Material sources for the Kerr metric.
Kerr metric as Einstein field equations solution, considering Synge g method as possible Kerr metric source
RELATIVITY THEORY↗
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Testing the Kerr metric with the iron line and the KRZ parametrization
The spacetime geometry around astrophysical black holes is supposed to be well approximated by the Kerr metric, but deviations from the Kerr solution are predicted in a number of scenarios involving new physics. Broad iron Kα lines are commonly observed in the X-ray spectrum of black holes and originate by X-ray fluorescence of the inner accretion disk. The profile of the iron line is sensitively affected by the spacetime geometry in the strong gravity region and can be used to test the Kerr black hole hypothesis. In this paper, we extend previous work in the literature. In particular: i ) as test-metric, we employ the parametrization recently proposed by Konoplya, Rezzolla, and Zhidenko, which has a number of subtle advantages with respect to the existing approaches; ii ) we perform simulations with specific X-ray missions, and we consider NuSTAR as a prototype of current observational facilities and eXTP as an example of the next generation of X-ray observatories. We find a significant difference between the constraining power of NuSTAR and eXTP. With NuSTAR, it is difficult or impossible to constrain deviations from the Kerr metric. With eXTP, in most cases we can obtain quite stringent constraints (modulo we have the correct astrophysical model).
79 ASTRONOMY AND ASTROPHYSICS↗
A study for testing the Kerr metric with AGN iron line eclipses
Recently, two of us have studied iron line reverberation mapping to test black hole candidates, showing that the time information in reverberation mapping can better constrain the Kerr metric than the time-integrated approach. Motivated by this finding, here we explore the constraining power of another time-dependent measurement: an AGN iron line eclipse. An obscuring cloud passes between the AGN and the distant observer, covering different parts of the accretion disk at different times. Similar to the reverberation measurement, an eclipse might help to better identify the relativistic effects affecting the X-ray photons. However, this is not what we find. In our study, we employ the Johannsen-Psaltis parametrisation, but we argue that our conclusions hold in a large class of non-Kerr metrics. We explain our results pointing out an important difference between reverberation and eclipse measurements.
79 ASTRONOMY AND ASTROPHYSICS↗
Kerr metric, rotating sources, and Machian effects.
Interior solution constructions serving as Kerr metric sources noting shape, mass density and rotation rates
Hernandez, W. C., Jr.↗
Angular momentum and the Kerr metric.
Angular momentum generated by body with Kerr rotating metric exterior
Cohen, J. M.↗
On testing the Kerr metric of the massive black hole in the galactic center via stellar orbital motion: Full general relativistic treatment
S-stars, discovered in the vicinity of the massive black hole (MBH) in the Galactic center (GC), are anticipated to provide unique dynamical constraints on the MBH spin and metric, in addition to the mass. In this paper, we develop a fast full general relativistic method to simultaneously constrain the MBH mass, spin, and spin direction by considering both the orbital motion of a star close to the GC MBH and the propagation of photons from the star to a distant observer. Based on the current observations and dynamical model predictions, we assume six example stars with different semimajor axes (a{sub orb}) and eccentricities (e{sub orb}) and numerically calculate their projected trajectories in the sky plane and redshift curves. Two of those stars are set to have orbital configurations similar to that of S0-2/S2 and S0-102. We find that the spin-induced effects on the projected trajectory and redshift curve of a given star, including the leading term by the Lense–Thirring precession and the frame dragging, and the high-order precession due to the quadruple moment, depend on both the absolute value and the direction of the spin. The maximum values of the spin-induced position displacement and the redshift differences of the star over a full orbit may differ by a factor of several to more than one order of magnitude for two cases with significantly different spin directions. The dependence patterns of the position displacements and redshift differences on the spin direction are different, and thus the position and the redshift data are complementary for constraining the MBH spin and its direction. Adopting the Markov Chain Monte Carlo fitting technique, we illustrate that the spin of the GC MBH is likely to be well constrained by using the motion of S0-2/S2 over a period of ∼45 years if the spin is close to one and if the astrometric and spectroscopic precisions can be as high as (σ{sub p},σ{sub Z})∼(10 μas,1 km s{sup −1}), which is expected to be realized by future facilities like GRAVITY on the Very Large Telescope Interferometer, the thirty meter telescope, and the European extremely large telescope. If σ{sub p} and σ{sub Z} can be further improved by a factor of several, the MBH spin can be well constrained by monitoring S0-2/S2 over a period of ∼15 years. In the mean time, the distance from the sun to the GC and the MBH mass can also be constrained to an unprecedented accuracy (0.01%–0.1%). If there exists a star with a semimajor axis that is a few times smaller, and eccentricity larger, than those of S0-2/S2, the MBH spin and its direction can be constrained with high accuracy over a period of ≲10 years by future facilities, even if the spin is only moderately large. Our results suggest that long-term monitoring of the motions of stars in the vicinity of the GC MBH by the next generation facilities is likely to provide a dynamical test, for the first time, to the spin and metric of the GC MBH.
