Kerr Spin Parameter Research Articles

Black hole perturbation theory meets CFT2 : Kerr-Compton amplitudes from Nekrasov-Shatashvili functions

We present a novel study of Kerr Compton amplitudes in a partial wave basis in terms of the Nekrasov-Shatashvili (NS) function of the confluent Heun equation (CHE). Remarkably, NS-functions enjoy analytic properties and symmetries that are naturally inherited by the Compton amplitudes. Based on this, we characterize the analytic dependence of the Compton phase shift in the Kerr spin parameter and provide a direct comparison to the standard post-Minkowskian (PM) perturbative approach within general relativity (GR). We also analyze the universal large frequency behavior of the relevant characteristic exponent of the CHE—also known as the renormalized angular momentum—and find agreement with numerical computations. Moreover, we discuss the analytic continuation in the harmonics quantum number ℓ of the partial wave, and show that the limit to the physical integer values commutes with the PM expansion of the observables. Finally, we obtain the contributions to the tree-level, point-particle, gravitational Compton amplitude in a covariant basis through O(aBH8), without the need to take the superextremal limit for Kerr spin. Published by the American Physical Society 2024

Testing theories of accretion and gravity with super-extremal Kerr discs

ABSTRACT Fitting the thermal continuum emission of accreting black holes observed across X-ray bands represents one of the principle means of constraining the properties (mass and spin) of astrophysical black holes. Recent ‘continuum fitting’ studies of Galactic X-ray binaries in the soft state have found best-fitting dimensionless spin values which run into the prior bounds placed on traditional models (a⋆ = 0.9999). It is of critical importance that these results are robust, and not a result solely of the presence of these prior bounds and deficiencies in conventional models of accretion. Motivated by these results we derive and present superkerr, an xspec model comprising of a thin accretion disc solution valid in the Kerr geometry for arbitrary spin parameter a⋆, extending previous models valid only for black holes (|a⋆| < 1). This extension into ‘super-extremal’ space–times with |a⋆| > 1 includes solutions which describe discs evolving around naked singularities, not black holes. While being valid solutions of Einstein’s field equations these naked singularities are not expected to be present in nature. We discuss how the ‘measurement’ of a Kerr spin parameter 1 < a⋆ < 5/3 would present compelling evidence for the requirement of a rethink in either standard accretion theory, or our theories of gravity.

Energetic processes around electromagnetically charged black hole in the Rastall gravity

Here we investigate the energetics of the charged-rotating-NUT-Kiselev black hole (CRNK-BH) in the Rastall modified theory of gravity. First, we study the dependence of the ergoregion around the CRNK-BH on the spacetime parameters, which is the key point to explain the energy extraction process from the BH. We show that the effect of the Kerr spin parameter a on this region is still dominating compared to the rest of the spacetime parameters. Then, we show that an increase in the NUT parameter l, electromagnetic charge q, and the parameter of equation-of-state of the quintessence ω, increases the efficiency of the Penrose-process while the effect of the rest of the spacetime parameters is just opposite. Moreover, we study the energy extraction process from the CRNK-BH in the Rastall modified theory of gravity due to the Blandford–Znajek mechanism. We demonstrate that the effect of all the spacetime parameters, except the spin and NUT parameters, on the efficiency of the Blandford–Znajek process is similar to that of the Penrose-process. We also give a comparison of the two energy extracting processes, discussed here, for the CRNK-BH in the Rastall modified theory of gravity.

Asymptotic Green’s function solutions of the general relativistic thin disc equations

ABSTRACT The leading order Green’s function solutions of the general relativistic thin disc equations are computed, using a pseudo-Newtonian potential and asymptotic Laplace mode matching techniques. This solution, valid for a vanishing innermost stable circular orbit (ISCO) stress, is constructed by ensuring that it reproduces the leading order asymptotic behaviour of the near-ISCO, Newtonian, and global Wentzel–Kramers–Brillouin limits. Despite the simplifications used in constructing this solution, it is typically accurate, for all values of the Kerr spin parameter a and at all radii, to less than a per cent of the full numerically calculated solutions of the general relativistic disc equations. These solutions will be of use in studying time-dependent accretion discs surrounding Kerr black holes.

