Raychaudhuri Equations, Tidal Forces, and the Weak-Field Limit in Schwarzshild–Finsler–Randers Spacetime
Abstract
:1. Introduction
2. Geometrical Structure of the Model
2.1. The Lorentz Tangent Bundle
2.1.1. The Adapted Basis
2.1.2. Metric Structure on TM
- F is continuous on and smooth on , i.e., the tangent bundle minus the null set .
- F is positively homogeneous to the first degree on its second argument:
- The form
2.1.3. Connection
2.1.4. Curvature and Torsion
2.1.5. Hilbert-like Action
2.2. The SFR Model
2.3. The Newtonial Limit
3. Generalized Deviation of Geodesics and Paths
3.1. General Equations
3.2. Application of the Weak-Field Limit
3.3. The Schwarzschild–Finsler–Randers spacetime
4. Generalized Raychaudhuri Equations
4.1. Horizontal Equations
4.2. Vertical Equations
4.3. Application to the SFR Model
5. Discussion and Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
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Triantafyllopoulos, A.; Kapsabelis, E.; Stavrinos, P.C. Raychaudhuri Equations, Tidal Forces, and the Weak-Field Limit in Schwarzshild–Finsler–Randers Spacetime. Universe 2024, 10, 26. https://doi.org/10.3390/universe10010026
Triantafyllopoulos A, Kapsabelis E, Stavrinos PC. Raychaudhuri Equations, Tidal Forces, and the Weak-Field Limit in Schwarzshild–Finsler–Randers Spacetime. Universe. 2024; 10(1):26. https://doi.org/10.3390/universe10010026
Chicago/Turabian StyleTriantafyllopoulos, Alkiviadis, Emmanuel Kapsabelis, and Panayiotis C. Stavrinos. 2024. "Raychaudhuri Equations, Tidal Forces, and the Weak-Field Limit in Schwarzshild–Finsler–Randers Spacetime" Universe 10, no. 1: 26. https://doi.org/10.3390/universe10010026