Angular Momentum Of Black Hole Research Articles

Determination of the angular momentum of the Kerr black hole from equatorial geodesic motion

We present a method to determine the angular momentum of a black hole based on observations of the trajectories of the bodies in the Kerr spacetime. We use the Hamilton equations to describe the dynamics of a particle and present results for equatorial trajectories, obtaining an algebraic equation for the magnitude of the black hole's angular momentum with coefficients given by observable quantities. We tailor a numerical code to solve the dynamical equations and use it to generate synthetic data. We apply the method in some representative examples, obtaining the parameters of the trajectories as well as the black hole's angular momentum in good agreement with the input data.

Rotating BTZ-like black hole and central charges in Einstein-bumblebee gravity

We obtain an exact rotating BTZ-like black hole solution by solving the corresponding gravitational field equations and the bumblebee motion equations in Einstein-bumblebee gravity theory. Result is presented for the purely radial Lorentz symmetry violating and can only exist with a linear functional potential of the bumblebee field. This black hole has two horizons and an ergosphere which are dependent on the bumblebee coupling constant ell . The concepts of the area and volume of the horizon should be renewed in this LV spacetime due to the nontrivial contribution of coupling between the bumblebee field and the Ricci tensor. Only in this way, the entropy-area relation, first law of thermodynamics and the Smarr formula can still be constructed. We also study the AdS/CFT correspondence of this black hole, find that the entropy product of its inner and outer horizons is universal. So the central charges of the dual CFT on the boundary can be obtained via the thermodynamic method, and they can reappear black hole mass and angular momentum in the bulk.

Violating the chaos bound in five-dimensional, charged, rotating Einstein-Maxwell-Chern-Simons black holes

We study the equilibrium orbit and violation of chaos bound of particle motion in the five-dimensional, charged, rotating Einstein-Maxwell-Chern-Simons black hole. Through numerical analysis, we find that the relative distance between the equilibrium orbit and the event horizon decreases with four independent parameters (particle's charge, black hole's charge and angular momentum parameters (a, b)) increase in specific regions, respectively. By adjusting the ratio of particle's charge to its angular momentum, we find that the equilibrium orbit can be close to the event horizon. We also find that the chaos bound of Einstein-Maxwell-Chern-Simons black holes can be greatly violated under certain parameter conditions. At the near horizon, the violation of chaos bound becomes more likely to occur.

Axion induced angular momentum reversal in Kerr-like black holes

We consider a pseudoscalar axion-like field coupled to a Chern-Simons gravitational anomaly term. The axion field backreacts on a rotating Kerr black hole background, resulting in modifications in the spacetime. In an attempt to determine potentially observable signatures, we study the angular momentum of the system of the modified Kerr-like black hole and the axionic matter outside the horizon of the black hole. As the strength of the coupling of the axion field to the Chern-Simons term is increasing, the requirement that the total angular momentum of the system remain constant forces the black hole angular momentum to decrease. There exists a critical value of this coupling beyond which the black hole starts to rotate in the opposite direction, with an increasing magnitude of its angular momentum. We interpret this effect as a consequence of the exchange of energy between the axionic matter and the gravitational anomaly, which is sourced by the rotating black hole.

Analytical study of higher-order ring images of the accretion disk around a black hole

Gravitational lensing of a light source by a black hole leads to the appearance of higher-order images produced by photons that loop around the black hole before reaching the observer. Higher-order images were widely investigated numerically and analytically, in particular using the so-called strong deflection limit of gravitational deflection. After recent observations of the black hole image, attention has been drawn to higher-order rings, which are lensed images of the accreting matter of the black hole environment and can appear near the boundary of the black hole shadow. In this article, we use the strong deflection limit technique to investigate higher-order ring images of the luminous accretion disk around a Schwarzschild black hole. We consider a thin disk given by the inner and outer radii and an observer located far from the black hole on the axis of symmetry. For this configuration, it becomes possible to find the angular radii, thicknesses, and solid angles of higher-order rings in the form of compact analytical expressions. We show that the size of the rings is mainly determined by the position of the inner boundary of the accretion disk, which makes it possible to use them to distinguish between different accretion models. Possible generalizations of our model to nonsymmetric images can help to make the estimation of black hole angular momentum. We also present the analytical estimation of fluxes from higher-order images. Our method makes it easy to investigate $n=2$ and $n=3$ higher-order rings, the possible observation of which in future projects is currently being discussed.

