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Luminous active galactic nuclei (AGN) and X-Ray binaries (XRBs) often contain geometrically thin, radiatively cooled accretion discs. According to theory, these are -- in many cases -- initially highly misaligned with the black hole equator. In this work, we present the first general relativistic magnetohydrodynamic simulations of very thin (h/r~0.015-0.05) accretion discs around rapidly spinning (a~0.9) black holes and tilted by 45-65 degrees. We show that the inner regions of the discs with h/r, 8 pages, 5 figures, accompanying animations included in YouTube playlist: https://www.youtube.com/playlist?list=PLDO1oeU33GwlaPSME1TdCto1Y3P6yG91L

We present a re-analysis of 47 Rossi X-ray Timing Explorer observations of the 11Hz accreting pulsar IGR J17480-2446 in Terzan 5 during its 2010 outburst. We studied the fast-time variability properties of the source and searched for quasi-periodic oscillations (QPOs) in a large frequency range. General Relativity predicts that frame-dragging occurs in the vicinity of a spinning compact object and induces the precession of matter orbiting said object. The relativistic precession model predicts that this frame-dragging can be observed as QPOs with a characteristic frequency in the light curves of accreting compact objects. Such QPOs have historically been classified as horizontal branch oscillations in neutron star systems, and for a neutron star spinning at 11 Hz these oscillations are expected at frequencies below 1 Hz. However, previous studies of IGR J17480-2446 have classified QPOs at 35-50 Hz as horizontal branch oscillations, thus casting doubts on the frame-dragging nature of such QPOs. Here we report the detection of seven very low-frequency QPOs, previously undetected, with centroid frequencies below 0.3 Hz, and which can be ascribed to frame-dragging. We also discuss the possible nature of the QPOs detected at 35-50 Hz in this alternative scenario., 9 pages, 4 figures, 2 tables

Radio pulsars in short-period eccentric binary orbits can be used to study both gravitational dynamics and binary evolution. The binary system containing PSR J1141$-$6545 includes a massive white dwarf (WD) companion that formed before the gravitationally bound young radio pulsar. We observe a temporal evolution of the orbital inclination of this pulsar that we infer is caused by a combination of a Newtonian quadrupole moment and Lense-Thirring precession of the orbit resulting from rapid rotation of the WD. Lense-Thirring precession, an effect of relativistic frame-dragging, is a prediction of general relativity. This detection is consistent with the evolutionary scenario in which the WD accreted matter from the pulsar progenitor, spinning up the WD to a period $< 200$ seconds., Accepted for publication in Science

We investigate frequency correlations of low frequency (LF, 16 pages, 22 figures

To answer the question posed in the title, we consider a novel diagnostic, viz., the difference in the time of arrival (TOA) at the observer of two light rays that simultaneously emanate from a source behind a spinning lens and pass by either side of the lens to reach the observer. This is completely different from the usual Shapiro gravitational time delay, where only one onward light ray is reflected back to the observer. The TOA essentially samples the frame dragging caused by the spinning lens, apart from other lens parameters. Assuming a charged regular Ayon-Beato and Garcia black hole as the spinning lens partner in some typical astrophysical pulsar black hole (PSR-BH) binaries, which provide the best laboratory for testing the TOA effect, we theoretically study how the prediction depends on the gyromagnetic ratio $$\left( Q/M\right) $$ and how it compares with those when the role of spinning lens partner is played by the centrally singular Kerr–Newman and Kerr black holes. The numerical estimates for two illustrative binary lens systems show microsecond-level delay at the zeroth order, which should be measurable. However, the TOA predictions under thin-lens approximation are shown to differ only at third or higher orders of smallness indicating that the regular and singular black holes cannot be observationally distinguished despite significant qualitative differences existing among them.

