Slow Rotation Limit Research Articles

Accretion onto disc galaxies via hot and rotating CGM inflows

ABSTRACT Observed accretion rates onto the Milky Way and other local spirals fall short of that required to sustain star formation for cosmological timescales. A potential avenue for this unseen accretion is a rotating inflow in the volume-filling hot phase ($\sim 10^6\, {\rm K}$) of the circumgalactic medium (CGM), as suggested by some cosmological simulations. Using hydrodynamic simulations and a new analytic solution valid in the slow-rotation limit, we show that a hot inflow spins up as it approaches the galaxy, while remaining hot, subsonic, and quasi-spherical. Within the radius of angular momentum support ($\sim 15\, {\rm kpc}$ for the Milky Way) the hot flow flattens into a disc geometry and then cools from $\sim 10^6$ to $\sim 10^4\, {\rm K}$ at the disc–halo interface. Cooling affects all hot gas, rather than just a subset of individual gas clouds, implying that accretion via hot inflows does not rely on local thermal instability in contrast with ‘precipitation’ models for galaxy accretion. Prior to cooling and accretion the inflow completes ≈tcool/tff radians of rotation, where tcool/tff is the cooling time to free-fall time ratio in hot gas immediately outside the galaxy. The ratio tcool/tff may thus govern the development of turbulence and enhancement of magnetic fields in gas accreting onto low-redshift spirals. We show that if rotating hot inflows are common in Milky-Way-size disc galaxies, as predicted, then signatures of the expected hot gas rotation profile should be observable with X-ray telescopes and fast radio burst surveys.

Shadow Implications: What Does Measuring the Photon Ring Imply for Gravity?

With the imaging and characterization of the horizon-scale images of M87* and Sgr A* by the Event Horizon Telescope (EHT), it has become possible to resolve the near-horizon region of astrophysical black holes. As a result, there has been considerable interest in the implications of the measurement of the shadow size, i.e., the asymptotic photon ring. We explore the general implications of such a measurement, identifying what is and, more importantly, is not constrained by such measurements, with applications to EHT and future instruments. We consider a general spherically symmetric metric, which effectively applies for a polar observer (appropriate for M87*) in the slow rotation limit. We propose a nonperturbative, nonparametric spacetime-domain characterization of shadow size and related measurements that makes explicit the nature and power (or lack thereof) of shadow-size-based constraints, and facilitates comparisons among observations and targets.

Slowly rotating black holes with exact Killing tensor symmetries

We present a novel family of slowly rotating black hole solutions in four, and higher dimensions, that extend the well known Lense-Thirring spacetime and solve the field equations to linear order in rotation parameter. As "exact metrics" in their own right, the new (non-vacuum) spacetimes feature the following two remarkable properties: i) near the black hole horizon they can be cast in the, manifestly regular, Painlev\'e-Gullstrand form and ii) they admit exact Killing tensor symmetries. We show these symmetries are inherited from the principal Killing-Yano tensor of the exact rotating black hole geometry in the slow rotation limit. This provides a missing link as to how the exact hidden symmetries emerge as rotation is switched on. Remarkably, in higher dimensions the novel generalized Lense-Thirring spacetimes feature a rapidly growing number of exact irreducible rank-2, as well as higher-rank, Killing tensors -- giving a first example of a physical spacetime with more hidden than explicit symmetries.

The evolutions of the innermost stable circular orbits in dynamical spacetimes

In this paper, we studied the evolutions of the innermost stable circular orbits (ISCOs) in dynamical spacetimes. At first, we reviewed the method to obtain the ISCO in Schwarzschild spacetime by varying its conserved orbital angular momentum. Then, we demonstrated this method is equivalent to the effective potential method in general static and stationary spacetimes. Unlike the effective potential method, which depends on the presence of the conserved orbital energy, this method requires the existence of conserved orbital angular momentum in spacetime. So it can be easily generalized to the dynamical spacetimes where there exists conserved orbital angular momentum. From this generalization, we studied the evolutions of the ISCOs in Vaidya spacetime, Vaidya-AdS spacetime and the slow rotation limit of Kerr–Vaidya spacetime. The results given by these examples are all reasonable and can be compared with the evolutions of the photon spheres in dynamical spacetimes.

