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The semiclassical Kepler-Coulomb problem and the quantum-mechanical Schr\"odinger-Coulomb problem are compared for their predictions of quadrupole E2 transitions. The semiclassical treatment involves an extension of previous work for the electric dipole transitions (Physical Review A 71, 020501), and rates are derived for $\Delta \ell= 0, \pm 2$ transitions on the basis of the multipolar properties of the emitted radiation. For the quantum case a derivation is presented within the Schr\"odinger framework without reference to spin. Comparison of the E2 rates shows reasonable agreement, but not as good as was found for the electric dipole case., Comment: 19 pages

The Kepler-Coulomb problem is solved in parabolic coordinates and the Larmor radiation problem is analyzed to complement a previous study performed for the usual representation in spherical polar coordinates. A comparison with quantum spontaneous decay rates shows that for azimuthal quantum number $m = 0$ states only transitions to nearby $n-\Delta n$ principal quantum number states are described properly by the Wentzel-Kramers-Brillouin quantized classical motions, but that for $m > 0$ reasonable results emerge for many values of $\Delta n$. A simple approximate expression for the lifetime of $m \ne 0$ states emerges from the semi-classical analysis., Comment: 37 pages, 8 figures, 44 references; revised after referee reports from J Phys B

Gravitational theories with multiple scalar fields coupled to the metric and each other --- a natural extension of the well studied single-scalar-tensor theories --- are interesting phenomenological frameworks to describe deviations from general relativity in the strong-field regime. In these theories, the $N$-tuple of scalar fields takes values in a coordinate patch of an $N$-dimensional Riemannian target-space manifold whose properties are poorly constrained by weak-field observations. Here we introduce for simplicity a non-trivial model with two scalar fields and a maximally symmetric target-space manifold. Within this model we present a preliminary investigation of spontaneous scalarization for relativistic, perfect fluid stellar models in spherical symmetry. We find that the scalarization threshold is determined by the eigenvalues of a symmetric scalar-matter coupling matrix, and that the properties of strongly scalarized stellar configurations additionally depend on the target-space curvature radius. In preparation for numerical relativity simulations, we also write down the $3+1$ decomposition of the field equations for generic tensor-multi-scalar theories., Comment: 32 pages, 8 figures, 1 table, invited contribution to the Classical and Quantum Gravity Focus Issue "Black holes and fundamental fields". v3: version in press in CQG, with various improvements in response to the referees' comments. In particular, the 3+1 decomposition now allows for matter

One century after its formulation, Einstein's general relativity has made remarkable predictions and turned out to be compatible with all experimental tests. Most of these tests probe the theory in the weak-field regime, and there are theoretical and experimental reasons to believe that general relativity should be modified when gravitational fields are strong and spacetime curvature is large. The best astrophysical laboratories to probe strong-field gravity are black holes and neutron stars, whether isolated or in binary systems. We review the motivations to consider extensions of general relativity. We present a (necessarily incomplete) catalog of modified theories of gravity for which strong-field predictions have been computed and contrasted to Einstein's theory, and we summarize our current understanding of the structure and dynamics of compact objects in these theories. We discuss current bounds on modified gravity from binary pulsar and cosmological observations, and we highlight the potential of future gravitational wave measurements to inform us on the behavior of gravity in the strong-field regime., Comment: 188 pages, 46 figures, 6 tables, 903 references. Matches version published in Classical and Quantum Gravity. Supplementary data files available at http://www.phy.olemiss.edu/~berti/research/ and http://centra.tecnico.ulisboa.pt/network/grit/files/

We study torsional oscillations of neutron stars in the scalar-tensor theory of gravity using the relativistic Cowling approximation. We compute unperturbed neutron star models adopting realistic equations of state for the neutron star's core and crust. For scalar-tensor theories that allow for spontaneous scalarization, the crust thickness can be significantly smaller than in general relativity. We derive the perturbation equation describing torsional oscillations in scalar-tensor theory, and we solve the corresponding eigenvalue problem to find the oscillation frequencies. The fundamental mode (overtone) frequencies become smaller (larger) than in general relativity for scalarized stellar models. Torsional oscillation frequencies may yield information on the crust microphysics if microphysics effects are not degenerate with strong-gravity effects, such as those due to scalarization. To address this issue, we consider two different models for the equation of state of the crust and we look at the effects of electron screening. The effect of scalarization on torsional oscillation frequencies turns out to be smaller than uncertainties in the microphysics for all spontaneous scalarization models allowed by binary pulsar observations. Our study shows that the observation of quasi-periodic oscillations (QPOs) following giant flares can be used to constrain the microphysics of neutron star crusts, whether spontaneous scalarization occurs or not., Comment: 13 pages, 8 figures

Scalar-tensor theories are a compelling alternative to general relativity and one of the most accepted extensions of Einstein's theory. Black holes in these theories have no hair, but could grow "wigs" supported by time-dependent boundary conditions or spatial gradients. Time-dependent or spatially varying fields lead in general to nontrivial black hole dynamics, with potentially interesting experimental consequences. We carry out a numerical investigation of the dynamics of single and binary black holes in the presence of scalar fields. In particular we study gravitational and scalar radiation from black-hole binaries in a constant scalar-field gradient, and we compare our numerical findings to analytical models. In the single black hole case we find that, after a short transient, the scalar field relaxes to static configurations, in agreement with perturbative calculations. Furthermore we predict analytically (and verify numerically) that accelerated black holes in a scalar-field gradient emit scalar radiation. For a quasicircular black-hole binary, our analytical and numerical calculations show that the dominant component of the scalar radiation is emitted at twice the binary's orbital frequency., Comment: 21 pages, 6 figures, matches version accepted in Physical Review D

Scalar-tensor theories are among the simplest extensions of general relativity. In theories with light scalars, deviations from Einstein's theory of gravity are determined by the scalar mass m_s and by a Brans-Dicke-like coupling parameter \omega_{BD}. We show that gravitational-wave observations of nonspinning neutron star-black hole binary inspirals can be used to set lower bounds on \omega_{BD} and upper bounds on the combination m_s/\sqrt{\omega_{BD}}$. We estimate via a Fisher matrix analysis that individual observations with signal-to-noise ratio \rho would yield (m_s/\sqrt{\omega_{BD}})(\rho/10)<10^{-15}, 10^{-16} and 10^{-19} eV for Advanced LIGO, ET and eLISA, respectively. A statistical combination of multiple observations may further improve these bounds., Comment: 9 pages, 4 figures. Matches version accepted in Physical Review D