Tensor-multi-scalar theories: relativistic stars and 3+1 decomposition

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 matte

On the absence of bound-state stabilization through short ultra-intense fields

We address the question of whether atomic bound states begin to stabilize in the short ultra-intense field limit. We provide a general theory of ionization probability and investigate its gauge invariance. For a wide range of potentials we find an upper and lower bound by non-perturbative methods, which clearly exclude the possibility that the ultra intense field might have a stabilizing effect on the atom. For short pulses we find almost complete ionization as the field strength increases.Comment: 34 pages Late

Semi-Analytic Stellar Structure in Scalar-Tensor Gravity

Precision tests of gravity can be used to constrain the properties of hypothetical very light scalar fields, but these tests depend crucially on how macroscopic astrophysical objects couple to the new scalar field. We develop quasi-analytic methods for solving the equations of stellar structure using scalar-tensor gravity, with the goal of seeing how stellar properties depend on assumptions made about the scalar coupling at a microscopic level. We illustrate these methods by applying them to Brans-Dicke scalars, and their generalization in which the scalar-matter coupling is a weak function of the scalar field. The four observable parameters that characterize the fields external to a spherically symmetric star (the stellar radius, R, mass, M, scalar `charge', Q, and the scalar's asymptotic value, phi_infty) are subject to two relations because of the matching to the interior solution, generalizing the usual mass-radius, M(R), relation of General Relativity. We identify how these relations depend on the microscopic scalar couplings, agreeing with earlier workers when comparisons are possible. Explicit analytical solutions are obtained for the instructive toy model of constant-density stars, whose properties we compare to more realistic equations of state for neutron star models.Comment: 39 pages, 9 figure

Cosmic Black-Hole Hair Growth and Quasar OJ287

An old result ({\tt astro-ph/9905303}) by Jacobson implies that a black hole with Schwarzschild radius $r_s$ acquires scalar hair, $Q \propto r_s^2 \mu$, when the (canonically normalized) scalar field in question is slowly time-dependent far from the black hole, $\partial_t \phi \simeq \mu M_p$ with $\mu r_s \ll 1$ time-independent. Such a time dependence could arise in scalar-tensor theories either from cosmological evolution, or due to the slow motion of the black hole within an asymptotic spatial gradient in the scalar field. Most remarkably, the amount of scalar hair so induced is independent of the strength with which the scalar couples to matter. We argue that Jacobson's Miracle Hair-Growth Formula${}^\copyright$ implies, in particular, that an orbiting pair of black holes can radiate {\em dipole} radiation, provided only that the two black holes have different masses. Quasar OJ 287, situated at redshift $z \simeq 0.306$, has been argued to be a double black-hole binary system of this type, whose orbital decay recently has been indirectly measured and found to agree with the predictions of General Relativity to within 6%. We argue that the absence of observable scalar dipole radiation in this system yields the remarkable bound $|\,\mu| < (16 \, \hbox{days})^{-1}$ on the instantaneous time derivative at this redshift (as opposed to constraining an average field difference, $\Delta \phi$, over cosmological times), provided only that the scalar is light enough to be radiated --- i.e. m \lsim 10^{-23} eV --- independent of how the scalar couples to matter. This can also be interpreted as constraining (in a more model-dependent way) the binary's motion relative to any spatial variation of the scalar field within its immediate vicinity within its host galaxy.Comment: 20 page

