Conserved current for the Cotton tensor, black hole entropy and equivariant Pontryagin forms

Abstract

The Chern-Simons lagrangian density in the space of metrics of a 3-dimensional manifold M is not invariant under the action of diffeomorphisms on M. However, its Euler-Lagrange operator can be identified with the Cotton tensor, which is invariant under diffeomorphims. As the lagrangian is not invariant, Noether Theorem cannot be applied to obtain conserved currents. We show that it is possible to obtain an equivariant conserved current for the Cotton tensor by using the first equivariant Pontryagin form on the bundle of metrics. Finally we define a hamiltonian current which gives the contribution of the Chern-Simons term to the black hole entropy, energy and angular momentum.

13 pages

References in corpus (5)

• Black Hole Entropy in the presence of Chern-Simons Terms
• BTZ Black Hole with Chern-Simons and Higher Derivative Terms
• BTZ Black Hole with Gravitational Chern-Simons: Thermodynamics and Statistical Entropy
• Background-independent charges in Topologically Massive Gravity
• Local Anomalies, Local Equivariant Cohomology and the Variational Bicomplex

Cited by in corpus (10)

• Gravitational Anomalies and Thermal Hall effect in Topological Insulators
• Gravitational Chern-Simons Lagrangians and black hole entropy
• Probing topological superconductors with emergent gravity
• Gravitational Chern-Simons Lagrangian terms and spherically symmetric spacetimes
• Boundary central charge from bulk odd viscosity - chiral superfluids
• Homogeneous Cotton solitons
• Entropy for gravitational Chern-Simons terms by squashed cone method
• Geometrical origin of the Kodama vector
• Gravitational Chern-Simons terms and black hole entropy. Global aspects
• Geometric and computational aspects of chiral topological quantum matter