Abstract:
Black-hole perturbation theory is a useful tool to investigate issues in astrophysics, high-energy physics, and fundamental problems in gravity. It is often complementary to fully-fledged nonlinear evolutions and instrumental to interpret some results of numerical simulations. Several modern applications require advanced tools to investigate the linear dynamics of generic small perturbations around stationary black holes. Here, we present an overview of these applications and introduce extensions of the standard semianalytical methods to construct and solve the linearized field equations in curved spacetime. Current state-of-the-art techniques are pedagogically explained and exciting open problems are presented.

Abstract:
The multipole moments and the tidal Love numbers of neutron stars and quark stars satisfy certain relations which are almost insensitive to the star's internal structure. A natural question is whether the same relations hold for different compact objects and how they possibly approach the black-hole limit. Here we consider ``gravastars'', which are hypothetical compact objects sustained by their internal vacuum energy. Such solutions have been proposed as exotic alternatives to the black-hole paradigm because they can be as compact as black holes and exist in any mass range. By constructing slowly-rotating, thin-shell gravastars to quadratic order in the spin, we compute the moment of inertia $I$, the mass quadrupole moment $Q$, and the tidal Love number $\lambda$ in exact form. The $I$-$\lambda$-$Q$ relations of a gravastar are dramatically different from those of an ordinary compact star, but the black-hole limit is continuous, i.e. these quantities approach their Kerr counterparts when the compactness is maximum. Therefore, such relations can be used to discern a gravastar from an ordinary compact star, but not to break the degeneracy with the black-hole case. Based on these results, we conjecture that the full multipolar structure and the tidal deformability of a spinning, ultracompact gravastar are identical to those of a Kerr black hole. The approach to the black-hole limit is nonpolynomial, thus differing from the critical behavior recently found for strongly anisotropic neutron stars.

Abstract:
During the motion of a binary pulsar around the galactic center, the pulsar and its companion experience a wind of dark-matter particles that can affect the orbital motion through dynamical friction. We show that this effect produces a characteristic seasonal modulation of the orbit and causes a secular change of the orbital period whose magnitude can be well within the astonishing precision of various binary-pulsar observations. Our analysis is valid for binary systems with orbital period longer than a day. By comparing this effect with pulsar-timing measurements, it is possible to derive model-independent upper bounds on the dark-matter density at different distances $D$ from the galactic center. For example, the precision timing of J1713+0747 imposes $\rho_{\rm DM}\lesssim 10^5\,{\rm GeV/cm}^3$ at $D\approx7\,{\rm kpc}$. The detection of a binary pulsar at $D\lesssim 10\,{\rm pc}$ could provide stringent constraints on dark-matter halo profiles and on growth models of the central black hole. The Square Kilometer Array can improve current bounds by two orders of magnitude, potentially constraining the local density of dark matter to unprecedented levels.

Abstract:
It is generally accepted that Einstein's theory will get some as yet unknown corrections, possibly large in the strong field regime. An ideal place to look for these modifications is around the vicinities of compact objects such as black holes. Our case study here are Dilatonic Black Holes, which arise in the framework of Gauss-Bonnet couplings and one-loop corrected four-dimensional effective theory of heterotic superstrings at low energies. These are interesting objects as a prototype for alternative, yet well-behaved gravity theories: they evade the "no-hair" theorem of General Relativity but were proved to be stable against radial perturbations. We investigate the viability of these black holes as astrophysical objects and try to provide some means to distinguish them from black holes in General Relativity. We start by extending previous works and establishing the stability of these black holes against axial perturbations. We then look for solutions of the field equations describing slowly rotating black holes and study geodesic motion around this geometry. Depending on the values of mass, dilaton charge and angular momentum of the solution, one can have measurable differences in the ISCO location and orbital frequency, relatively to black holes in General Relativity. Such differences may be useful in future experiments, to discriminate between alternative theories of gravity.

Abstract:
Tidal effects have long ago locked the Moon in synchronous rotation with the Earth and progressively increase the Earth-Moon distance. This "tidal acceleration" hinges on dissipation. Binaries containing black holes may also be tidally accelerated, dissipation being caused by the event horizon - a flexible, viscous one-way membrane. In fact, this process is known for many years under a different guise: superradiance. In General Relativity, tidal acceleration is obscured by gravitational-wave emission. However, when coupling to light scalar degrees of freedom is allowed, an induced dipole moment produces a "polarization acceleration", which might be orders of magnitude stronger than tidal quadrupolar effects. Consequences for optical and gravitational-wave observations are intriguing and it is not impossible that imprints of such mechanism have already been observed.