Relativistic effective action of dynamical gravitomagnetic tides for slowly rotating neutron stars

Gravitomagnetic quasi-normal modes of neutron stars are resonantly excited by tidal effects during a binary inspiral, leading to a potentially measurable effect in the gravitational-wave signal. We take an important step towards incorporating these effects in waveform models by developing a relativistic effective action for the gravitomagnetic dynamics that clarifies a number of subtleties. Working in the slow-rotation limit, we first consider the post-Newtonian approximation and explicitly derive the effective action from the equations of motion. We demonstrate that this formulation opens a way to compute mode frequencies, yields insights into the relevant matter variables, and elucidates the role of a shift symmetry of the fluid properties under a displacement of the gravitomagnetic mode amplitudes. We then construct a fully relativistic action based on the symmetries and a power counting scheme. This action involves four coupling coefficients that depend on the internal structure of the neutron star and characterize the key matter parameters imprinted in the gravitational waves. We show that, after fixing one of the coefficients by normalization, the other three directly involve the two kinds of gravitomagnetic Love numbers (static and irrotational), and the mode frequencies. We discuss several interesting features and dynamical consequences of this action, and analyze the frequency-domain response function (the frequency-dependent ratio between the induced flux quadrupole and the external gravitomagnetic field), and a corresponding Love operator representing the time-domain response. Our results provide the foundation for deriving precision predictions of gravitomagnetic effects, and the nuclear physics they encode, for gravitational-wave astronomy.

Light bending by a slowly rotating source in quadratic theories of gravity

In this paper we study the light bending caused by a slowly rotating source in the context of quadratic theories of gravity, in which the Einstein--Hilbert action is extended by additional terms quadratic in the curvature tensors. The deflection angle is computed employing the method based on the Gauss--Bonnet theorem and working in the approximation of a weak lens; also, we assume that the source and observer are at an infinite distance. The formalism presented is very general and applies to any spacetime metric in the limit of weak gravitational field and slow rotation. We find the explicit formula for the deflection angle for several local and nonlocal theories, and also discuss some phenomenological implications.

Blackhole in nonlocal gravity: comparing metric from Newmann\u2013Janis algorithm with slowly rotating solution

The strong gravitational field near massive blackhole is an interesting regime to test General Relativity (GR) and modified gravity theories. The knowledge of spacetime metric around a blackhole is a primary step for such tests. Solving field equations for rotating blackhole is extremely challenging task for the most modified gravity theories. Though the derivation of Kerr metric of GR is also demanding job, the magical Newmann–Janis algorithm does it without actually solving Einstein equation for rotating blackhole. Due to this notable success of Newmann–Janis algorithm in the case of Kerr metric, it has been being used to obtain rotating blackhole solution in modified gravity theories. In this work, we derive the spacetime metric for the external region of a rotating blackhole in a nonlocal gravity theory using Newmann–Janis algorithm. We also derive metric for a slowly rotating blackhole by perturbatively solving field equations of the theory. We discuss the applicability of Newmann–Janis algorithm to nonlocal gravity by comparing slow rotation limit of the metric obtained through Newmann–Janis algorithm with slowly rotating solution of the field equation.

Black hole magnetospheres in the Born–Infeld theory

We study the force-free electrodynamics on rotating black holes in the Born–Infeld (BI) effective theory. The stream equation describing a steady and axisymmetric magnetosphere is derived. From its near-horizon behavior, we obtain the modified Znajek regularity condition, with which we find that the horizon resistivity in the BI theory is generally not a constant. As expected, the outer boundary condition far away from the hole remains unchanged. In terms of the conditions at both boundaries, we derive the perturbative solution of split monopole in the slow rotation limit. It is interesting to realize that the correction to the solution relies not only on the parameter in the BI theory, but also on the radius (or the mass) of the hole. We also show that the quantum effects can undermine the energy extraction process of the magnetosphere in the nonlinear theory and the extraction rate gets the maximum in the Maxwell theory.

Existence of the Blandford-Znajek monopole for a slowly rotating Kerr black hole

The Blandford-Znajek monopole is a conjectured solution of force-free electrodynamics in the vicinity of a slowly rotating Kerr black hole, supposedly defined as a perturbation in small angular momentum. It is used to argue for the extraction of energy from rotating black holes by the Blandford-Znajek process. We set up a careful analysis of the perturbative definition of the Blandford-Znajek monopole, showing in particular that the regime in which it is defined allows to use the technique of matched asymptotic expansions. Our conclusion is that the Blandford-Znajek monopole, as it is defined, is not consistent with demanding physically reasonable boundary conditions far away from the event horizon. This puts into question the existence of the Blandford-Znajek monopole, at least in the limit of slow rotation of the Kerr black hole.

Towards a Gordon form of the Kerr spacetime

It is not currently known how to put the Kerr spacetime metric into the so-called Gordon form, although the closely related Kerr–Schild form of the Kerr metric is well known. A Gordon form for the Kerr geometry, if it could be found, would be particularly useful in developing analogue models for the Kerr spacetime, since the Gordon form is explicitly given in terms of the 4-velocity and ‘refractive index’ of an effective medium. In the current article we report progress toward this goal. First we present the Gordon form for an approximation to Kerr spacetime in the slow-rotation limit, obtained by suitably modifying the well-known Lense–Thirring form of the slow-rotation metric. Second we present the Gordon form for the Kerr spacetime in the near-null limit, (the 4-velocity of the medium being close to null). That these two perturbative approximations to the Kerr spacetime in Gordon form exist gives us some confidence that ultimately one might be able to write the exact Kerr spacetime in this form.

