engleski

Gravitational Chern–Simons Lagrangian terms and spherically symmetric spacetimes

We show that for general spherically symmetric configurations, contributions of broad class of gravitational and mixed gauge-gravitational Chern–Simons (CS) 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 the D > 3 static spherically symmetric case, CS terms do not contribute to the entropy either. Moreover, if one requires only for the metric tensor to be spherically symmetric, letting other fields be unrestricted, the results extend almost completely, with only one possible exception—CS Lagrangian terms in which the gravitational part is just the n = 2 irreducible gravitational CS term.

black holes; spherical symmetry; Chern-Simons terms

art. no. 195009.