Frame-dragging Research Articles

Frame-dragging effects on magnetic fields near a rotating black hole

We discuss the role of general relativity frame dragging acting on magnetic field lines near a rotating (Kerr) black hole. Near ergosphere the magnetic structure becomes strongly influenced and magnetic null points can develop. We consider aligned magnetic fields as well as fields inclined with respect to the rotation axis, and the two cases are shown to behave in profoundly different ways. Further, we construct surfaces of equal values of local electric and magnetic intensities, which have not yet been discussed in the full generality of a boosted rotating black hole.

VLBI FOR GRAVITY PROBE B . I. OVERVIEW

We describe the NASA/Stanford gyroscope relativity mission, Gravity Probe B (GP-B), and provide an overview of the following series of six astrometric and astrophysical papers that report on our radio observations and analyses made in support of this mission. The main goal of this 8.5 year program of differential VLBI astrometry was to determine the proper motion of the guide star of the GP-B mission, the RS CVn binary IM Pegasi (IM Peg; HR 8703). This proper motion is determined with respect to compact, extragalactic reference sources. The results are: -20.833 +- 0.090 mas/yr and -27.267 +- 0.095 mas/yr for, respectively, the right ascension and declination, in local Cartesian coordinates, of IM Peg's proper motion, and 10.370 +- 0.074 mas (i.e., 96.43 +- 0.69 pc) for its parallax (and distance). Each quoted uncertainty is meant to represent an ~70% confidence interval that includes the estimated contribution from systematic error. These results are accurate enough not to discernibly degrade the GP-B estimates of its gyroscopes' relativistic precessions: the frame-dragging and geodetic effects.

TIDAL DISRUPTIONS OF WHITE DWARFS FROM ULTRA-CLOSE ENCOUNTERS WITH INTERMEDIATE-MASS SPINNING BLACK HOLES

We present numerical relativity results of tidal disruptions of white dwarfs from ultra-close encounters with a spinning, intermediate mass black hole. These encounters require a full general relativistic treatment of gravity. We show that the disruption process and prompt accretion of the debris strongly depend on the magnitude and orientation of the black hole spin. However, the late-time accretion onto the black hole follows the same decay, $\dot{M}$ ~ t^{-5/3}, estimated from Newtonian gravity disruption studies. We compute the spectrum of the disk formed from the fallback material using a slim disk model. The disk spectrum peaks in the soft X-rays and sustains Eddington luminosity for 1-3 yrs after the disruption. For arbitrary black hole spin orientations, the disrupted material is scattered away from the orbital plane by relativistic frame dragging, which often leads to obscuration of the inner fallback disk by the outflowing debris. The disruption events also yield bursts of gravitational radiation with characteristic frequencies of ~3.2 Hz and strain amplitudes of ~10^{-18} for galactic intermediate mass black holes. The optimistic rate of considered ultra-close disruptions is consistent with no sources found in ROSAT all-sky survey. The future missions like Wide-Field X-ray Telescope (WFXT) could observe dozens of events.

PROSPECTS FOR PROBING THE SPACETIME OF Sgr A* WITH PULSARS

The discovery of radio pulsars in compact orbits around Sgr A* would allow an unprecedented and detailed investigation of the spacetime of the supermassive black hole. This paper shows that pulsar timing, including that of a single pulsar, has the potential to provide novel tests of general relativity, in particular its cosmic censorship conjecture and no-hair theorem for rotating black holes. These experiments can be performed by timing observations with 100 micro-second precision, achievable with the Square Kilometre Array for a normal pulsar at frequency above 15 GHz. Based on the standard pulsar timing technique, we develop a method that allows the determination of the mass, spin, and quadrupole moment of Sgr A*, and provides a consistent covariance analysis of the measurement errors. Furthermore, we test this method in detailed mock data simulations. It seems likely that only for orbital periods below ~0.3 yr is there the possibility of having negligible external perturbations. For such orbits we expect a ~10^-3 test of the frame dragging and a ~10^-2 test of the no-hair theorem within 5 years, if Sgr A* is spinning rapidly. Our method is also capable of identifying perturbations caused by distributed mass around Sgr A*, thus providing high confidence in these gravity tests. Our analysis is not affected by uncertainties in our knowledge of the distance to the Galactic center, R0. A combination of pulsar timing with the astrometric results of stellar orbits would greatly improve the measurement precision of R0.