Energy extraction from Kerr black holes by rigidly rotating strings

In this paper, we show that a rigidly rotating string can extract the rotational energy from a rotating black hole. We consider Nambu-Goto strings stationary with respect to a corotating Killing vector with an uniform angular velocity $\omega$ in the Kerr spacetime. We show that a necessary condition of the energy-extraction process is that an effective horizon on the string world sheet, which corresponds to the inner light surface, is inside the ergosphere of the Kerr black hole and the angular velocity $\omega$ is less than that of the black hole $\Omega_\mathrm{h}$. Furthermore, we discuss global configurations of such strings in both of a slow-rotation limit and the extremal Kerr case.

Slowly rotating charged fluid balls in the presence of a cosmological constant

We examine charged slowly rotating perfect fluids in the presence of a cosmological constant. The asymptotic form of the vacuum solutions to the linearised Einstein-Maxwell field equations is found and the possibility of matching this vacuum to the slow rotating Garc\'ia metric is considered. We show that, contrary to the case of zero cosmological constant, this Garc\'ia metric can be matched to an asymptotically de Sitter vacuum in the slow rotation limit. We conclude the Garc\'ia metric may potentially be suitable for describing a charged isolated rotating body in a cosmological background.

Effect of particle rotation on the drift velocity for nonspherical aerosol particles

The theoretical drift velocity of a randomly oriented nonspherical aerosol particles in an external field has been previously computed both in the limit of slow rotation and in the limit of fast rotation but not in the intermediate interval. The low rotation limit has been widely used to calculate the drift velocity for a range of nonspherical particles. The fast rotation limit, which is equivalent to the projected area method, has been used for molecular ions and agglomerates. A 1-D model equation containing the particle acceleration and an orientation dependent friction coefficient is proposed to predict the drift velocity between the two limits. This model has the essential physical phenomena without the complications of the 3-D treatment of the combined translation and rotation behavior. As an example, the drift velocity is computed for model parameters based on the friction tensor and rotational diffusion coefficient for circular cross section nanorods in the free molecular limit. For a momentum accommodation coefficient of 0.9 and a particle density of 1000kg/m3, the largest percent deviation from the low rotation velocity limit is 14% and the deviation is at most 1% for nanorods of any length for diameters of 20nm diameter or larger. Much larger changes in the velocity ratio are shown to occur if the momentum accommodation coefficient is reduced. Also, examples are given where the dimensionless rotation rate increases by about a factor of 7 from either a change in density or a change in the mean free path of the background gas. The results of recent experiments and model calculation of the collision cross section and mobilities of large molecular ions are discussed in regard to our model predictions on the effect of rotation on the drift velocity.

Angular momentum redistribution by mixed modes in evolved low-mass stars

Seismic observations by the space-borne mission \emph{Kepler} have shown that the core of red giant stars slows down while evolving, requiring an efficient physical mechanism to extract angular momentum from the inner layers. Current stellar evolution codes fail to reproduce the observed rotation rates by several orders of magnitude, and predict a drastic spin-up of red giant cores instead. New efficient mechanisms of angular momentum transport are thus required. In this framework, our aim is to investigate the possibility that mixed modes extract angular momentum from the inner radiative regions of evolved low-mass stars. To this end, we consider the Transformed Eulerian Mean (TEM) formalism, introduced by Andrews \& McIntyre (1978), that allows us to consider the combined effect of both the wave momentum flux in the mean angular momentum equation and the wave heat flux in the mean entropy equation as well as their interplay with the meridional circulation. In radiative layers of evolved low-mass stars, the quasi-adiabatic approximation, the limit of slow rotation, and the asymptotic regime can be applied for mixed modes and enable us to establish a prescription for the wave fluxes in the mean equations. The formalism is finally applied to a $1.3 M_\odot$ benchmark model, representative of observed CoRoT and \emph{Kepler} oscillating evolved stars. We show that the influence of the wave heat flux on the mean angular momentum is not negligible and that the overall effect of mixed modes is to extract angular momentum from the innermost region of the star. A quantitative and accurate estimate requires realistic values of mode amplitudes. This is provided in a companion paper.