Abstract:
We investigate bulk and holographic features of finite-temperature black brane solutions of 4D anti-de Sitter Einstein-Maxwell-dilaton-gravity (EMDG). We construct, numerically, black branes endowed with non trivial scalar hairs for broad classes of EMDG. We consider both exponential and power-law forms for the coupling functions, as well as several charge configurations: purely electric, purely magnetic and dyonic solutions. At finite temperature the field theory holographically dual to these black brane solutions has a rich and interesting phenomenology reminiscent of electron motion in metals: phase transitions triggered by nonvanishing VEV of scalar operators, non-monotonic behavior of the electric conductivities as function of the frequency and of the temperature, Hall effect and sharp synchrotron resonances of the conductivity in presence of a magnetic field. Conversely, in the zero temperature limit the conductivities for these models show a universal behavior. The optical conductivity has a power-law behavior as a function of the frequency, whereas the DC conductivity is suppressed at small temperatures.

Abstract:
In a close encounter with a neutron star, a primordial black hole can get gravitationally captured by depositing a considerable amount of energy into nonradial stellar modes of very high angular number $l$. If the neutron-star equation of state is sufficiently stiff, we show that the total energy loss in the point-particle approximation is formally divergent. Various mechanisms -including viscosity, finite-size effects and the elasticity of the crust- can damp high-$l$ modes and regularize the total energy loss. Within a short time, the black hole is trapped inside the star and disrupts it by rapid accretion. Estimating these effects, we predict that the existence of old neutron stars in regions where the dark-matter density rho_{DM}>10^2 sigma/(km/s) GeV/cm^3 (where sigma is the dark-matter velocity dispersion) limits the abundance of primordial black holes in the mass range 10^{17} g < m_{PBH} < 10^{24} g, which was previously unconstrained. In combination with existing limits, our results suggest that primordial black holes cannot be the dominant dark matter constituent.

Abstract:
We construct models of slowly rotating, perfect-fluid neutron stars by extending the classical Hartle-Thorne formalism to generic scalar-tensor theories of gravity. Working at second order in the dimensionless angular momentum, we compute the mass M, radius R, scalar charge q, moment of inertia I and spin-induced quadrupole moment Q, as well as the tidal and rotational Love numbers. Our formalism applies to generic scalar-tensor theories, but we focus in particular on theories that allow for spontaneous scalarization. It was recently discovered that the moment of inertia, quadrupole moment and Love numbers are connected by approximately universal (i.e., equation-of-state independent) "I-Love-Q" relations. We find that similar relations hold also for spontaneously scalarized stars. More interestingly, the I-Love-Q relations in scalar-tensor theories coincide with the general relativistic ones within less than a few percent, even for spontaneously scalarized stars with the largest couplings allowed by current binary-pulsar constraints. This implies that astrophysical measurements of these parameters cannot be used to discriminate between general relativity and scalar-tensor theories, even if spontaneous scalarization occurs in nature. Because of the well known equivalence between f(R) theories and scalar-tensor theories, the theoretical framework developed in this paper can be used to construct rotating compact stellar models in f(R) gravity. Our slow-rotation expansion can also be used as a benchmark for numerical calculations of rapidly spinning neutron stars in generic scalar-tensor theories.

Abstract:
We consider the imprint of superradiant instabilities of nonevaporating primordial black holes (PBHs) on the spectrum of the cosmic microwave background (CMB). In the radiation dominated era, PBHs are surrounded by a roughly homogeneous cosmic plasma which endows photons with an effective mass through the plasma frequency. In this setting, spinning PBHs are unstable to a spontaneous spindown through the well-known "black-hole bomb" mechanism. At linear level, the photon density is trapped by the effective photon mass and grows exponentially in time due to superradiance. As the plasma density declines due to cosmic expansion, the associated energy around PBHs is released and dissipated in the CMB. We evaluate the resulting spectral distortions of the CMB in the redshift range 10^3 < z < 2x10^6. Using the existing COBE/FIRAS bounds on CMB spectral distortions, we derive upper limits on the fraction of dark matter that can be associated with spinning PBHs in the mass range 10^{-8}*Msun < M < 0.2*Msin. For maximally-spinning PBHs, our limits are much tighter than those derived from microlensing or other methods. Future data from the proposed PIXIE mission could improve our limits by several orders of magnitude.

Abstract:
Eddington-inspired Born-Infeld gravity was recently proposed as an alternative to general relativity that offers a resolution of spacetime singularities. The theory differs from Einstein's gravity only inside matter due to nondynamical degrees of freedom, and it is compatible with all current observations. We show that the theory is reminiscent of Palatini f(R) gravity and that it shares the same pathologies, such as curvature singularities at the surface of polytropic stars and unacceptable Newtonian limit. This casts serious doubts on its viability.