The Hamilton equations in $f(T)$ teleparallel gravity and in New General Relativity

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Summary

The paper presents the Hamiltonian and Hamilton equations for extended teleparallel theories of gravity, including f(T) gravity and New General Relativity (NGR), in both covariant and Weitzenbo¨ck gauge formulations.

Highlights

• The Hamiltonian for f(T) gravity is derived in the covariant formulation and Weitzenbo¨ck gauge.
• The Hamilton equations for f(T) gravity are presented in both formulations.
• The Hamiltonian for NGR is derived in the covariant formulation and Weitzenbo¨ck gauge.
• The Hamilton equations for NGR are presented in both formulations.
• The results are compared with TEGR and f(R) gravity.
• The implications for numerical relativity and the study of gravitational waves are discussed.
• The covariant formulation is argued to be more fundamental and useful for certain applications.

Key Insights

• The Hamiltonian for f(T) gravity in the covariant formulation is given by Eq. (53), which includes the scalar field φ and its conjugate momentum π.
• The Hamilton equations for f(T) gravity in the covariant formulation are given by Eqs. (56)-(65), which describe the time evolution of the fields and their conjugate momenta.
• The Hamiltonian for NGR in the covariant formulation is given by Eq. (76), which includes the parameter ρ and the conjugate momenta π.
• The Hamilton equations for NGR in the covariant formulation are given by Eqs. (77)-(85), which describe the time evolution of the fields and their conjugate momenta.
• The Weitzenbo¨ck gauge formulation simplifies the Hamiltonian and Hamilton equations for both f(T) gravity and NGR.
• The covariant formulation is more fundamental and useful for certain applications, such as numerical relativity and the study of gravitational waves.
• The results have implications for our understanding of the gravitational force and the behavior of gravity in different regimes.

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Citation

Bajardi, F., Blixt, D., & Capozziello, S. (2024). The Hamilton equations in $f(T)$ teleparallel gravity and in New General Relativity (Version 1). arXiv. https://doi.org/10.48550/ARXIV.2412.20592