School of Mathematical Sciences and School of Physics and Astronomy, University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom.
SISSA, Via Bonomea 265, 34136 Trieste, Italy and INFN, Sezione di Trieste, Via Valerio 2, 34127 Trieste, Italy.
Phys Rev Lett. 2014 Jun 27;112(25):251102. doi: 10.1103/PhysRevLett.112.251102. Epub 2014 Jun 26.
The most general action for a scalar field coupled to gravity that leads to second-order field equations for both the metric and the scalar--Horndeski's theory--is considered, with the extra assumption that the scalar satisfies shift symmetry. We show that in such theories, the scalar field is forced to have a nontrivial configuration in black hole spacetimes, unless one carefully tunes away a linear coupling with the Gauss-Bonnet invariant. Hence, black holes for generic theories in this class will have hair. This contradicts a recent no-hair theorem which seems to have overlooked the presence of this coupling.
考虑了与引力耦合的标量场的最一般作用，这导致了度规和标量的二阶场方程——霍恩德斯基理论——并且额外假设标量满足平移对称性。我们表明，在这种理论中，除非仔细调谐与 Gauss-Bonnet 不变量的线性耦合，否则标量场将被迫在黑洞时空中具有非平凡的配置。因此，对于此类通用理论中的黑洞将具有毛发。这与最近的无毛定理相矛盾，后者似乎忽略了这种耦合的存在。