79 ASTRONOMY AND ASTROPHYSICS↗
Optically thin accretion disks in the Kerr metric
We calculate the structure of an effectively optically thin and geometrically thin accretion disk in the Kerr geometry, including electron-positron pairs. We show that the properties of the disk solutions are strongly dependent on the angular momentum of the central black hole. We find that close to a rapidly rotating hole there can be an appreciable pair density even for modest accretion rates. Pair critical accretion rates recently discovered in Newtonian disk models are also shown to be present in the general relativistic models, and we show that the geometrically thin disk approximations easily break down for rapidly rotating holes.
Bjornsson, G.↗
Single Kerr-Schild metric for Taub-NUT instanton
It is shown that a complex coordinate transformation maps the Taub-Newman-Unti-Tamburino instanton metric to a Kerr-Schild metric. This metric involves a semi-infinite line defect as the gravitational analog of the Dirac string, much like the original metric. Moreover, it facilitates three versions of classical double copy correspondence with the self-dual dyon in electromagnetism, one of which involves a nonlocal operator. The relevance to the Newman-Janis algorithm is briefly noted. Published by the American Physical Society 2025
Kim, Joon-Hwi (ORCID:000000025474123X)↗
Static spherically symmetric Kerr-Schild metrics and implications for the classical double copy
Here, we discuss the physical interpretation of stress-energy tensors that source static spherically symmetric Kerr-Schild metrics. We find that the sources of such metrics with no curvature singularities or horizons do not simultaneously satisfy the weak and strong energy conditions. Sensible stress-energy tensors usually satisfy both of them. Under most circumstances, these sources are not perfect fluids and contain shear stresses. Furthermore, we show that for these systems the classical double copy associates the electric charge density to the Komar energy density. In addition, we demonstrate that the stress-energy tensors are determined by the electric charge density and their conservation equations.
79 ASTRONOMY AND ASTROPHYSICS↗
STU black holes and SgrA{sup *}
The equations of null geodesics in the STU family of rotating black hole solutions of supergravity theory, which may be considered as deformations of the vacuum Kerr metric, are completely integrable. We propose that they be used as a foil to test, for example, with what precision the gravitational field external to the black hole at the centre of our galaxy is given by the Kerr metric. By contrast with some metrics proposed in the literature, the STU metrics satisfy by construction the dominant and strong energy conditions. Our considerations may be extended to include the effects of a cosmological term. We show that these metrics permit a straightforward calculation of the properties of black hole shadows.