Quantum Mechanics and General Relativity Identify Standard Model Particles as Black Holes

The Standard Model of particle physics does not account for charged fermion mass values and neutrino mass, or explain why only three particles are in each charge state 0, -e/3, 2e/3, and -e. These issues are addressed by treating Standard Model particles with mass m as spheres with diameter equal to their Compton wavelength l =ħ/mc, where ħ is Planck’s constant and c the speed of light, and any charge in diametrically opposed pairs ±ne/6 with n = 1, 2, or 3 at the axis of rotation on the sphere surface. Particles are ground state solutions of quantized Friedmann equations from general relativity, with differing internal gravitational constants. Energy distribution within particles identifies Standard Model particles with spheres containing central black holes with mass m, and particle spin resulting from black hole angular momentum. In each charge state, energy distribution within particles satisfies a cubic equation in l, allowing only three particles in the charge state and requiring neutrino mass. Cosmic vacuum energy density is a lower limit on energy density of systems in the universe, and setting electron neutrino average energy density equal to cosmic vacuum energy density predicts neutrino masses consistent with experiment. Relations between charged fermion wavelength solutions to cubic equations in different charge states determine charged fermion masses relative to electron mass as a consequence of charge neutrality of the universe. An appendix shows assigning charge ±e/6 to bits of information on the event horizon available for holographic description of physics in the observable universe accounts for dominance of matter over anti-matter. The analysis explains why only three Standard Models are in each charge state and predicts neutrino masses based on cosmic vacuum energy density as a lower bound on neutrino energy density.

Axionlike dark matter clouds around rotating black holes

Numerical analysis of dark matter axion-like cloud in the vicinity of rotating black hole has been performed. The model where axion-like scalar field is non-trivially coupled to Maxwell field is studied in the spacetime of Kerr black hole in uniform magnetic field and in Kerr-Newman one. The dependence of scalar mass and black hole angular momentum on accumulation of axion dark matter cloud was given. It was revealed that condensation of the dark matter clouds is preferable for a very small mass of axion.

Spin-induced scalarization of Kerr black holes with a massive scalar field

In the present paper we study the onset of the spin-induced scalarization of a Kerr black hole in scalar-Gauss–Bonnet gravity with a massive scalar field. Our approach is based on a (2+1) time evolution of the relevant linearized scalar field perturbation equation. We examine the region where the Kerr black hole becomes unstable giving rise to new scalarized rotating black holes with a massive scalar field. With increasing of the scalar field mass, the minimum value of the Gauss–Bonnet coupling parameter at which scalarization is possible, increases and thus the instability region shrinks. Interestingly, the introduction of scalar field mass does not change the critical minimal value of the black hole angular momentum a_{mathrm{crit}}/M where the instability of the Kerr black hole develops.

The Polarization of X-Rays from Warped Black Hole Accretion Disks

Abstract It is commonly assumed that in black hole (BH) accretion disks the angular momenta of the disk and the BH are aligned. However, for a significant fraction of stellar-mass BHs and supermassive BHs, the momenta may not be aligned. In such systems, the interplay of disk viscosity and general relativistic frame dragging can cause the disk to warp or break into two (or more) distinct planes; this is called the Bardeen–Petterson effect. We have developed a general relativistic ray-tracing code to find the energy spectra and polarization of warped accretion disks, accounting for the emission from the disk and for photons reflecting one or multiple times off the warped accretion disk segments. We find that polarization angle can be used to give a lower limit on the misalignment angle when a previous measurement of the jet, which is thought be aligned with the BH angular momentum, can be spatially resolved.

