additional non-Schwarzschild parameter corresponding to the value of the Bach tensor invariant on the horizon. We study its geometrical and physical properties, such as basic thermodynamical quantities and tidal effects on free test particles induced by the presence of the Bach tensor. We also compare our results with previous findings in the literature obtained using the standard spherically symmetric coordinates.'
author:
- |
    J. Podolský$^\star$, R. Švarc$^\star$, V. Pravda$^\diamond$, A. Pravdov' a$^\diamond$\
    \
    \
    [$^\star$ Institute of Theoretical Physics, Faculty of Mathematics and Physics,]{}\
    [Charles University, V Holešovičkách 2, 180 00 Prague 8, Czech Republic.]{}\
    [$^\diamond$ Institute of Mathematics, Academy of Sciences of the Czech Republic]{},\
    [Žitn' a 25, 115 67 Prague 1, Czech Republic.]{}\
    [E-mail: `podolsky@mbox.troja.mff.cuni.cz, robert.svarc@mff.cuni.cz, `]{}\
    [`pravda@math.cas.cz, pravdova@math.cas.cz`]{}
title:  Black holes and other exact spherical solutions in Quadratic Gravity
---

PACS numbers: 04.20.Jb, 04.50.–h, 04.70.Bw, 04.70.Dy, 11.25.–w

Keywords: black holes, exact solutions, Quadratic Gravity, Einstein–Weyl gravity, Schwarzschild metric, Bach tensor, Robinson–Trautman spacetimes, Kundt spacetimes

Introduction {#intro}
============

Soon after Albert Einstein formulated his General Relativity in November 1915 and David Hilbert found an elegant procedure how to derive Einstein’s field equations from the variational principle, various attempts started to extend and generalize this gravity theory. One possible 