Tidal disruption of white dwarfs by intermediate mass black holes

Modeling ultra-close encounters between a white dwarf and a spinning, intermediate mass black hole requires a full general relativistic treatment of gravity. This paper summarizes results from such a study. Our results show that the disruption process and prompt accretion of the debris strongly depend on the magnitude and orientation of the black hole spin. On the other hand, the late-time accretion onto the black hole follows the same decay, ˙ M ∝ t −5/3 , estimated from Newtonian gravity disruption studies. The spectrum of the fallback material peaks in the soft X-rays and sustains Eddington luminosity for 1-3yrs after the disruption. The orientation of the black hole spin has also a profound effect on how the outflowing debris obscures the central region. The disruption produces a burst of gravitational radiation with characteristic frequencies of ∼3.2Hz and strain amplitudes of ∼10 −18 for galactic intermediate mass black holes. In a tidal disruption event, the spin of black hole (BH) will most likely not be aligned with the orbital angular momentum of the incoming star. As a consequence, the tidal debris when it falls back will form a tilted disk (1). For thin disks, the Bardeen-Petterson effect will help align the inner part of the disk with the BH spin (2), but for the thick disks expected from tidal disruptions, the alignment may not happen (3-5), potentially changing our conventional picture of these explosive events. Even more remarkable will be ultra-close encounters, where an incoming star and associated tidal debris will experience general relativistic effects. Examples of strong curvature effects altering the dynamics of the disruption are frame dragging and the location of the innermost stable orbit, responsible for changing the traditional S-shape debris observed in Newtonian gravity simulations to a shell-like appearance, engulfing the BH. There are very few tidal disruption numerical simulations that account for general relativistic effects (6- 9). This paper summarizes the results from a study published recently (10). The study was primarily aimed at investigating observational signatures associated with strong gravity that may shed light on the presence of intermediate mass BHs. It included estimates of electromagnetic transient radiation using a slim disk model to compute the spectrum during the fallback phase. We found that the sources shine at Eddington luminosity ∼10 41 erg s −1 for about 1-3yrs, and then fade approximately as ∝ t −5/3 . Furthermore, there is a 50/50 chance that the inner disk will be obscured by outflowing debris for a fully misaligned BH spin. The study also included estimates of the gravitational wave burst signal produced during the encounters.

Slowly rotating stars and black holes in dynamical Chern-Simons gravity

Chern-Simons (CS) modified gravity is an extension to general relativity (GR) in which the metric is coupled to a scalar field, resulting in modified Einstein field equations. In the dynamical theory, the scalar field is itself sourced by the Pontryagin density of the space-time. In this paper, the coupled system of equations for the metric and the scalar field is solved numerically for slowly-rotating neutron stars described with realistic equations of state and for slowly-rotating black holes. An analytic solution for a constant-density nonrelativistic object is also presented. It is shown that the black hole solution cannot be used to describe the exterior spacetime of a star as was previously assumed. In addition, whereas previous analysis were limited to the small-coupling regime, this paper considers arbitrarily large coupling strengths. It is found that the CS modification leads to two effects on the gravitomagnetic sector of the metric: (i) Near the surface of a star or the horizon of a black hole, the magnitude of the gravitomagnetic potential is decreased and frame-dragging effects are reduced in comparison to GR. (ii) In the case of a star, the angular momentum J, as measured by distant observers, is enhanced in CS gravity as compared to standard GR. For a large coupling strength, the near-zone frame-dragging effects become significantly screened, whereas the far-zone enhancement saturate at a maximum value max(Delta J) ~ (M/R) J. Using measurements of frame-dragging effects around the Earth by Gravity Probe B and the LAGEOS satellites, a weak but robust constraint is set to the characteristic CS lengthscale, xi^{1/4} <~ 10^8 km.