Kerr black hole shadow: non-parametric description and analytic methods of spin extraction

In this paper we study the asymmetry of the shadow cast by a rotating Kerr black hole. Using Bardeen parametric formulas we plot contours of black hole shadows for different values of black hole’s angular momentum and different observer’s positions. In the case of the equatorial observer we present an equation that explains the behaviour of the numeric Hioki-Maeda curve, which is used to measure the black hole angular momentum from it’s shadow. Also in this case we introduce a new observable of the shadow and derive a simple formula that allows to constrain the black hole spin via measuring this observable. Finally we come out with the formula that provides the non-parametric description of the black hole shadow.

Bardeen–Petterson alignment, jets, and magnetic truncation in GRMHD simulations of tilted thin accretion discs

Prevalent around luminous accreting black holes, thin discs are challenging to resolve in numerical simulations. When the disc and black hole angular momentum vectors are misaligned, the challenge becomes extreme, requiring adaptive meshes to follow the disc proper as it moves through the computational grid. With our new high-performance general relativistic magnetohydrodynamic (GRMHD) code H-AMR we have simulated the thinnest accretion disc to date, of aspect ratio H/R~0.03, around a rapidly spinning (a=0.9375) black hole, using a cooling function. Initially tilted at 10 degrees, the disc warps inside r~5 r_g into alignment with the black hole, where r_g is the gravitational radius. This is the first demonstration of Bardeen-Petterson alignment in MHD with viscosity self-consistently generated by magnetized turbulence. The disc develops a low-density high-viscosity (alpha_eff ~ 1.0) magnetic-pressure--dominated inner region at r<25 r_g that rapidly empties itself into the black hole. This inner region may in reality, due to thermal decoupling of ions and electrons, evaporate into a radiatively inefficient accretion flow if, as we propose, the cooling time exceeds the accretion time set by the order unity effective viscosity. We furthermore find the unexpected result that even our very thin disc can sustain large-scale vertical magnetic flux on the black hole, which launches powerful relativistic jets that carry 20-50% of the accretion power along the angular momentum vector of the outer tilted disc, providing a potential explanation for the origin of jets in radio-loud quasars.

The interior volume calculation for an axially symmetric black hole

Since an axially symmetric metric is much more complicated than a spherically symmetric metric, the largest hypersurface that corresponds to the interior volume of a black hole proposed by Christodoulou and Rovelli, cannot be found easily. Analogous to a Schwarzschild black hole, the particular hypersurface at constant r in a Kerr black hole has been selected directly. Using the extrinsic curvature of the hypersurface, we investigate how the hypersurface deviates from the largest hypersurface as the black hole angular momentum increases. It is shown that the hypersurface is very close to the largest hypersurface and the spinning of spacetime has pretty limited influence. Therefore, the hypersurface can be regarded as the largest hypersurface approximately in a Kerr black hole. So the volume of the hypersurface can be regarded as the interior volume of a Kerr black hole. Subsequently, we also calculate the interior volume of a Kerr–Newman black hole.

Mass and angular momentum of black holes in 3D gravity theories with first order formalism

We apply the Wald formalism to obtain masses and angular momenta of black holes in three dimensional gravity theories using the first order formalism. Wald formalism suggests that the entropy of a black hole can be defined by an integration of a conserved charge on the bifurcation horizon, and mass and angular momentum of a black hole as an integration of some charge variation form at spatial infinity. The action of three dimensional gravity theories can be represented by a form including some auxiliary fields. As well-known examples we have calculated masses and angular momenta of some black holes in topologically massive gravity and new massive gravity theories using the first order formalism. We have also calculated mass and angular momentum of BTZ black hole and new type black hole in minimal massive gravity theory with the action represented by the first order formalism. We have also calculated the entropy and central charges of new type black hole. According to AdS / CFT correspondence we suggest that the left and right moving temperatures should be equal to the Hawking temperature in the case of new type black hole in minimal massive gravity.

