Black holes in

f(Q)

gravity

We systematically study the €eld equations of f(Q) gravity for spherically symmetric and stationary metricane spacetimes. Such spacetimes are described by a metric as well as a ƒat and torsionless ane connection. In the Symmetric Teleparallel Equivalent of GR (STEGR), the connection is pure gauge and hence unphysical. However, in the non-linear extension f(Q), it is promoted to a dynamical €eld which changes the physics. Starting from a general metric-ane geometry, we construct the most general static and spherically symmetric forms of the metric and the ane connection. We then use these symmetry reduced geometric objects to prove that the €eld equations of f(Q) gravity admit GR solutions as well as beyondGR solutions, contrary to what has been claimed in the literature. We formulate precise criteria, under which conditions it is possible to obtain GR solutions and under which conditions it is possible to obtain beyond-GR solutions. We subsequently construct several perturbative corrections to the Schwarzschild solution for di‚erent choices of f(Q), which in particular include a hair stemming from the now dynamical ane connection. We also present an exact beyond-GR vacuum solution. Lastly, we apply this method of constructing spherically symmetric and stationary solutions to f(T) gravity, which reproduces similar solutions but without a dynamical connection.