There is a drag force on objects moving in the background cosmological metric, known from galaxy cluster dynamics. The force is quite small over laboratory timescales, yet it applies in principle to all moving bodies in the universe. It means it is possible for matter to exchange momentum and energy with the gravitational field of the universe, and that the cosmological metric can be determined in principle from local measurements on moving bodies. The drag force can be understood as inductive rectilinear frame dragging. This dragging force exists in the rest frame of a moving object, and arises from the off-diagonal components induced in the boosted-frame metric. Unlike the Kerr metric or other typical frame-dragging geometries, cosmological inductive dragging occurs at uniform velocity, along the direction of motion, and dissipates energy. Proposed gravito-magnetic invariants formed from contractions of the Riemann tensor do not appear to capture inductive dragging effects, and this might be the first identification of inductive rectilinear dragging., 13 pages, 1 figure

The authors study general relativistic effects in multi-photon quantum interference, for quantum-optical platforms restricted to the earth's surface.

We investigate the Casimir effect between parallel plates placed along a circular trajectory around the rotating Damour–Solodkhin (D–S) and Teo wormholes. This is made through the calculation of the renormalized quantum vacuum energy density of a massless scalar field obeying the Dirichlet boundary conditions, initially at zero temperature. We use the zero tidal approximation inside the cavity. Then, we compare our results with those ones previously obtained in the literature with respect to the Kerr black hole. We also compare the computed Casimir energy density in a static D–S wormhole spacetime with that one recently found for a static Ellis wormhole. In what follows, we investigate the effect around the rotating Teo wormhole by calculating the Casimir energy density between the plates, and compare it with the same quantities obtained previously. Finally, we investigate the phenomenon at finite temperature, obtaining some Casimir thermodynamic quantities in the rotating D–S wormhole spacetime, comparing them with the ones valid in the Kerr black hole spacetime. With this, the ways as gravito-inertial and frame dragging effects influence the vacuum quantum fluctuations inside the Casimir apparatus allows to distinct among the different types of rotating wormholes and black holes.

An experimental test at the intersection of quantum physics and general relativity is proposed: measurement of relativistic frame dragging and geodetic precession using intrinsic spin of electrons. The behavior of intrinsic spin in spacetime dragged and warped by a massive rotating body is an experimentally open question, hence the results of such a measurement could have important theoretical consequences. Such a measurement is possible by using mm-scale ferromagnetic gyroscopes in orbit around the Earth. Under conditions where the rotational angular momentum of a ferromagnet is sufficiently small, a ferromagnet's angular momentum is dominated by atomic electron spins and is predicted to exhibit macroscopic gyroscopic behavior. If such a ferromagnetic gyroscope is sufficiently isolated from the environment, rapid averaging of quantum uncertainty via the spin-lattice interaction enables readout of the ferromagnetic gyroscope dynamics with sufficient sensitivity to measure both the Lense-Thirring (frame dragging) and de Sitter (geodetic precession) effects due to the Earth., 10 pages, 7 figures

LARES, an Italian satellite launched in 2012, and its successor LARES-2 approved by the Italian Space Agency, aim at the precise measurement of frame dragging predicted by General Relativity and other tests of fundamental physics. Both satellites are equipped with Laser retro-reflectors for Satellite Laser Ranging (SLR). Both satellites are also the most dense particles ever placed in an orbit around the Earth thus being nearly undisturbed by nuisance forces as atmospheric drag or solar radiation pressure. They are, therefore, ideally suited to contribute to the terrestrial reference frame (TRF). At GFZ we have implemented a tool to realistically simulate observations of all four space-geodetic techniques and to generate a TRF from that. Here we augment the LAGEOS based SLR simulation by LARES and LARES-2 simulations. It turns out that LARES and LARES-2, alone or in combination, can not deliver TRFs that meet the quality of the LAGEOS based TRF. However, once the LARES are combined with the LAGEOS satellites the formal errors of the estimated ground station coordinates and velocities and the co-estimated Earth Rotation Parameters are considerably reduced. The improvement is beyond what is expected from error propagation due to the increased number of observations. Also importantly, the improvement concerns in particular origin and scale of the TRF of about 25% w.r.t. the LAGEOS-combined TRF. Furthermore, we find that co-estimation of weekly average range biases for all stations does not change the resulting TRFs in this simulation scenario free of systematic errors.

