Riemann–Cartan gravitational and axial anomalies in electrodynamics and black holes

Abstract

In this paper two examples are given of a chiral torsional anomaly Nieh–Yan (NY) topological invariant in Riemann–Cartan (RC) spacetime: in the first it is shown that a certain class of RC spacetime metrics yields a chiral torsional axial anomaly possessing a term proportional to E ⋅ B. Here E and B are respectively the electric and magnetic fields. Besides, since Cartan connection does not vanish, this example is a mixed gravitational axial anomaly. In this case the axial torsional anomaly in RC manifold is computed. Second example is that of a Kerr metric of non-stationary black hole (BH) which possesses gravitational anomaly. The metric which produces the axial anomaly keeps some similarity with Eddington–Schroedinger–Einstein–Strauss metric of unified field theories of gravity and electromagnetism. These ideas, show us the possibility of having analogous BHs models in Weyl semimetals. Moreover, electrodynamics in Cartan spacetime is discussed in this context. This is based on teleparallel metrics used by Letelier (1995 Class Quantum Grav. 12 2221) and Tod (1994 Class Quantum Grav. 11 5). NY RC gravitational anomalies are obtained for BHs Kerr metric using an orthogonal tetrad system.