Gravitational Chern-Simons Lagrangian terms and spherically symmetric spacetimes

Understand

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.