We consider the Dirac electron as a nonperturbative particle-like solution consistent with its own Kerr-Newman (KN) gravitational and electromagnetic field. We develop the earlier models of the KN electron regularized by Israel and López, and consider the non-perturbative electron model as a bag model formed by Higgs mechanism of symmetry breaking. The The López regularization determines the unique shape of the electron in the form of a thin disk with a Compton radius reduced by 4π. In our model this disk is coupled with a closed circular string which is placed on the border of the disk and creates the caused by gravitation frame-dragging string tension produced by the vector potential of the Wilson loop. Using remarkable features of the Kerr-Schild coordinate system, which linearizes the Dirac equation, we obtain solutions of the Dirac equation consistent with the KN gravitational and electromagnetic field, and show that this solution takes the form of a massless relativistic string. Parallelism of this model with quantum representations in Heisenberg and Schrodinger pictures explains remarkable properties of the stringy electron model in the relativistic scattering processes.

The current race in quantum communication -- endeavouring to establish a global quantum network -- must account for special and general relativistic effects. The well-studied general relativistic effects include Shapiro time-delay, gravitational lensing, and frame dragging which all are due to how a mass distribution alters geodesics. Here, we report how the curvature of spacetime geometry affects the propagation of information carriers along an arbitrary geodesic. An explicit expression for the distortion onto the carrier wavefunction in terms of the Riemann curvature is obtained. Furthermore, we investigate this distortion for anti-de Sitter and Schwarzschild geometries. For instance, the spacetime curvature causes a 0.10~radian phase-shift for communication between Earth and the International Space Station on a monochromatic laser beam and quadrupole astigmatism can cause a 12.2 % cross-talk between structured modes traversing through the solar system. Our finding shows that this gravitational distortion is significant, and it needs to be either pre- or post-corrected at the sender or receiver to retrieve the information., Main article and the Supplementary information matching the published version

We study the Vainshtein mechanism in the context of slowly rotating stars in scalar-tensor theories. While the Vainshtein screening is well established for spherically symmetric spacetimes, we examine its validity in the axisymmetric case for slowly rotating sources. We show that the deviations from the general relativity solution are small in the weak-field approximation outside the star: the solution for the frame-dragging function is the same as in general relativity at leading order. Moreover, in most cases the corrections are suppressed by powers of the Vainshtein radius provided that the screening operates in spherical symmetry. Outside the Vainshtein radius, the frame dragging function receives corrections that are not suppressed by the Vainshtein radius, but which are still subleading. This suggests that the Vainshtein mechanism in general can be extended to slowly rotating stars and that it works analogously to the static case inside the Vainshtein radius. We also study relativistic stars and show that for some theories the frame-dragging function in vacuum does not receive corrections at all, meaning that the screening is perfect outside the star., 25 pages, v2 matches published version

Originally introduced in connection with general relativistic Coriolis forces, the term $\textit{frame-dragging}$ is associated today with a plethora of effects related to the off-diagonal element of the metric tensor. It is also frequently the subject of misconceptions leading to incorrect predictions, even of nonexistent effects. We show that there are three different levels of frame-dragging corresponding to three distinct gravitomagnetic objects: gravitomagnetic potential 1-form, field, and tidal tensor, whose effects are independent, and sometimes opposing. It is seen that, from the two analogies commonly employed, the analogy with magnetism holds strong where it applies, whereas the fluid-dragging analogy (albeit of some use, qualitatively, in the first level) is, in general, misleading. Common misconceptions (such as viscous-type "body-dragging") are debunked. Applications considered include rotating cylinders (Lewis-Weyl metrics), Kerr, Kerr-Newman and Kerr-dS spacetimes, black holes surrounded by disks/rings, and binary systems., Comment: 20+8 pages, 4 figures. Invited feature paper for Universe special issue on "Frame-Dragging and Gravitomagnetism"; matches the final published version

