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’.

We study the effect of a mass term in the spontaneous scalarization of neutron stars, for a wide range of scalar field parameters and neutron star equations of state. Even though massless scalars have been the focus of interest in spontaneous scalarization so far, recent observations of binary systems rule out most of their interesting parameter space. We point out that adding a mass term to the scalar field potential is a natural extension to the model that avoids these observational bounds if the Compton wavelength of the scalar is small compared to the binary separation. Our model is formally similar to the asymmetron scenario recently introduced in application to cosmology, though here we are interested in consequences for neutron stars and thus consider a mass term that does not modify the geometry on cosmological scales. We review the allowed values for the mass and scalarization parameters in the theory given current binary system observations and black hole spin measurements. We show that within the allowed ranges, spontaneous scalarization can have nonperturbative, strong effects that may lead to observable signatures in binary neutron star or black hole-neutron star mergers, or even in isolated neutron stars.

Avian brain area HVC is known to be important for the production of birdsong. In zebra finches, each RA-projecting neuron in HVC emits a single burst of spikes during a song motif. The population of neurons is activated in a precisely timed, stereotyped sequence. We propose a model of these burst sequences that relies on two hypotheses. First, we hypothesize that the sequential order of bursting is reflected in the excitatory synaptic connections between neurons. Second, we propose that the neurons are intrinsically bursting, so that burst duration is set by cellular properties. Our model generates burst sequences similar to those observed in HVC. If intrinsic bursting is removed from the model, burst sequences can also be produced. However, they require more fine-tuning of synaptic strengths, and are therefore less robust. In our model, intrinsic bursting is caused by dendritic calcium spikes, and strong spike frequency adaptation in the soma contributes to burst termination.

We show that the spontaneous scalarization scenario in scalar-tensor theories is a specific case of a more general phenomenon. The key fact is that the instability causing the spontaneous growth in scalars is due to the nonminimal coupling in the theory, and not related to the nature of the scalar. Another field with the same form of coupling undergoes spontaneous growth as well. We explicitly demonstrate this idea for vectors, naming it "spontaneous vectorization", and study spherically symmetric neutron stars in such a theory. We also comment on other tensor fields the idea can be applied, naming the general mechanism "spontaneous tensorization".Comment: 5 pages, 2 figure