79 ASTRONOMY AND ASTROPHYSICS↗
Gravitational Test beyond the First Post-Newtonian Order with the Shadow of the M87 Black Hole
In this study, the 2017 Event Horizon Telescope (EHT) observations of the central source in M87 have led to the first measurement of the size of a black-hole shadow. This observation offers a new and clean gravitational test of the black-hole metric in the strong-field regime. We show analytically that spacetimes that deviate from the Kerr metric but satisfy weak-field tests can lead to large deviations in the predicted black-hole shadows that are inconsistent with even the current EHT measurements. We use numerical calculations of regular, parametric, non-Kerr metrics to identify the common characteristic among these different parametrizations that control the predicted shadow size. We show that the shadow-size measurements place significant constraints on deviation parameters that control the second post-Newtonian and higher orders of each metric and are, therefore, inaccessible to weak-field tests. The new constraints are complementary to those imposed by observations of gravitational waves from stellar-mass sources.
79 ASTRONOMY AND ASTROPHYSICS↗
First Sagittarius A* Event Horizon Telescope Results. VI. Testing the Black Hole Metric
Astrophysical black holes are expected to be described by the Kerr metric. This is the only stationary, vacuum, axisymmetric metric, without electromagnetic charge, that satisfies Einstein’s equations and does not have pathologies outside of the event horizon. We present new constraints on potential deviations from the Kerr prediction based on 2017 EHT observations of Sagittarius A* (Sgr A*). We calibrate the relationship between the geometrically defined black hole shadow and the observed size of the ring-like images using a library that includes both Kerr and non-Kerr simulations. We use the exquisite prior constraints on the mass-to-distance ratio for Sgr A* to show that the observed image size is within ∼10% of the Kerr predictions. We use these bounds to constrain metrics that are parametrically different from Kerr, as well as the charges of several known spacetimes. To consider alternatives to the presence of an event horizon, we explore the possibility that Sgr A* is a compact object with a surface that either absorbs and thermally reemits incident radiation or partially reflects it. Using the observed image size and the broadband spectrum of Sgr A*, we conclude that a thermal surface can be ruled out and a fully reflective one is unlikely. We compare our results to the broader landscape of gravitational tests. Together with the bounds found for stellar-mass black holes and the M87 black hole, our observations provide further support that the external spacetimes of all black holes are described by the Kerr metric, independent of their mass.
79 ASTRONOMY AND ASTROPHYSICS↗
Testing the Kerr nature of black hole candidates using iron line spectra in the CPR framework
The iron Kα line commonly observed in the X-ray spectrum of both stellar-mass and supermassive black hole (BH) candidates originates from X-ray fluorescence of the inner accretion disk. Accordingly, it can be used to map the spacetime geometry around these objects. In this paper, we extend previous work using the iron Kα line to test the Kerr BH hypothesis. We adopt the Cardoso–Pani–Rico parametrization and we test the possibility of constraining possible deviations from the Kerr solution that can be obtained from observations across the range of BH spins and inclination angles. We confirm previous claims that the iron Kα line is potentially a quite powerful probe for testing the Kerr metric given sufficiently high quality data and with systematics under control, especially in the case of fast-rotating BHs and high inclination angles since both conditions serve to maximize relativistic effects. We find that some geometric perturbations from Kerr geometry manifest more strongly in the iron line profile than others. While the perturbation parameter ϵ{sub 3}{sup t} can be well constrained by the iron line profile, an orthogonal data set is necessary to constrain departures from Kerr geometry in ϵ{sub 3}{sup r}.
79 ASTRONOMY AND ASTROPHYSICS↗
Superposed metric for spinning black hole binaries approaching merger
Here, we construct an approximate metric that represents the spacetime of spinning binary black holes (BBH) approaching merger. We build the metric as an analytical superposition of two Kerr metrics in harmonic coordinates, where we transform each black hole term with time-dependent boosts describing an inspiral trajectory. The velocities and trajectories of the boost are obtained by solving the post-Newtonian (PN) equations of motion at 3.5 PN order. We analyze the spacetime scalars of the new metric and we show that it is an accurate approximation of Einstein’s field equations in vacuum for a BBH system in the inspiral regime. Furthermore, to prove the effectiveness of our approach, we test the metric in the context of a 3D general relativistic magnetohydrodynamical (GRMHD) simulation of accreting minidisks around the black holes. We compare our results with a previous well-tested spacetime construction based on the asymptotic matching method. We conclude that our new spacetime is well-suited for long-term GRMHD simulations of spinning binary black holes on their way to the merger.