The orbital Lense-Thirring precession is considered in the context of constraints for weak-field General Relativity involving the cosmological constant $\Lambda$. It is shown that according to the current accuracy of satellite measurements the obtained error limits for $\Lambda$ is self-consistent with cosmological observations. The corrections of $\Lambda$ term are derived for the strong field Lense-Thirring precession i.e. the frame dragging effect and for the nutation. As a result, in the context of recently proposed $\Lambda$-gravity we obtain constraints for $\Lambda$ in both relativistic and weak-field limits. Namely, for the latter we analyze several Keplerian systems at different scales. We find that the obtained constraints for the modified gravity corrections are several orders of magnitude tighter than those available for such effects as gravitational redshift, gravitational time delay and geodetic precession in Solar System., Comment: 6 pages, 8 tables, Eur.Phys.J Plus (in press)

We present a numerical weak-lensing analysis that is fully relativistic and non-perturbative for the scalar part of the gravitational potential and first-order in the vector part, frame dragging. Integrating the photon geodesics backwards from the observer to the emitters, we solve the Sachs optical equations and study in detail the weak-lensing convergence, ellipticity and rotation. For the first time, we apply such an analysis to a high-resolution relativistic N-body simulation, which consistently includes the leading-order corrections due to general relativity on both large and small scales. These are related to the question of gauge choice and to post-Newtonian corrections, respectively. We present the angular power spectra and one-point probability distribution functions for the weak-lensing variables, which we find are broadly in agreement with comparable Newtonian simulations. Our geometric approach, however, is more robust and flexible, and can therefore be applied consistently to non-standard cosmologies and modified theories of gravity., Comment: 20 pages, 17 figures, corresponds to published version

Black hole and neutron star X-ray binary systems routinely show quasi-periodic oscillations (QPOs) in their X-ray flux. Despite being strong, easily measurable signals, their physical origin has long remained elusive. However, recent observational and theoretical work has greatly improved our understanding. Here, we briefly review the basic phenomenology of the different varieties of QPO in both black hole and neutron star systems before focusing mainly on low frequency QPOs in black hole systems, for which much of the recent progress has been made. We describe the detailed statistical properties of these QPOs and review the physical models proposed in the literature, with particular attention to those based on Lense-Thirring precession. This is a relativistic effect whereby a spinning massive object twists up the surrounding spacetime, inducing nodal precession in inclined orbits. We review the theory describing how an accretion flow reacts to the Lense-Thirring effect, including analytic theory and recent numerical simulations. We then describe recent observational tests that provide very strong evidence that at least a certain type of low frequency QPOs are a geometric effect, and good evidence that they are the result of precession. We discuss the possibility of the spin axis of the compact object being misaligned with the binary rotation axis for a large fraction of X-ray binaries, as is required for QPOs to be driven specifically by Lense-Thirring precession, as well as some outstanding gaps in our understanding and future opportunities provided by X-ray polarimeters and/or high throughput X-ray detectors., Comment: Accepted for publication in New Astronomy Reviews; 67 pages, 22 figures

The Lewis solutions describe the exterior gravitational field produced by infinitely long rotating cylinders, and are useful models for global gravitational effects. When the metric parameters are real (Weyl class), the exterior metrics of rotating and static cylinders are locally indistinguishable, but known to globally differ. The significance of this difference, both in terms of physical effects (gravitomagnetism) and of the mathematical invariants that detect the rotation, remain open problems in the literature. In this work we show that, by a rigid coordinate rotation, the Weyl class metric can be put into a "canonical" form where the Killing vector field $\partial_{t}$ is time-like everywhere, and which depends explicitly only on three parameters with a clear physical significance: the Komar mass and angular momentum per unit length, plus the angle deficit. This new form of the metric reveals that the two settings differ only at the level of the gravitomagnetic vector potential which, for a rotating cylinder, cannot be eliminated by any global coordinate transformation. It manifests itself in the Sagnac and gravitomagnetic clock effects. The situation is seen to mirror the electromagnetic field of a rotating charged cylinder, which likewise differs from the static case only in the vector potential, responsible for the Aharonov-Bohm effect, formally analogous to the Sagnac effect. The geometrical distinction between the two solutions is also discussed, and the notions of local and global staticity revisited. The matching in canonical form to the van Stockum interior cylinder is also addressed., 43 pages, 6 Figures. Minor re-write/simplifications to the text, new section 5.2.4 added discussing the spinning cosmic string limit, titles of subsections 5.4 and 5.4.2 changed, references added, typos corrected. Matches the final published version

