Testing modified gravity and no-hair relations for the Kerr-Newman metric through quasi-periodic oscillations of galactic microquasars

We construct multipole moments for stationary, asymptotically flat, spacetime solutions to higher-order curvature theories of gravity. The moments are defined using $3+1$ techniques involving timelike Killing vector constructions as in the classic papers by Geroch and Hansen. Using the fact that the Kerr-Newman metric is a vacuum solution to a particular class of $f(R)$ theories of gravity, we compute all its moments, and find that they admit recurrence relations similar to those for the Kerr solution in general relativity. It has been proposed previously that modelling the measured frequencies of quasi-periodic oscillations from galactic microquasars enables experimental tests of the no-hair theorem. We explore the possibility that, even if the no-hair relation is found to break down in the context of general relativity, there may be an $f(R)$ counterpart that is preserved. We apply the results to the microquasars GRS $1915$+$105$ and GRO J$1655$-$40$ using the diskoseismology and kinematic resonance models, and constrain the spins and `charges' [which are not really electric charges in the $f(R)$ context] of their black holes.Comment: 14 pages, 5 figures; Accepted for publication in PR

Neutron star deformation due to poloidal-toroidal magnetic fields of arbitrary multipole order: a new analytic approach

A recipe is presented to construct an analytic, self-consistent model of a non-barotropic neutron star with a poloidal-toroidal field of arbitrary multipole order, whose toroidal component is confined in a torus around the neutral curve inside the star, as in numerical simulations of twisted tori. The recipe takes advantage of magnetic-field-aligned coordinates to ensure continuity of the mass density at the surface of the torus. The density perturbation and ellipticity of such a star are calculated in general and for the special case of a mixed dipole-quadrupole field as a worked example. The calculation generalises previous work restricted to dipolar, poloidal-toroidal and multipolar, poloidal-only configurations. The results are applied, as an example, to magnetars whose observations (e.g., spectral features and pulse modulation) indicate that the internal magnetic fields may be at least one order of magnitude stronger than the external fields, as inferred from their spin downs, and are not purely dipolar.Comment: 14 pages, 6 figures, 1 table. Accepted for publication in the Monthly Notices of the Royal Astronomical Societ

Gravitational perturbations of a Kerr black hole in f(R)f(R) gravity

Modified theories of gravity are often built such that they contain general relativity as a limiting case. This inclusion property implies that the Kerr metric is common to many families of theories. For example, all analytic $f(R)$ theories with vanishing constant term admit the Kerr solution. In any given theory, however, the response of the gravitational field to astrophysical disturbances is tied to the structure of the field equations. As such, even if black holes are Kerr, the underlying theory can, in principle, be probed through gravitational distortions. In this paper, we study linear perturbations of a Kerr black hole in $f(R)$ gravity using the Newman-Penrose formalism. We show that, as in general relativity, the equations governing the perturbed metric, which depend on the quadratic term of the function $f$, completely decouple.Comment: 8 pages. Accepted for publication in Phys. Rev.