Quasinormal modes of weakly charged Kerr-Newman spacetimes

The resonant mode spectrum of the Kerr-Newman spacetime is presently unknown. These modes, called the quasinormal modes, play a central role in determining the stability of Kerr-Newman black holes and their response to perturbations. We present a new formalism, generalized from time-independent perturbation theory in quantum mechanics, for calculating the quasinormal mode frequencies of weakly charged Kerr-Newman spacetimes of arbitrary spin. Our method makes use of an original technique for applying perturbation theory to zeroth-order solutions that are not square- integrable, and it can be applied to other problems in theoretical physics. The new formalism reveals no unstable modes, which together with previous results in the slow-rotation limit strongly indicates the modal stability of the Kerr-Newman spacetime. Our techniques and results are of interest in the areas of holographic duality, foundational problems in General Relativity, and possibly in astrophysical systems.

UNIVERSALITY OF THE ACCELERATION DUE TO GRAVITY ON THE SURFACE OF A RAPIDLY ROTATING NEUTRON STAR

On the surface of a rapidly rotating neutron star, the effective centrifugal force decreases the effective acceleration due to gravity (as measured in the rotating frame) at the equator while increasing the acceleration at the poles due to the centrifugal flattening of the star into an oblate spheroid. We compute the effective gravitational acceleration for relativistic rapidly rotating neutron stars and show that for a star with mass $M$, equatorial radius $R_e$, and angular velocity $\Omega$, the deviations of the effective acceleration due to gravity from the nonrotating case take on a universal form that depends only on the compactness ratio $M/R_e$, the dimensionless square of the angular velocity $\Omega^2R_e^3/GM$, and the latitude on the star's surface. This dependence is universal, in that it has very little dependence on the neutron star's equation of state. The effective gravity is expanded in the slow rotation limit to show the dependence on the effective centrifugal force, oblate shape of the star and the quadrupole moment of the gravitational field. In addition, an empirical fit and simple formula for the effective gravity is found. We find that the increase in the acceleration due to gravity at the poles is of the same order of magnitude as the decrease in the effective acceleration due to gravity at the equator for all realistic value of mass, radius and spin. For neutron stars that spin with frequencies near 600 Hz the difference between the effective gravity at the poles and the equator is about 20%.

A Vortex Model for Rotating Compact Objects

In this paper a rotating stationary solution of the vacuum Einstein equations with a cosmological constant is exhibited which reduces to de Sitter’s interior cosmological solution when the angular momentum goes to zero. This solution is locally isomorphic to de Sitter space, but as one approaches the axis of rotation it has a novel feature: a conical event horizon. This suggests that in reality rotating compact objects have a vortex structure similar to that conjectured for rotating superfluid droplets. In the limit of slow rotation the vortex core would be nearly cylindrical and the space-time inside � �

BREAKDOWN OF I -LOVE- Q UNIVERSALITY IN RAPIDLY ROTATING RELATIVISTIC STARS

It was shown recently, that normalized relations between the moment of inertia (I), the quadrupole moment (Q) and the tidal deformability (Love number) exist and for slowly-rotating neutron stars they are almost independent of the equation of state (EOS). We extend the computation of the I-Q relation to models rotating up to the mass-shedding limit and show that the universality of the relations is lost. With increasing rotation rate, the normalized I-Q relation departs significantly from its slow-rotation limit deviating up to 40% for neutron stars and up to 75% for strange stars. The deviation is also EOS dependent and for a broad set of hadronic and strange matter EOS the spread due to rotation is comparable to the spread due to the EOS, if one considers sequences with fixed rotational frequency. Still, for a restricted sample of modern realistic EOS one can parameterize the deviations from universality as a function of rotation only. The previously proposed I-Love-Q relations should thus be used with care, because they lose their universality in astrophysical situations involving compact objects rotating faster than a few hundred Hz.

The excitation spectrum of rotating strings with masses at the ends

We compute the spectrum of excitations of the rotating Nambu-Goto string with masses at the ends. We find interesting quasi-massless modes in the limit of slow rotation and comment on the nontrivial relation between world-sheet and target space energy.

Scalar, electromagnetic, and gravitational perturbations of Kerr-Newman black holes in the slow-rotation limit

In Einstein-Maxwell theory, according to classic uniqueness theorems, the most general stationary black-hole solution is the axisymmetric Kerr-Newman metric, which is defined by three parameters: mass, spin and electric charge. The radial and angular dependence of gravitational and electromagnetic perturbations in the Kerr-Newman geometry do not seem to be separable. In this paper we circumvent this problem by studying scalar, electromagnetic and gravitational perturbations of Kerr-Newman black holes in the slow-rotation limit. We extend (and provide details of) the analysis presented in a recent Letter [arXiv:1304.1160]. Working at linear order in the spin, we present the first detailed derivation of the axial and polar perturbation equations in the gravito-electromagnetic case, and we compute the corresponding quasinormal modes for any value of the electric charge. Our study is the first self-consistent stability analysis of the Kerr-Newman metric, and in principle it can be extended to any order in the small rotation parameter. We find numerical evidence that the axial and polar sectors are isospectral at first order in the spin, and speculate on the possible implications of this result.