The anomalous energy difference observed during the Earth flybys is modelled here as a dynamical effect resulting from the coupling of the gravitational and the magnetic fields of the Earth. The theoretical analysis shows that general relativistic frame-dragging can become modified under the Earth’s magnetic field by orders of magnitude. For 12 flyby cases, including the null results reported in some recent flybys, the predicted velocities correspond to the observed velocities within the observational error. The gravitomagnetic effect is also shown to account for the linear distance relation, time-variation of the anomalous energy, and the reduction in the anomalous velocity for high-altitude flybys near the Earth.

We report the improved test of frame-dragging, an intriguing phenomenon predicted by Einstein's General Relativity, obtained using 7 years of Satellite Laser Ranging (SLR) data of the satellite LARES (ASI, 2012) and 26 years of SLR data of LAGEOS (NASA, 1976) and LAGEOS 2 (ASI and NASA, 1992). We used the static part and temporal variations of the Earth gravity field obtained by the space geodesy mission GRACE (NASA and DLR) and in particular the static Earth's gravity field model GGM05S augmented by a model for the 7-day temporal variations of the lowest degree Earth spherical harmonics. We used the orbital estimator GEODYN (NASA). We measured frame-dragging to be equal to 0.9910 +/- 0.02, where 1 is the theoretical prediction of General Relativity normalized to its frame-dragging value and +/- 0.02 is the estimated systematic error due to modelling errors in the orbital perturbations, mainly due to the errors in the Earth's gravity field determination. Therefore, our measurement confirms the prediction of General Relativity for frame-dragging with a few percent uncertainty., Comment: Submitted on September 27, 2019; accepted for publication on October 8, 2019 and published on October 23, 2019 in The European Physical Journal C: Eur. Phys. J. C (2019) 79:872 https://doi.org/10.1140/epjc/s10052-019-7386-z

I impose the Newtonian criteria of inertial frames on the c.o.m.trajectories of massive objects undergoing spontaneous collapse of their wave function. The corresponding modification of the so far used stochastic Schr&ouml, dinger equation eliminates the Brownian motion of the c.o.m., and restores the exact inertial motion for free masses. For the collapse of Schr&ouml, dinger cat states the Born rule is satisfied invariably. The proposed machinery comes from the radical assumption that, in the vicinity of the spontaneously localized mass, the stochastic fluctuations of the c.o.m.&mdash, inevitable in the collapse process&mdash, would drag the physical inertial frame with themselves. The perspective of a general theory is presented where the spontaneous-collapse-caused breakdown of local energy-momentum conservation could be remedied by altering the metric, resulting in collapse-induced curvature of the space-time. My assumption of frame-drag by quantized masses is independent of the general relativistic frame-drag by classical masses.

The detection of a pulsar (PSR) in a tight, relativistic orbit around a supermassive or intermediate mass black hole - such as those in the Galactic centre or in the centre of Globular clusters - would allow for precision tests of general relativity (GR) in the strong-field, non-linear regime. We present a framework for calculating the theoretical time-frequency signal from a PSR in such an Extreme Mass Ratio Binary (EMRB). This framework is entirely relativistic with no weak-field approximations and so able to account for all higher-order strong-field gravitational effects, relativistic spin dynamics, the convolution with astrophysical effects and the combined impact on the PSR timing signal. Specifically we calculate both the spacetime path of the pulsar radio signal and the complex orbital and spin dynamics of a spinning pulsar around a Kerr black hole, accounting for spacetime curvature and frame dragging, relativistic and gravitational time delay, gravitational light bending, temporal and spatial dispersion induced by the presence of plasma along the line of sight and relativistic aberration. This then allows for a consistent time-frequency solution to be generated. Such a framework is key for assessing the use of PSR as probes of strong field GR, helping to inform the detection of an EMRB system hosting a PSR and, most essentially, for providing an accurate theoretical basis to then compare with observations to test fundamental physics., Comment: 19 pages, 15 Figures. Accepted for publication in MNRAS

