2020/10/31 by Sinya Aoki, T. Onogi, Tetsuya Onogi +1 · 2 citations
Physics and Astronomy · #Black Holes and Theoretical Physics #Black hole thermodynamics #Charge (physics) #Charge conservation #Classical mechanics #Conservation law #Conserved quantity #Cosmology and Gravitation Theories #Entropy (arrow of time) #General relativity #Gravitation #Gravitational energy #Gravitational field #Mathematical physics #Physics #Quantum Electrodynamics and Casimir Effect #Quantum mechanics #Theoretical physics #cond-mat.stat-mech #gr-qc #hep-ph #hep-th
paper · pdf · open access · doi:10.1142/s0217751x21502018
published in International Journal of Modern Physics A 36(29) (World Scientific) · 14 pages, 2 figures, published version
openalex publication_date 2021/10/20 · arxiv created 2021/12/02 · arxiv updated 2021/12/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We propose a new class of vector fields to construct a conserved charge in a general field theory whose energy–momentum tensor is covariantly conserved. We show that there always exists such a vector field in a given field theory even without global symmetry. We also argue that the conserved current constructed from the (asymptotically) timelike vector field can be identified with the entropy current of the system. As a piece of evidence we show that the conserved charge defined therefrom satisfies the first law of thermodynamics for an isotropic system with a suitable definition of temperature. We apply our formulation to several gravitational systems such as the expanding universe, Schwarzschild and Banãdos, Teitelboim and Zanelli (BTZ) black holes, and gravitational plane waves. We confirm the conservation of the proposed entropy density under any homogeneous and isotropic expansion of the universe, the precise reproduction of the Bekenstein–Hawking entropy incorporating the first law of thermodynamics, and the existence of gravitational plane wave carrying no charge, respectively. We also comment on the energy conservation during gravitational collapse in simple models.