The grand challenges of contemporary fundamental physics—dark matter, dark energy, vacuum energy, inflation and early universe cosmology, singularities and the hierarchy problem—all involve gravity as a key component. And of all gravitational phenomena, black holes stand out in their elegant simplicity, while harbouring some of the most remarkable predictions of General Relativity: event horizons, singularities and ergoregions. The hitherto invisible landscape of the gravitational Universe is being unveiled before our eyes: the historical direct detection of gravitational waves by the LIGO-Virgo collaboration marks the dawn of a new era of scientific exploration. Gravitational-wave astronomy will allow us to test models of black hole formation, growth and evolution, as well as models of gravitational-wave generation and propagation. It will provide evidence for event horizons and ergoregions, test the theory of General Relativity itself, and may reveal the existence of new fundamental fields. The synthesis of these results has the potential to radically reshape our understanding of the cosmos and of the laws of Nature. The purpose of this work is to present a concise, yet comprehensive overview of the state of the art in the relevant fields of research, summarize important open problems, and lay out a roadmap for future progress. This write-up is an initiative taken within the framework of the European Action on ‘Black holes, Gravitational waves and Fundamental Physics’.

In the present Letter, 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 that are formed by spontaneous scalarization of the Schwarzschild black holes in the extreme curvature regime. In this regime, below certain mass, the Schwarzschild solution becomes unstable and a new branch of solutions with a nontrivial scalar field bifurcates from the Schwarzschild one. As a matter of fact, more than one branch with a 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 to 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.

We show that two stationary, asymptotically flat vacuum black holes in 5 dimensions with two commuting axial symmetries are identical if and only if their masses, angular momenta, and their "rod structures" coincide. We also show that the horizon must be topologically either a 3-sphere, a ring, or a Lens-space. Our argument is a generalization of constructions of Morisawa and Ida (based in turn on key work of Maison) who considered the spherical case, combined with basic arguments concerning the nature of the factor manifold of symmetry orbits.

We perform the first study of the oscillation frequencies of rapidly rotating neutron stars in alternative theories of gravity, focusing mainly on the fundamental f-modes. We concentrated on a particular class of alternative theories-the (massive) scalar-tensor theories. The generalization to rapid rotation is important because on one hand the rapid rotation can magnify the deviations from general relativity compared to the static case and on the other hand some of the most efficient emitters of gravitational radiation, such as the binary neutron star merger remnants, are supposed to be rotating close to their Kepler (mass-shedding) limits shortly after their formation. We have constructed several sequences of models starting from the nonrotating case and reaching up to the Kepler limit, with different values of the scalar-tensor theory coupling constant and the scalar field mass. The results show that the deviations from pure Einstein's theory can be significant especially in the case of nonzero scalar field mass. An important property of the oscillation modes of rapidly rotating stars is that they can become secularly unstable due to the emission of gravitational radiation, that is so-called Chandrasekhar-Friedman-Schutz instability. Such unstable modes are efficient emitters of gravitational radiation. Our studies show that the inclusion of nonzero scalar field would decrease the threshold value of the normalized angular momentum where this instability stars to operate, but the growth time of the instability seems to be increased compared to pure general relativity.

We prove a uniqueness theorem for stationary D-dimensional Kaluza-Klein black holes with D−2 Killing fields, generating the symmetry group R×U (1) D−3 . It is shown that the topology and metric of such black holes is uniquely determined by the angular momenta and certain other invariants consisting of a number of real moduli, as well as integer vectors subject to certain constraints. * HollandsS@Cardiff.ac.uk

Recently a new class of scalarized black holes in Einstein-Gauss-Bonnet (EGB) theories was discovered. What is special for these black hole solutions is that the scalarization is not due to the presence of matter, but it is induced by the curvature of spacetime itself. Moreover, more than one branch of scalarized solutions can bifurcate from the Schwarzschild branch, and these scalarized branches are characterized by the number of nodes of the scalar field. The next step is to consider the linear stability of these solutions, which is particularly important due to the fact that the Schwarzschild black holes lose stability at the first point of bifurcation. Therefore we here study in detail the radial perturbations of the scalarized EGB black holes. The results show that all branches with a nontrivial scalar field with one or more nodes are unstable. The stability of the solutions on the fundamental branch, whose scalar field has no radial nodes, depends on the particular choice of the coupling function between the scalar field and the Gauss-Bonnet invariant. We consider two particular cases based on the previous studies of the background solutions. If this coupling has the form used in [1] the fundamental branch of solutions is stable, except for very small masses. In the case of a coupling function quadratic in the scalar field [2], though, the whole fundamental branch is unstable.

No abstract

Abstract. In the present paper we investigate non-perturbatively and self-consistently the structure of neutron stars in R-squared gravity by simultaneously solving the interior and exterior problem. The mass-radius relations are obtained for several equations of state and for wide range of the R-squared gravity parameter a. Even though the deviation from general relativity for nonzero values of a can be large, they are still comparable with the variations due to different modern realistic equations of state. That is why the current observations of the neutron star masses and radii alone can not put constraints on the value of the parameter a. We also compare our results with those obtained within the perturbative method and we discuss the differences between them.