The experimental measurement of frame-dragging or the Lense-Thirring (LT) effect based on Satellite Laser Ranging (SLR) observations to the LAGEOS satellites was successfully demonstrated with an accuracy of about 10%. Here we look in detail into the effect of the node drift induced by the time variable part of the C(2,0) term of the gravity field model describing the flattening of the Earth. We demonstrate that errors in C(2,0) can effectively be taken care of by analyzing two satellites for the LT measurement. We also adopt some recent gravity field models in order to independently repeat and extend the LT experiments so far. The gravity field models used for this are derived either partly depending on LAGEOS SLR observations or completely independent from LAGEOS, and based on dedicated gravity field satellite missions like CHAMP, GRACE and GOCE. It turns out that from all the gravity field models tested the claimed accuracy of 10% of the LT measurement can be confirmed.

We present results from general relativistic calculations of nuclear ignition in white dwarf stars triggered by near encounters with rotating intermediate mass black holes with different spin and alignment parameters. These encounters create thermonuclear environments characteristic of Type Ia supernovae capable of producing both calcium and iron group elements in arbitrary ratios, depending primarily on the proximity of the interaction which acts as a strong moderator of nucleosynthesis. We explore the effects of black hole spin and spin-orbital alignment on burn product synthesis to determine whether they might also be capable of moderating reactive flows. When normalized to equivalent impact penetration, accounting for frame dragging corrections, the influence of spin is weak, no more than 25% as measured by nuclear energy release and mass of burn products, even for near maximally rotating black holes. Stars on prograde trajectories approach closer to the black hole and produce significantly more unbound debris and iron group elements than is possible by encounters with nonrotating black holes or by retrograde orbits, at more than 50% mass conversion efficiency. The debris contains several radioisotopes, most notably Ni56, made in amounts that produce sub-luminous (but still observable) light curves compared to branch-normal SNe Ia., Comment: 20 pages, 7 figures, submitted to ApJ

Solar system observations have traditionally allowed for very stringent tests of Einstein's theory of general relativity. We here revisit the possibility of using these observations to constrain gravitational parity violation as encapsulated in dynamical Chern-Simons gravity. Working in the small-coupling and post-Newtonian approximations, we calculate analytically the scalar field and the gravitomagnetic sector of the gravitational field in the interior and the exterior of an isolated, weakly-gravitating object with uniform rotation and a quadrupolar mass deformation. We find that the asymptotic peeling-off behavior of the exterior fields is consistent with that found for black holes and neutron stars, as well as for non-relativistic objects, with overall coefficients that are different and dependent on the structure of the weak-field source. We then use these fields to explicitly calculate the dynamical Chern-Simons correction to the spin precession of gyroscopes in orbit around Earth, which we find to be in the same direction as the Lense-Thirring effect of General Relativity. We then compare this correction to the spin precession prediction of General Relativity to the results of the Gravity Probe B experiment to place a constraint on dynamical Chern-Simons theory that is consistent with previous approximate estimates. Although we focus primarily on a single body, our methods can be straightforwardly extended to binary systems or N-bodies., 29 pages, 2 figures, submitted to CQG

Here, we derive the metric for the spacetime around rotating object for the gravity action having nonlocal correction of $R\Box^{-2} R $ to the Einstein-Hilbert action. Starting with the generic stationary, axisymmetric metric, we solve the equations of motion in linearized gravity limit for the modified action including energy-momentum tensor of the rotating mass. We also derive the rotating metric from the static metric using the Demanski-Janis-Newmann algorithm. Finally, we obtain the constraint on the value of $M$ by calculating the frame dragging effect in our theory and comparing it with that of General Relativity and Gravity Probe B results, where $M$ is the mass scale of the theory., 13 pages, 3 figures

