Physics

Tensor (intrinsic definition)

Mathematics

Mathematical physics

Scalar curvature

Gauss–Bonnet theorem

Einstein

Curvature

Geometry

Theoretical physics

Scalar (mathematics)

Classical mechanics

Physical Review Letters

In the present paper we consider a class of extended scalar-tensor-Gauss-Bonnet (ESTGB) theories for which the scalar degree of freedom is excited only in the extreme curvature regime. We show that in the mentioned class of ESTGB theories there exist new black hole solutions which are formed by spontaneous scalarization of the Schwarzaschild balck holes in the extreme curvature regime. In this regime, below certain mass, the Schwarzschild solution becomes unstable and new branch of solutions with nontrivial scalar field bifurcate from the Schwarzschild one. As a matter of fact, more than one branches with nontrivial scalar field can bifurcate at different masses but only the first one is supposed to be stable. This effect is quite similar to the spontaneous scalarization of neutron stars. In contrast with the standard spontaneous scalarization of neutron stars which is induced by the presence of matter, in our case the scalarization is induced by the curvature of the spacetime.

New Gauss-Bonnet Black Holes with Curvature-Induced Scalarization in Extended Scalar-Tensor Theories