijcrt.org/viewpaperforall.php?paper=IJCRT2510314
SP - c639-c649
ER -
Issue
Volume 13 Issue 10,
October-2025
Pages : c639-c649
Article Information
- Published In
- International Journal of Creative Research Thoughts — Volume 13, Issue 10, October 2025
- Pages
- c639-c649
- Published
- October 2025
- Registration ID
- IJCRT_295017
- Published Paper ID
- IJCRT2510314
- Research Area
- Mathematics All
- Author Type
- Indian Author
- Location
- patna, bihar, India
- Peer Review
- Request Peer Review Report
- Licence
- CC BY 4.0 · Open Access
- ISSN & Impact Factor
- 2320-2882 · IF 9.17
- Downloads
- 153
- Permanent Link
- https://ijcrt.org/viewpaperforall.php?paper=IJCRT2510314
- Published Paper PDF
- https://ijcrt.org/papers/IJCRT2510314.pdf
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International Journal of Creative Research Thoughts
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