New Gauss-Bonnet black holes with curvature induced scalarization in the extended scalar-tensor theories

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.Comment: 13 pages, 7 figure

Tidal Love numbers of neutron stars in f(R)f(R) gravity

The recent detection of gravitational waves from a neutron star merger was a significant step towards constraining the nuclear matter equation of state by using the tidal Love numbers (TLNs) of the merging neutron stars. Measuring or constraining the neutron star TLNs allows us in principle to exclude or constraint many equations of state. This approach, however, has the drawback that many modified theories of gravity could produce deviations from General Relativity similar to the deviations coming from the uncertainties in the equation of state. The first and the most natural step in resolving the mentioned problem is to quantify the effects on the TLNs from the modifications of General Relativity. With this motivation in mind, in the present paper we calculate the TLNs of (non-rotating) neutron stars in $f(R)$ gravity. For this purpose, we first derived the equations describing both the polar and the axial stationary perturbations of neutron stars in a particular class of $f(R)$ gravity, the so-called $R^2$-gravity. Then, by solving numerically the perturbation equations, we calculate explicitly the polar and the axial $l=2$ TLNs of the neutron stars in $R^2$-gravity for three characteristic realistic equations of state. Our results show that while the polar TLNs are slightly influenced by the $R^2$ modification of General Relativity, the axial TLNs can be several times larger (in terms of the absolute value) compared to the general relativistic case.Comment: 10 pages, 3 figure