New exact solution of Dirac-Coulomb equation with exact boundary condition

It usually writes the boundary condition of the wave equation in the Coulomb field as a rough form without considering the size of the atomic nucleus. The rough expression brings on that the solutions of the Klein-Gordon equation and the Dirac equation with the Coulomb potential are divergent at the origin of the coordinates, also the virtual energies, when the nuclear charges number Z > 137, meaning the original solutions do not satisfy the conditions for determining solution. Any divergences of the wave functions also imply that the probability density of the meson or the electron would rapidly increase when they are closing to the atomic nucleus. What it predicts is not a truth that the atom in ground state would rapidly collapse to the neutron-like. We consider that the atomic nucleus has definite radius and write the exact boundary condition for the hydrogen and hydrogen-like atom, then newly solve the radial Dirac-Coulomb equation and obtain a new exact solution without any mathematical and physical difficulties. Unexpectedly, the K value constructed by Dirac is naturally written in the barrier width or the equivalent radius of the atomic nucleus in solving the Dirac equation with the exact boundary condition, and it is independent of the quantum energy. Without any divergent wave function and the virtual energies, we obtain a new formula of the energy levels that is different from the Dirac formula of the energy levels in the Coulomb field.Comment: 12 pages,no figure

The Decay ηc→γγ\eta_c \rightarrow \gamma \gamma : A Test for Potential Models

We use a simple perturbation theory argument and measurements of charmonium leptonic widths $\Gamma (\psi_{NS} \rightarrow e^+e^-)$ to estimate the ratio \mbox{$R_\circ \equiv {\vert \Psi _{\eta_{c1S}}(0) \vert}^2 /{\vert\Psi_{\psi_{1 S}}(0)\vert}^2$} in the general context of non- relativistic potential models. We obtain $R_\circ = 1.4 \pm 0.1$. We then apply well known potential model formulas, which include lowest order QCD corrections, to find $\Gamma (\eta_c \rightarrow \gamma \gamma )/\Gamma (\psi_{1S} \rightarrow e^+e^-) \approx 2.2\pm 0.2$. The central value for $\Gamma (\psi_{1S} \rightarrow e^+ e^-)$in the 1992 Particle Data Tables then leads to a (non relativistic) prediction $\Gamma (\eta_c \rightarrow \gamma \gamma )\approx 11.8\pm 0.8$ keV. This prediction is in good agreement with a recent measurement by the ARGUS collaboration, is consistent with a recent measurement by the L3 collaboration but is significantly higher than several earlier measurements and than previous theoretical estimates, which usually assume $R_\circ =1$. The correction to $R_\circ =1$ is estimated to be smaller but nonnegligible for the $b\bar b$ system. Using the current central measurement for $\Gamma (\Upsilon_{1S}\rightarrow e^+e^-)$ we find $\Gamma (\eta_b\rightarrow \gamma \gamma )\approx 0.58\pm 0.03$ keV. A rough estimate of relativistic corrections reduces the expected two photon rates to about 8.8 keV and 0.52 keV for the $\eta_c$ and $\eta_b$ mesons respectively. Such correctionsComment: Estimates of likely relativistic corrections to the results have been adde

Testing General Relativity with Present and Future Astrophysical Observations

One century after its formulation, Einstein's general relativity has maderemarkable predictions and turned out to be compatible with all experimentaltests. Most of these tests probe the theory in the weak-field regime, and thereare theoretical and experimental reasons to believe that general relativityshould be modified when gravitational fields are strong and spacetime curvatureis large. The best astrophysical laboratories to probe strong-field gravity areblack holes and neutron stars, whether isolated or in binary systems. We reviewthe motivations to consider extensions of general relativity. We present a(necessarily incomplete) catalog of modified theories of gravity for whichstrong-field predictions have been computed and contrasted to Einstein'stheory, and we summarize our current understanding of the structure anddynamics of compact objects in these theories. We discuss current bounds onmodified gravity from binary pulsar and cosmological observations, and wehighlight the potential of future gravitational wave measurements to inform uson the behavior of gravity in the strong-field regime

Exploring new physics frontiers through numerical relativity

The demand to obtain answers to highly complex problems within strong-field gravity has been met with significant progress in the numerical solution of Einstein's equations - along with some spectacular results - in various setups. We review techniques for solving Einstein's equations in generic spacetimes, focusing on fully nonlinear evolutions but also on how to benchmark those results with perturbative approaches. The results address problems in high-energy physics, holography, mathematical physics, fundamental physics, astrophysics and cosmology