Measuring gravitomagnetic effects by a multi-ring-laser gyroscope

We propose an under-ground experiment to detect the general relativistic effects due to the curvature of space-time around the Earth (de Sitter effect) and to rotation of the planet (dragging of the inertial frames or Lense-Thirring effect). It is based on the comparison between the IERS value of the Earth rotation vector and corresponding measurements obtained by a tri-axial laser detector of rotation. The proposed detector consists of six large ring-lasers arranged along three orthogonal axes. In about two years of data taking, the 1% sensitivity required for the measurement of the Lense-Thirring drag can be reached with square rings of 6 $m$ side, assuming a shot noise limited sensitivity ($ 20 prad/s/\sqrt{Hz}$). The multi-gyros system, composed of rings whose planes are perpendicular to one or the other of three orthogonal axes, can be built in several ways. Here, we consider cubic and octahedron structures. The symmetries of the proposed configurations provide mathematical relations that can be used to study the stability of the scale factors, the relative orientations or the ring-laser planes, very important to get rid of systematics in long-term measurements, which are required in order to determine the relativistic effects.

Testing gravitational physics with satellite laser ranging

Laser ranging, both Lunar (LLR) and Satellite Laser Ranging (SLR), is one of the most accurate techniques to test gravitational physics and Einstein’s theory of General Relativity. Lunar Laser Ranging has provided very accurate tests of both the strong equivalence principle, at the foundations of General Relativity, and of the weak equivalence principle, at the basis of any metric theory of gravity; it has provided strong limits to the values of the so-called PPN (Parametrized Post-Newtonian) parameters, that are used to test the post-Newtonian limit of General Relativity, strong limits to conceivable deviations to the inverse square law for very weak gravity and accurate measurements of the geodetic precession, an effect predicted by General Relativity. Satellite laser ranging has provided strong limits to deviations to the inverse square gravity law, at a different range with respect to LLR, and in particular has given the first direct test of the gravitomagnetic field by measuring the gravitomagnetic shift of the node of a satellite, a frame-dragging effect also called Lense-Thirring effect. Here, after an introduction to gravitomagnetism and frame-dragging, we describe the latest results in measuring the Lense-Thirring effect using the LAGEOS satellites and the latest gravity field models obtained by the space mission GRACE. Finally, we describe an update of the LARES (LAser RElativity Satellite) mission. LARES is planned for launch in 2011 to further improve the accuracy in the measurement of frame-dragging.

Rotation, the Equivalence Principle, and the Gravity Probe B Experiment

The ultraprecise Gravity Probe B experiment measured the frame-dragging effect and geodetic precession on four quartz gyros. We use this result to test WEP II (weak equivalence principle II) which includes rotation in the universal free-fall motion. The free-fall Eötvös parameter η for a rotating body is ≤10(-11) with a four-order improvement over previous results. The anomalous torque per unit angular momentum parameter λ is constrained to (-0.05±3.67)×10(-15) s(-1), (0.24±0.98)×10(-15) s(-1), and (0±3.6)×10(-13) s(-1), respectively, in the directions of geodetic effect, frame-dragging effect, and angular momentum axis; the dimensionless frequency-dependence parameter κ is constrained to (1.75±4.96)×10(-17), (1.80±1.34)×10(-17), and (0±3)×10(-14), respectively.

Gravity Probe B: Final Results of a Space Experiment to Test General Relativity

Gravity Probe B, launched 20 April 2004, is a space experiment testing two fundamental predictions of Einstein's theory of general relativity (GR), the geodetic and frame-dragging effects, by means of cryogenic gyroscopes in Earth orbit. Data collection started 28 August 2004 and ended 14 August 2005. Analysis of the data from all four gyroscopes results in a geodetic drift rate of -6601.8±18.3 mas/yr and a frame-dragging drift rate of -37.2±7.2 mas/yr, to be compared with the GR predictions of -6606.1 mas/yr and -39.2 mas/yr, respectively ("mas" is milliarcsecond; 1 mas=4.848×10(-9) rad).

Frame-Dragging Vortexes and Tidal Tendexes Attached to Colliding Black Holes: Visualizing the Curvature of Spacetime

When one splits spacetime into space plus time, the spacetime curvature (Weyl tensor) gets split into an "electric" part E(jk) that describes tidal gravity and a "magnetic" part B(jk) that describes differential dragging of inertial frames. We introduce tools for visualizing B(jk) (frame-drag vortex lines, their vorticity, and vortexes) and E(jk) (tidal tendex lines, their tendicity, and tendexes) and also visualizations of a black-hole horizon's (scalar) vorticity and tendicity. We use these tools to elucidate the nonlinear dynamics of curved spacetime in merging black-hole binaries.