Critical gravitational collapse with angular momentum. II. Soft equations of state

We study critical phenomena in the collapse of rotating ultrarelativistic perfect fluids, in which the pressure $P$ is related to the total energy density $\rho$ by $P=\kappa\rho$, with $\kappa$ a constant. We generalize earlier results for radiation fluids with $\kappa=1/3$ to other values of $\kappa$, focussing on $\kappa < 1/9$. For $1/9<\kappa \lesssim 0.49$, the critical solution has only one unstable, growing mode, which is spherically symmetric. For supercritical data it controls the black hole mass, while for subcritical data it controls the maximum density. For $\kappa<1/9$, an additional axial $l=1$ mode becomes unstable. This controls either the black hole angular momentum, or the maximum angular velocity. In theory, the additional unstable $l=1$ mode changes the nature of the black hole threshold completely: at sufficiently large initial rotation rates $\Omega$ and sufficient fine-tuning of the initial data to the black hole threshold we expect to observe nontrivial universal scaling functions (familiar from critical phase transitions in thermodynamics) governing the black hole mass and angular momentum, and, with further fine-tuning, eventually a finite black hole mass almost everywhere on the threshold. In practice, however, the second unstable mode grows so slowly that we do not observe this breakdown of scaling at the level of fine-tuning we can achieve, nor systematic deviations from the leading-order power-law scalings of the black hole mass. We do see systematic effects in the black-hole angular momentum, but it is not clear yet if these are due to the predicted non-trivial scaling functions, or to nonlinear effects at sufficiently large initial angular momentum (which we do not account for in our theoretical model).

General relativistic effects on the orbit of the S2 star with GRAVITY

Context. The first observations of the GRAVITY instrument obtained in 2016, have shown that it should become possible to probe the spacetime close to the supermassive black hole Sagittarius A* (Sgr A*) at the Galactic center by using accurate astrometric positions of the S2 star. Aims. The goal of this paper is to investigate the detection by GRAVITY of different relativistic effects affecting the astrometric and/or spectroscopic observations of S2 such as the transverse Doppler shift, the gravitational redshift, the pericenter advance and higher-order general relativistic (GR) effects, in particular the Lense-Thirring effect due to the angular momentum of the black hole. Methods. We implement seven stellar-orbit models to simulate both astrometric and spectroscopic observations of S2 beginning near its next pericenter passage in 2018. Each model takes into account a certain number of relativistic effects. The most accurate one is a fully GR model and is used to generate the mock observations of the star. For each of the six other models, we determine the minimal observation times above which it fails to fit the observations, showing the effects that should be detected. These threshold times are obtained for different astrometric accuracies as well as for different spectroscopic errors. Results. Transverse Doppler shift and gravitational redshift can be detected within a few months by using S2 observations obtained with pairs of accuracies (σA,σV) = (10−100 μas, 1−10 km s-1) where σA and σV are the astrometric and spectroscopic accuracies, respectively. Gravitational lensing can be detected within a few years with (σA,σV) = (10 μas, 10 km s-1). Pericenter advance should be detected within a few years with (σA,σV) = (10 μas, 1−10 km s-1). Cumulative high-order photon curvature contributions, including the Shapiro time delay, affecting spectroscopic measurements can be observed within a few months with (σA,σV) = (10 μas, 1 km s-1). By using a stellar-orbit model neglecting relativistic effects on the photon path except the major contribution of gravitational lensing, S2 observations obtained with accuracies (σA,σV) = (10 μas, 10 km s-1), and a black hole angular momentum (a,i′,Ω′) = (0.99,45°,160°), the 1σ error on the spin parameter a is of about 0.4, 0.2, and 0.1 for a total observing run of 16, 30, and 47 yr, respectively. The 1σ errors on the direction of the angular momentum reach σi′ ≈ 25° and σΩ′ ≈ 40° when considering the three orbital periods run. We found that the uncertainties obtained with a less spinning black hole (a = 0.7) are similar to those evaluated with a = 0.99. Conclusions. The combination of S2 observations obtained with the GRAVITY instrument and the spectrograph SINFONI (Spectrograph for INtegral Field Observations in the Near Infrared) also installed at the VLT (Very Large Telescope) will lead to the detection of various relativistic effects. Such detections will be possible with S2 monitorings obtained within a few months or years, depending on the effect. Strong constraints on the angular momentum of Sgr A* (e.g., at 1σ = 0.1) with the S2 star will be possible with a simple stellar-orbit model without using a ray-tracing code but with approximating the gravitational lensing effect. However, long monitorings are necessary, and we thus must rely on the discovery of closer-in stars near Sgr A* if we want to efficiently constrain the black hole parameters with stellar orbits in a short time, or monitor the flares if they orbit around the black hole.