We will mainly discuss the measurable angle (local angle) of the light ray $\psi_P$ at the position of the observer $P$ instead of the total deflection angle (global angle) $\alpha$ in Kerr spacetime. We will investigate not only the effect of the gravito-magnetic field or frame dragging but also the contribution of the motion of the observer with a coordinate radial velocity $v^r$ and a coordinate transverse velocity $bv^{\phi}$ ($b$ is the impact parameter and $v^{\phi}$ is a coordinate angular velocity) which are converted from the components of the 4-velocity of the observer $u^r$ and $u^{\phi}$, respectively. Because the motion of observer causes an aberration, we will employ the general relativistic aberration equation to obtain the measurable angle $\psi$. The measurable angle $\psi$ given in this paper can be applied not only to the case of the observer located in an asymptotically flat region but also to the case of the observer placed within the curved and finite-distance region. Moreover, when the observer is in radial motion, the total deflection angle $\alpha_{\rm radial}$ can be expressed by $\alpha_{\rm radial} = (1 + v^r)\alpha_{\rm static}$ which is consistent with the overall scaling factor $1 - v$ with respect to the total deflection angle $\alpha{\rm static}$ in the static case. instead of $1 - 2v$ where $v$ is the velocity of the lens object. On the other hand, when the observer is in transverse motion, the total deflection angle is given by the form $\alpha_{\rm transverse} = (1 + bv^{\phi}/2)\alpha_{\rm static}$ if we define the transverse velocity as having the form $bv^{\phi}$., Comment: 17 pages, 4 figures

We study stationary, electrically charged fluid structures encircling a rotating compact object with a dipole magnetic field oriented along the rotation axis. This situation is described in an idealized way by the Kerr metric and a magnetic dipole ``test'' field, that does not affect the spacetime. The self-gravitational and self-electromagnetic field of the fluid are neglected and the fluid is assumed to be nonconductive and in rigid motion. Our work generalizes a previous study by Kov\'a\ifmmode \check{r}\else \v{r}\fi{} et al. [1] by taking into account the rotation of the central object. Therefore, we focus on the influence of the rotation onto the existence and position of bound fluid structures. Frame dragging effects allow the existence of polar clouds, which could not be found in nonrotating case. Furthermore counterrotating equatorial tori become more preferred the faster the central object is spinning.

We investigate various aspects of energy extraction via the Penrose process in the Kerr-de Sitter spacetime. We show that the increase in the value of a positive cosmological constant, $\Lambda$, always reduces the efficiency of this process. The Kerr-de Sitter spacetime has two ergospheres -- associated with the black hole and the cosmological event horizons. We prove by analysing turning points of the trajectory that the Penrose process in the cosmological ergoregion is never possible. We next show that in this process both black hole and cosmological event horizons' areas increase, the later becomes possible when the particle coming from the black hole ergoregion escapes through the cosmological event horizon. We identify a new, local mass function instead of the mass parameter, to prove this generalized area theorem. This mass function takes care of the local spacetime energy due to the cosmological constant as well, including that arises due to the frame dragging effect due to spacetime rotation. While the current observed value of $\Lambda$ is much tiny, its effect in this process could be considerable in the early universe scenario endowed with a rather high value of it, where the two horizons could have comparable sizes. In particular, the various results we obtain here are also evaluated in a triply degenerate limit of the Kerr-de Sitter spacetime we find, in which radial values of the inner, the black hole and the cosmological event horizons are nearly coincident., Comment: v2, 21pp; added references and discussions, improved presentation, accepted in PRD

Nonminimal spin-gravity interaction through unit gravimagnetic moment leads to modified Mathisson-Papapetrou-Tulczyjew-Dixon equations with improved behavior in the ultrarelativistic limit. We present exact Hamiltonian of the resulting theory and compute an effective $\frac{1}{c^2}$\,-Hamiltonian and leading post-Newtonian corrections to the trajectory and spin. Gravimagnetic moment causes the same precession of spin ${\bf S}$ as a fictitious rotation of the central body with angular momentum ${\bf J}=\frac{M}{m}{\bf S}$. So the modified equations imply a number of qualitatively new effects, that could be used to test experimentally, whether a rotating body in general relativity has null or unit gravimagnetic moment., 4 pages. arXiv admin note: substantial text overlap with arXiv:1709.06894