79 ASTRONOMY AND ASTROPHYSICS↗
A Superposed Metric for Spinning Black Hole Binaries Approaching Merger
We construct an approximate metric that represents the spacetime of spinning binary black holes (BBH) approaching merger. We build the metric as an analytical superposition of two Kerr metrics in harmonic coordinates, where we transform each black hole term with time-dependent boosts describing an inspiral trajectory. The velocities and trajectories of the boost are obtained by solving the post-Newtonian (PN) equations of motion at 3.5 PN order. We analyze the spacetime scalars of the new metric and we show that it is an accurate approximation of Einstein’s field equations in vacuum for a BBH system in the inspiral regime. Furthermore, to prove the effectiveness of our approach, we test the metric in the context of a 3D general relativistic magnetohydrodynamical (GRMHD) simulation of accreting minidisks around the black holes. We compare our results with a previous well-tested spacetime construction based on the asymptotic matching method. We conclude that our new spacetime is well-suited for long-term GRMHD simulations of spinning binary black holes on their way to the merger.
Luciano Combi↗
Toroidal–Poloidal Magnetic Field Generation in Neutron Stars by Spacetime Frame-dragging
Neutron star magnetic fields, particularly in magnetars, have strong poloidal and toroidal components, reaching magnitudes up to 10{sup 15} T and extending into the magnetosphere, where they cause twisted magnetic fields and surface currents. Here, we show that to a large extent neutron star toroidal and poloidal magnetic fields are due to frame-dragging of spacetime in the stellar exterior. In the explicit case of linearized Kerr metric we show that general relativistic Maxwell equations admit a mixed poloidal and toroidal magnetic field configuration in which the toroidal field strength is comparable with the poloidal magnetic field. Calculations are performed to show that the frame-dragging-induced magnetic field has the observed order of magnitude at the stellar surface, and exhibits the flare-like phenomenon observed in magnetars.
79 ASTRONOMY AND ASTROPHYSICS↗
ON THE NEWTONIAN AND SPIN-INDUCED PERTURBATIONS FELT BY THE STARS ORBITING AROUND THE MASSIVE BLACK HOLE IN THE GALACTIC CENTER
The S-stars discovered in the Galactic center are expected to provide unique dynamical tests of the Kerr metric of the massive black hole (MBH) that they orbit. In order to obtain unbiased measurements of its spin and the related relativistic effects, a comprehensive understanding of the gravitational perturbations of the stars and stellar remnants around the MBH is quite essential. Here, we study the perturbations on the observables of a typical target star, i.e., the apparent orbital motion and the redshift, due to both the spin-induced relativistic effects and the Newtonian attractions of a single object or a cluster of disturbing objects. We find that, in most cases, the Newtonian perturbations on the observables are mainly attributed to the perturbed orbital period of the target star rather than the Newtonian orbital precessions. Looking at the currently detected star S2/S0-2, we find that its spin-induced effects are very likely obscured by the gravitational perturbations from the star S0-102 alone. We also investigate and discuss the Newtonian perturbations on a hypothetical S-star located inside the orbits of those currently detected. By considering a number of possible stellar distributions near the central MBH, we find that the spin-induced effects on the apparent position and redshift dominate over the stellar perturbations for target stars with orbital semimajor axis smaller than 100–400 au if the MBH is maximally spinning. Our results suggest that, in principle, the stellar perturbations can be removed because they have morphologies distinct from those of the relativistic Kerr-type signatures.
79 ASTRONOMY AND ASTROPHYSICS↗