1998/07/17 by Wolfgang Kummer, W. Kummer, G. Tieber · 1 citation
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Classical mechanics #Conservation law #Conserved current #Conserved quantity #Cosmology and Gravitation Theories #Covariant transformation #Geometry #Lagrangian #Mathematical physics #Mathematics #Noether's theorem #Noncommutative and Quantum Gravity Theories #Physics #Quantum mechanics #Symmetry (geometry) #Theoretical physics #hep-th
paper · pdf · doi:10.1103/physrevd.59.044001
published as Phys. Rev. D 59, 044001 (1998) · 30
arxiv created 1998/07/17 · openalex publication_date 1998/12/31 · openalex created_date 2016/06/24 · arxiv updated 2016/08/24 · openalex updated_date 2026/08/05
It is well known that all 2D models of gravity---including theories with nonvanishing torsion and dilaton theories---can be solved exactly, if matter interactions are absent. An absolutely (in space and time) conserved quantity determines the global classification of all (classical) solutions. For the special case of spherically reduced Einstein gravity it coincides with the mass in the Schwarzschild solution. The corresponding Noether symmetry has been derived previously by Widerin and one of the authors (W.K.) for a specific 2D model with nonvanishing torsion. In the present paper this is generalized to all covariant 2D theories, including interactions with matter. The related Noether-like symmetry differs from the usual one. The parameters for the symmetry transformation of the geometric part and those of the matter fields are distinct. The total conservation law (a zero-form current) results from a two-stage argument which also involves a consistency condition expressed by the conservation of a one-form matter ``current.'' The black hole is treated as a special case.