Testing the Kerr black hole hypothesis with the continuum-fitting and the iron line methods: the case of GRS 1915+105

The continuum-fitting and the iron line methods are currently the two leading techniques for probing the strong gravity region around accreting black holes. In the present work, we test the Kerr black hole hypothesis with the stellar-mass black hole in GRS 1915+105 by analyzing five disk-dominated RXTE spectra and one reflection-dominated Suzaku spectrum. The combination of the constraints from the continuum-fitting and the iron line methods has the potential to provide more stringent tests of the Kerr metric. Our constraint on the Johannsen deformation parameter α13 is -0.15 < α13 < 0.14 at 3σ, where the Kerr metric is recovered when α13 = 0.

Photon boomerang in a nearly extreme Kerr metric

The Kerr rotating black hole metric has unstable photon orbits that orbit around the hole at fixed values of the Boyer-Lindquist coordinate r that depend on the axial angular momentum of the orbit, as well as on the parameters of the hole. For zero orbital axial angular momentum, these orbits cross the rotational axes at a fixed value of r that depends on the mass M and angular momentum J of the black hole. Nonzero angular momentum of the hole causes the photon orbit to rotate so that its direction when crossing the north polar axis changes from one crossing to the next by an angle I shall call ∆φ, which depends on the black hole dimensionless rotation parameter a/M = cJ/(GM2) by an equation involving a complete elliptic integral of the first kind. When the black hole has a/M ≈ 0.994 341 179 923 26, which is nearly maximally rotating, a photon sent out in a constant-r direction from the north polar axis at r ≈ 2.423 776 210 035 73 GM/c2returns to the north polar axis in precisely the opposite direction (in a frame nonrotating with respect to the distant stars), a photon boomerang.

Rotating bodies; the Kerr metric

Spacetime around a general rigidly rotating body is discussed, and the Kerr solution explored in detail. First we obtain generic properties of stationary, axisymmetric metrics. The stationary limit surface and ergoregion is defined. Then the Kerr metric is presented (without derivation) and discussed. Horizons and limit surfaces are obtained, and the overall structure of the Kerr black hole deduced. The mass and angular momentum is extracted. Equations for particle orbits are obtained, and their properties discussed.

Testing Kerr black hole mimickers with quasi-periodic oscillations from GRO J1655-40

The measurements of quasi-periodic oscillations (QPOs) provide a quite powerful tool to test the nature of astrophysical black hole candidates in the strong gravitational field regime. In this paper, we use QPOs within the relativistic precession model to test a recently proposed family of rotating black hole mimickers, which reduce to the Kerr metric in a limiting case, and can represent traversable wormholes or regular black holes with one or two horizons, depending on the values of the parameters. In particular, assuming that the compact object of GRO J1655-40 is described by a rotating black hole mimicker, we perform a $$\chi $$ χ -square analysis to fit the parameters of the mimicker with two sets of observed QPO frequencies from GRO J1655-40. Our results indicate that although the metric around the compact object of GRO J1655-40 is consistent with the Kerr metric, a regular black hole with one horizon is favored by the observation data of GRO J1655-40.

Regular Bardeen Black Holes in Anti-de Sitter Spacetime versus Kerr Black Holes through Particle Dynamics

In this work, test particle dynamics around a static regular Bardeen black hole (BH) in Anti-de Sitter spacetime has been studied. It has been shown for neutral test particles that parameters of a regular Bardeen black hole in Anti-de Sitter spacetime can mimic the rotation parameter of the Kerr metric up to the value a≈0.9 providing the same innermost stable circular orbit (ISCO) radius. We have also explored the dynamics of magnetized particles with a magnetic dipole moment around a magnetically charged regular Bardeen black hole in Anti-de Sitter spacetime. As a realistic astrophysical scenario of the study, we have treated neutron stars orbiting a supermassive black hole (SMBH), in particular, the magnetar PSR J1745-2900 orbiting Sgr A* with the parameter β=10.2, as magnetized test particles. The magnetized particles dynamics shows that the parameter β, negative values of cosmological constant and magnetic charge parameter of the central BH cause a decrease in the ISCO radius. We have compared the effects of the magnetic charge of the Bardeen BH with the spin of rotating Kerr BH and shown that magnetic charge parameter can mimic the spin in the range a/M≃(0,0.7896) when Λ=0 at the range of its values g/M≃(0,0.648).

The CPR black hole with acceleration

Different deformations and modifications have been proposed in the Kerr black hole solution. In the so-called non-Kerr metric a deformation function was proposed. This approach has been generalized to include two different deformation functions to obtain the CPR black hole (Cardoso et al. in Phys Rev D 89:064007, 2014). In this letter we develop the accelerating version of this spacetime and study its thermodynamics.

The Goursat problem at the horizons for the Klein–Gordon equation on the de Sitter–Kerr metric

The main topic of this paper is the Goursat problem at the horizon for the Klein–Gordon equation on the De Sitter–Kerr metric when the angular momentum (per unit of mass) of the black hole is small. Indeed, we solve the Goursat problem for fixed angular momentum [Formula: see text] of the field (with the restriction that [Formula: see text] is not zero in the case of a massless field).

Inductive Rectilinear Frame Dragging and Local Coupling to the Gravitational Field of the Universe

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. The drag force can be understood as inductive rectilinear frame dragging because it also exists in the rest frame of a moving object, and it arises in that frame 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 capture inductive dragging effects, and this might be the first identification of inductive rectilinear dragging. The existence of this drag force proves it is possible for matter in motion through a finite region to exchange momentum and energy with the gravitational field of the universe. The cosmological metric can in principle be determined through this force from local measurements on moving bodies, at resolutions similar to that of the Pound–Rebka experiment.

On the Kerr metric in a synchronous reference frame

The Kerr metric is considered in a synchronous frame of reference obtained by using proper time and initial conditions for particles that freely move along a certain set of trajectories as coordinates. Modifying these coordinates in a certain way (keeping their interpretation as initial values at large distances), we still have a synchronous frame and the direct analogue of the Lemaitre metric, the singularities of which are exhausted by the physical Kerr singularity (the singularity ring).