GW190521 formation scenarios via relativistic accretion

The recent gravitational wave transient GW190521 has been interpreted by the LIGO-Virgo collaboration (LVC) as sourced by a binary black hole (BH) merger. According to the LVC parameter estimation, at least one of these progenitors falls into the so-called pair-instability supernova mass gap. This raises the important question of how and when these progenitors formed.In this paper we use an accretion model with super-Eddington mass accretion rate obtained from General Relativity hydrodynamics simulations to analyse the scenario wherein the GW190521 original progenitors (OPs) formed at lower masses (and spins) and grew to their estimated LVC parameters by relativistic accretion. We consider that the environment wherein the binary is immersed has density gradients as well as a dependence on the Mach number of the gas. Taking the LVC parameter estimation at z = 0.82 as the endpoint of the accretion evolution, we estimate the initial masses and spins of the OPs at three different red-shifts z = 100, 50, and 20. We found three distinct possible types of OPs: (i) 10-4 M ☉ - 3 M ☉ almost non-rotating (with Kerr spin parameter a ☆ < 10-2) primordial BHs; (ii) 3M ☉ - 40M ☉ slowly rotating (10-2 < a ☆ < 0.5) stellar mass BHs; (iii) 40M ☉ - 70M ☉ BHs with a moderate spin parameter a ☆ ∼ 0.5, which could originate from the collapse of high mass Pop III stars. The mass spread is due to varying the density gradient and the relativistic Mach number of the cosmic plasma; the variation of the masses due to the origin at different red-shifts, on the other hand, is negligible, ∼ 2%.For high Mach number scenarios, the BHs have low mass and spin accretion rates, leading to OPs with masses and spins close to the GW190521 LVC estimated values.We have also compared our results with previous studies where the Newtonian accretion model was used, finding relativistic corrections of ∼ 13% for the OPs masses. In particular, the relativistic model leads to smaller initial masses.

Three-dimensional general relativistic Poynting-Robertson effect. II. Radiation field from a rigidly rotating spherical source

We investigate the three-dimensional, general relativistic Poynting-Robertson effect in the case of rigidly rotating spherical source which emits radiation radially in the local comoving frame. Such radiation field is meant to approximate the field produced by the surface of a rotating neutron star, or by the central radiating hot corona of accreting black holes; it extends the purely radial radiation field that we considered in a previous study. Its angular momentum is expressed in terms of the rotation frequency and radius of the emitting source. For the background we adopt a Kerr spacetime geometry. We derive the equations of motion for test particles influenced by such radiation field, recovering the classical and weak-field approximation for slow rotation. We concentrate on solutions consisting of particles orbiting along circular orbits off and parallel to the equatorial plane, which are stabilized by the balance between gravitational attraction, radiation force and PR drag. Such solutions are found to lie on a critical hypersurface, whose shape may morph from prolate to oblate depending on the Kerr spin parameter and the luminosity, rotation and radius of the radiating sphere. For selected parameter ranges, the critical hypersurface intersects the radiating sphere giving rise to a bulging equatorial region or, alternatively, two lobes above the poles. We calculate the trajectories of test particles in the close vicinity of the critical hypersurface for a selected set of initial parameters and analyze the spatial and angular velocity of test particles captured on the critical hypersurface.

Black holes: The next generation—repeated mergers in dense star clusters and their gravitational-wave properties

When two black holes merge in a dense star cluster, they form a new black hole with a well-defined mass and spin. If that "second-generation" black hole remains in the cluster, it will continue to participate in dynamical encounters, form binaries, and potentially merge again. Using a grid of 96 dynamical models of dense star clusters and a cosmological model of cluster formation, we explore the production of binary black hole mergers where at least one component of the binary was forged in a previous merger. We create four hypothetical universes where every black hole born in the collapse of a massive star has a dimensionless Kerr spin parameter, $\chi_{\rm birth}$, of 0.0, 0.1, 0.2, or 0.5. We show that if all stellar-born black holes are non-spinning ($\chi_{\rm birth} = 0.0$), then more than 10% of merging binary black holes from clusters have components formed from previous mergers, accounting for more than 20% of the mergers from globular clusters detectable by LIGO/Virgo. Furthermore, nearly 7% of detectable mergers would have a component with a mass $\gtrsim 55M_{\odot}$, placing them clearly in the mass "gap" region where black holes cannot form from isolated collapsing stars due to the pulsational-pair instability mechanism. On the other hand, if black holes are born spinning, then the contribution from these second-generation mergers decreases, making up as little as 1% of all detections from globular clusters when $\chi_{\rm birth} = 0.5$. We make quantitative predictions for the detected masses, mass ratios, and spin properties of first- and second-generation mergers from dense star clusters, and show how these distributions are highly sensitive to the birth spins of black holes.

