Gravitational Chern-Simons Lagrangian terms and spherically symmetric spacetimes

Abstract

We show that for general spherically symmetric configurations, contributions of general gravitational and mixed gauge-gravitational Chern-Simons terms to the equations of motion vanish identically in $D>3$ dimensions. This implies that such terms in the action do not affect Birkhoff's theorem or any previously known spherically symmetric solutions. Furthermore, we investigate the thermodynamical properties using the procedure described in an accompanying paper. We find that in $D>3$ static spherically symmetric case Chern-Simons terms do not contribute to the entropy either. Moreover, if one requires only for the metric tensor to be spherically symmetric, letting other fields unrestricted, the results extend almost completely, with only one possible exception --- Chern-Simons Lagrangian terms in which the gravitational part is just the $n=2$ irreducible gravitational Chern-Simons term.

16 pages, updated to match published version

References in corpus (10)

• Black Hole Entropy in the presence of Chern-Simons Terms
• How do Black Holes Spin in Chern-Simons Modified Gravity?
• Perturbations of Schwarzschild Black Holes in Chern-Simons Modified Gravity
• BTZ Black Hole with Gravitational Chern-Simons: Thermodynamics and Statistical Entropy
• Birkhoff's Theorem in Higher Derivative Theories of Gravity
• Dirichlet boundary value problem for Chern-Simons modified gravity
• Gravitational Chern-Simons Lagrangians and black hole entropy
• Einstein-Cartan formulation of Chern-Simons Lorentz-violating Gravity
• Asymptotically flat, stable black hole solutions in Einstein--Yang-Mills--Chern-Simons theory
• Einstein-Yang-Mills-Chern-Simons solutions in D=2n+1 dimensions

Cited by in corpus (16)

• Anomalous Transport from Kubo Formulae
• Quasilocal Conserved Charges with a Gravitational Chern-Simons Term
• Quasi-local conserved charges and holography
• Symmetry inheritance of scalar fields
• Black hole entropy in the Chern-Simons-like theories of gravity and Lorentz-diffeomorphism Noether charge
• Covariant Noether Charge for Higher Dimensional Chern-Simons Terms
• Symmetries and gravitational Chern-Simons Lagrangian terms
• Does three dimensional electromagnetic field inherit the spacetime symmetries?
• A new look at hidden conformal symmetries of black holes
• Generalizations and challenges for the spacetime block-diagonalization
• Stationary rotating black holes in theories with gravitational Chern-Simons Lagrangian term
• Stationary spacetimes with time-dependent real scalar fields
• Gravitational Chern-Simons terms and black hole entropy. Global aspects
• Weighing the curvature invariants
• Parity-odd surface anomalies and correlation functions on conical defects
• Symmetry Inheritance and Jebsen-Birkhoff Theorem