Geodetic precession and frame dragging observed far from massive objects and close to a gyroscope

Abstract Total precession (geodetic precession and frame dragging) depends on the velocity of each source of gravitation, which means that it depends on the choice of the coordinate system. We consider the latter as an anomaly specifically in the Gravity Probe B experiment, we investigated it and solved this anomaly. Thus, we proved that if our present expression for the geodetic precession is correct, then the frame dragging should be 25% less than its predicted value.

TOWARD RELATIVISTIC ORBIT FITTING OF GALACTIC CENTER STARS AND PULSARS

The S stars orbiting the Galactic center black hole reach speeds of up to a few percent the speed of light during pericenter passage. This makes, for example, S2 at pericenter much more relativistic than known binary pulsars, and opens up new possibilities for testing general relativity. This paper develops a technique for fitting nearly-Keplerian orbits with perturbations from Schwarzschild curvature, frame dragging, and spin-induced torque, to redshift measurements distributed along the orbit but concentrated around pericenter. Both orbital and light-path effects are taken into account. It turns out that absolute calibration of rest-frame frequency is not required. Hence, if pulsars on orbits similar to the S stars are discovered, the technique described here can be applied without change, allowing the much greater accuracies of pulsar timing to be taken advantage of. For example, pulse timing of 3 microsec over one hour amounts to an effective redshift precision of 30 cm/s, enough to measure frame dragging and the quadrupole moment from an S2-like orbit, provided problems like the Newtonian "foreground" due to other masses can be overcome. On the other hand, if stars with orbital periods of order a month are discovered, the same could be accomplished with stellar spectroscopy from the E-ELT at the level of 1 km/s.

Gravity Probe B experiment and gravitomagnetism

Gravitomagnetism is a low velocity and weak gravitational field approximation of general relativity. It provides a simple approach to post-Newtonian gravitational phenomena via electromagnetic analogy. Intended for advanced undergraduate students, the present paper applies gravitomagnetism to the quantitative study of the geodetic precession and frame dragging effects, both verified recently in the Gravity Probe B experiment. The result obtained is identical with Schiff's formula.

Multiband Photometry of the Chromospherically Active & Spotted Binary System IM Peg—the Guide Star for the Gravity Probe B Mission

ABSTRACTWe report on the starspot properties of IM Pegasi—the guide star of the Gravity Probe B (GP-B) satellite. GP-B’s mission is to measure two predicted consequences of general relativity—the frame-dragging and geodetic effects—via its extremely precise onboard gyroscopes. However, IM Peg is a chomospherically active binary system with a luminous K2 III primary star showing rotationally modulated (Prot ≈ 24.5 days) light variations from starspots. The starspots can potentially cause problems as GP-B can erroneously interpret a change in starspot coverage (and corresponding shifts in the light center) as the star’s movement. This apparent shift can also be exacerbated by possible changes in the light center (photocenter) of the binary system arising from changes in the light balance with the fainter ∼1 M⊙(main-sequence early G-type star) component. Since 2000, we have carried out multiband high-precision photoelectric photometry of IM Peg to determine its activity and starspot coverage. Our photometry uses Strömgren uvby intermediate-band filters, VRI filters, and TiO (720/750 nm) narrowband filter sets. Measurements were made relative to nearby comparison and check stars using 0.8 m and 0.25 m telescopes. Analysis of TiO and multiband continuum photometry constrains the starspot areas, temperatures, and surface distributions. The photometry has been modeled using the maximum entropy and Tikhonov regularizations to determine the properties of starspots and to evaluate the effects of changing starspot areas and distributions on the light center of the binary. Our results indicate that IM Peg’s activity should not affect the GP-B mission. We also present a study of IM Peg’s long-term starspot cycle, which shows evidence of being 20 yr long. Lastly, we have determined the intrinsic (unspotted) brightness of the star to be V mag = 5.62 ± 0.03.