Gravitational self-force corrections to gyroscope precession along circular orbits in the Kerr spacetime

We generalize to Kerr spacetime previous gravitational self-force results on gyroscope precession along circular orbits in the Schwarzschild spacetime. In particular we present high order post- Newtonian expansions for the gauge invariant precession function along circular geodesics valid for arbitrary Kerr spin parameter and show agreement between these results and those derived from the full post-Newtonian conservative dynamics. Finally we present strong field numerical data for a range of the Kerr spin parameter, showing agreement with the GSF-PN results, and the expected lightring divergent behaviour. These results provide useful testing benchmarks for self- force calculations in Kerr spacetime, and provide an avenue for translating self-force data into the spin-spin coupling in effective-one-body models.

Canonical Hamiltonian for an extended test body in curved spacetime: To quadratic order in spin

We derive a Hamiltonian for an extended spinning test body in a curved background spacetime, to quadratic order in the spin, in terms of three-dimensional position, momentum, and spin variables having canonical Poisson brackets. This requires a careful analysis of how changes of the spin supplementary condition are related to shifts of the body's representative worldline and transformations of the body's multipole moments, and we employ bitensor calculus for a precise framing of this analysis. We apply the result to the case of the Kerr spacetime and thereby compute an explicit canonical Hamiltonian for the test-body limit of the spinning two-body problem in general relativity, valid for generic orbits and spin orientations, to quadratic order in the test spin. This fully relativistic Hamiltonian is then expanded in post-Newtonian orders and in powers of the Kerr spin parameter, allowing comparisons with the test-mass limits of available post-Newtonian results. Both the fully relativistic Hamiltonian and the results of its expansion can inform the construction of waveform models, especially effective-one-body models, for the analysis of gravitational waves from compact binaries.

Finite escape fraction for ultrahigh energy collisions around Kerr naked singularity

We investigate the issue of observability of high-energy collisions around Kerr naked singularity and show that results are in contrast with the Kerr black hole case. We had shown that it would be possible to have ultrahigh energy collisions between the particles close to the location r = M around the Kerr naked singularity if the Kerr spin parameter transcends unity by an infinitesimally small amount a → 1+. The collision is between initially ingoing particle that turns back as an outgoing particle due to angular momentum barrier, with another ingoing particle. We assume that two massless particles are produced in such a collision and their angular distribution is isotropic in the centre-of-mass frame. We calculated the escape fraction for the massless particles to reach infinity. We showed that the escape fraction is finite and approximately equal to half for the ultrahigh energy collisions. Therefore, the particles produced in high-energy collisions would escape to infinity providing the signature of the nature of basic interactions at those energies. This result is in contrast with the case of extremal Kerr black hole where almost all particles produced in high-energy collisions are absorbed by the black hole rendering collisions unobservable.

Measuring the Kerr spin parameter of regular black holes from their shadow

In a previous paper, one of us has showed that, at least in some cases,the Kerr-nature of astrophysical black hole candidates is extremely difficult to test and current techniques, even in presence of excellent data not available today, cannot distinguish a Kerr black hole from a Bardeen one, despite the substantial difference of the two backgrounds. In this paper, we investigate if the detection of the ``shadow'' of nearby super-massive black hole candidates by near future mm/sub-mm very long baseline interferometry experiments can do the job. More specifically, we consider the measurement of the Kerr spin parameter of the Bardeen and Hayward regular black holes from their shadow, and we then compare the result with the estimate inferred from the Kα iron line and from the frequency of the innermost stable circular orbit. For non-rotating black holes, the shadow approach provides different values, and therefore the Kerr black hole hypothesis can potentially be tested. For near extremal objects, all the approaches give quite similar results, and therefore it is not possible to constrain deviations from theKerr solution. The present work confirms that it is definitively challenging to test this kind of metrics, even with future facilities. However, the detection of a source that looks like a fast-rotating Kerr black hole can put meaningful constraints on the nature of the compact object.