Scalar absorption by charged rotating black holes

We compute numerically the absorption cross section of planar massless scalar waves impinging upon a Kerr-Newman black hole with different incidence angles. We investigate the influence of the black hole electric charge and angular momentum in the absorption spectrum, comparing our numerical computations with analytical results for the limits of high and low frequency.

Status of GRMHD simulations and radiative models of Sgr A*

AbstractThe Galactic center is a perfect laboratory for testing various theoretical models of accretion flows onto a supermassive black hole. Here, I review general relativistic magnetohydrodynamic simulations that were used to model emission from the central object - Sgr A*. These models predict dynamical and radiative properties of hot, magnetized, thick accretion disks with jets around a Kerr black hole. Models are compared to radio-VLBI, mm-VLBI, NIR, and X-ray observations of Sgr A*. I present the recent constrains on the free parameters of the model such as accretion rate onto the black hole, the black hole angular momentum, and orientation of the system with respect to our line of sight.

Pre-Hawking radiation may allow for reconstruction of the mass distribution of the collapsing object

Hawking radiation explicitly depends only on the black hole's total mass, charge and angular momentum. It is therefore generally believed that one cannot reconstruct the information about the initial mass distribution of an object that made the black hole. However, instead of looking at radiation from a static black hole, we can study the whole time-dependent process of the gravitational collapse, and pre-Hawking radiation which is excited because of the time-dependent metric. We compare radiation emitted by a single collapsing shell with that emitted by two concentric shells of the equivalent total mass. We calculate the gravitational trajectory and the momentum energy tensor. We show that the flux of energy emitted during the collapse by a single shell is significantly different from the flux emitted by two concentric shells of the equivalent total mass. When the static black hole is formed, the fluxes become indistinguishable. This implies that an observer studying the flux of particles from a collapsing object could in principle reconstruct information not only about the total mass of the collapsing object, but also about the mass distribution.

Mass and angular momentum of black holes in low-energy heterotic string theory

We investigate conserved charges in the low-energy effective field theory describing heterotic string theory. Starting with a general Lagrangian that consists of a metric, a scalar field, a vector gauge field, together with a two-form potential, we derive off-shell Noether potentials of the Lagrangian and generalize the Abbott–Deser–Tekin (ADT) formalism to the off-shell level by establishing one-to-one correspondence between the ADT potential and the off-shell Noether potential. It is proved that the off-shell generalized ADT formalism is conformally invariant. Then, we apply the formulation to compute mass and angular momentum of the four-dimensional Kerr–Sen black hole and the five-dimensional rotating charged black string in the string frame without a necessity to transform the metrics into the Einstein frame.

Lense–Thirring precession around supermassive black holes during tidal disruption events

A tidal disruption event (TDE) occurs when a star wanders close enough to a black hole to be disrupted by its tidal force. The debris of a tidally disrupted star are expected to form an accretion disc around the supermassive black hole. The light curves of these events sometimes show a quasi-periodic modulation of the flux that can be associated with the precession of the accretion disc due to the Lense-Thirring ("frame-dragging") effect. Since the initial star orbit is in general inclined with respect to the black hole spin, this misalignment combined with the Lense-Thirring effect leads to a warp in the disc. In this paper we provide a simple model of the system composed by a thick and narrow accretion disc surrounding a spinning supermassive black hole, with the aim to: (a) compute the expected precession period as a function of the system parameters, (b) discuss the conditions that have to be satisfied in order to have rigid precession, (c) investigate the alignment process, highlighting how different mechanisms play a role leading the disc and the black hole angular momenta into alignment.