ON MASS CONSTRAINTS IMPLIED BY THE RELATIVISTIC PRECESSION MODEL OF TWIN-PEAK QUASI-PERIODIC OSCILLATIONS IN CIRCINUS X-1

Boutloukos et al. (2006) discovered twin-peak quasi-periodic oscillations (QPOs) in 11 observations of the peculiar Z-source Circinus X-1. Among several other conjunctions the authors briefly discussed the related estimate of the compact object mass following from the geodesic relativistic precession model for kHz QPOs. Neglecting the neutron star rotation they reported the inferred mass M_0 = 2.2 +/- 0.3 M_\sun. We present a more detailed analysis of the estimate which involves the frame-dragging effects associated with rotating spacetimes. For a free mass we find acceptable fits of the model to data for (any) small dimensionless compact object angular momentum j=cJ/GM^2. Moreover, quality of the fit tends to increase very gently with rising j. Good fits are reached when M ~ M_0[1+0.55(j+j^2)]. It is therefore impossible to estimate the mass without the independent knowledge of the angular momentum and vice versa. Considering j up to 0.3 the range of the feasible values of mass extends up to 3M_\sun. We suggest that similar increase of estimated mass due to rotational effects can be relevant for several other sources.

Slowly rotating relativistic stars in tensor-vector-scalar theory

In order to examine the rotational effect around neutron star in tensor-vector-scalar (TeVeS) theory, we consider the slowly rotating relativistic stars with a uniform angular velocity. As a result, we find that similar to the case in general relativity (GR), the angular momentum is proportional to the angular velocity. Additionally, as the value of coupling constant $K$ becomes higher, the frame dragging in TeVeS becomes quite different distribution from that in GR, where we can also see the deviation even in the interior of star. While with smaller value of $K$, although the frame dragging approaches to that expected in GR, the induced vector field due to the rotation does not vanish and still exists. Thus, through the observations associated with relativistic object, one could be possible to distinguish the gravitational theory in strong field regime even in the case that the value of coupling constant $K$ is quite small.

Bound orbits of solar sails and general relativity

We study general relativistic effects on the bound orbits of solar sails. The combined effects of spacetime curvature and solar radiation pressure (SRP) lead to deviations from Kepler’s third law. Such kind of deviations also arise from frame dragging, the gravitational multipole moments of the sun, a net electric charge on the sun, and a positive cosmological constant. The SRP increases these deviations by several orders of magnitude, possibly rendering some of them detectable. We consider how the SRP modifies the perihelion shift of non-circular orbits, as well as the Lense-Thirring effect involving the precession of polar orbits. We investigate how the pitch angle for non-Keplerian orbits changes due to the partial absorption of light, general relativistic effects, and the oblateness of the sun. It is predicted that there is an analog of the Lense-Thirring effect for non-Keplerian orbits, in that the orbital plane precesses around the sun. We also consider the Poynting–Robertson effect and show that this effect can, in principle, be compensated for by an extremely small tilt of the solar sail.

Do spinors give rise to a frame-dragging effect?

We investigate the effect of the intrinsic spin of a fundamental spinor field on the surrounding spacetime geometry. We show that despite the lack of a rotating stress-energy source (and despite claims to the contrary) the intrinsic spin of a spin-half fermion gives rise to a frame-dragging effect analogous to that of orbital angular momentum, even in Einstein-Hilbert gravity where torsion is constrained to be zero. This resolves a paradox regarding the counter-force needed to restore Newton's third law in the well-known spin-orbit interaction. In addition, the frame-dragging effect gives rise to a long-range gravitationally mediated spin-spin dipole interaction coupling the internal spins of two sources. We argue that despite the weakness of the interaction, the spin-spin interaction will dominate over the ordinary inverse square Newtonian interaction in any process of sufficiently high energy for quantum field theoretical effects to be non-negligible.

GENERALIZED GENERAL RELATIVISTIC MAGNETOHYDRODYNAMIC EQUATIONS AND DISTINCTIVE PLASMA DYNAMICS AROUND ROTATING BLACK HOLES

To study phenomena of plasmas around rotating black holes, we have derived a set of 3+1 formalism of generalized general relativistic magnetohydrodynamic (GRMHD) equations. Especially, we investigated general relativistic phenomena with respect to the Ohm's law. We confirmed the electromotive force due to the gravitation, centrifugal force, and frame-dragging effect in plasmas near the black holes. These effects are significant only in the local small-scale phenomena compared to the scale of astrophysical objects. We discuss the possibility of magnetic reconnection, which is triggered by one of these effects in a small-scale region and influences the plasmas globally. We clarify the conditions of applicability of the generalized GRMHD, standard resistive GRMHD, and ideal GRMHD for plasmas in black hole magnetospheres.