Self-force on a scalar charge in Kerr spacetime: Eccentric equatorial orbits

We present a numerical code for calculating the self force on a scalar charge moving in a bound (eccentric) geodesic in the equatorial plane of a Kerr black hole. We work in the frequency domain and make use of the method of extended homogeneous solutions [Phys.\ Rev.\ D {\bf 78}, 084021 (2008)], in conjunction with mode-sum regularization. Our work is part of a program to develop a computational architecture for fast and efficient self-force calculations, alternative to time-domain methods. We find that our frequency-domain method outperforms existing time-domain schemes for small eccentricities, and, remarkably, remains competitive up to eccentricities as high as $\sim 0.7$. As an application of our code we (i) compute the conservative scalar-field self-force correction to the innermost stable circular equatorial orbit, as a function of the Kerr spin parameter; and (ii) calculate the variation in the rest mass of the scalar particle along the orbit, caused by the component of the self force tangent to the four-velocity.

Self-force on a scalar charge in Kerr spacetime: Circular equatorial orbits

We present a calculation of the scalar field self-force (SSF) acting on a scalar-charge particle in a strong-field orbit around a Kerr black hole. Our calculation specializes to circular and equatorial geodesic orbits. The analysis is an implementation of the standard mode-sum regularization scheme: We first calculate the multipole modes of the scalar-field perturbation using numerical integration in the frequency domain, and then apply a certain regularization procedure to each of the modes. The dissipative piece of the SSF is found to be consistent with the flux of energy and angular momentum carried by the scalar waves through the event horizon and out to infinity. The conservative (radial) component of the SSF is found to be attractive (inward pointing) for $r_0>r_{\rm c}(a)$ and repulsive (outward pointing) for $r_0<r_{\rm c}(a)$, where $a$ is the Kerr spin parameter, $r_0$ is the Boyer-Lindquist orbital radius, and $r_{\rm c}$ is a critical $a$-dependent radius at which the conservative SSF vanishes. When the motion is retrograde the conservative SSF is repulsive for all $r_0$ (as in the Schwarzschild case). The dominant conservative effect of the SSF in Schwarzschild spacetime is known to be of 3rd post-Newtonian (PN) order (with a logarithmic running). Our numerical results suggest that the leading-order PN correction due to the black hole's spin arises from spin-orbit coupling at 3PN, which dominates the overall SSF effect at large $r_0$. In PN language, the change-of-sign of the radial SSF is attributed to an interplay between the spin-orbit term ($\propto -ar_0^{-4.5}$) and the "Schwarzschild" term ($\propto r_0^{-5}\log r_0$).

Metric of a tidally perturbed spinning black hole

We explicitly construct the metric of a Kerr black hole that is tidally perturbed by the external universe in the slow-motion approximation. This approximation assumes that the external universe changes slowly relative to the rotation rate of the hole, thus allowing the parameterization of the Newman-Penrose scalar $\psi_0$ by time-dependent electric and magnetic tidal tensors. This approximation, however, does not constrain how big the spin of the background hole can be and, in principle, the perturbed metric can model rapidly spinning holes. We first generate a potential by acting with a differential operator on $\psi_0$. From this potential we arrive at the metric perturbation by use of the Chrzanowski procedure in the ingoing radiation gauge. We provide explicit analytic formulae for this metric perturbation in spherical Kerr-Schild coordinates, where the perturbation is finite at the horizon. This perturbation is parametrized by the mass and Kerr spin parameter of the background hole together with the electric and magnetic tidal tensors that describe the time evolution of the perturbation produced by the external universe. In order to take the metric accurate far away from the hole, these tidal tensors should be determined by asymptotically matching this metric to another one valid far from the hole. The tidally perturbed metric constructed here could be useful in initial data constructions to describe the metric near the horizons of a binary system of spinning holes. This perturbed metric could also be used to construct waveforms and study the absorption of mass and angular momentum by a Kerr black hole when external processes generate gravitational radiation.