Complete set of quasi-conserved quantities for spinning particles around Kerr

We revisit the conserved quantities of the Mathisson-Papapetrou-Tulczyjew equations describing the motion of spinning particles on a fixed background. Assuming Ricci-flatness and the existence of a Killing-Yano tensor, we demonstrate that besides the two non-trivial quasi-conserved quantities, i.e. conserved at linear order in the spin, found by Rüdiger, non-trivial quasi-conserved quantities are in one-to-one correspondence with non-trivial mixed-symmetry Killing tensors. We prove that no such stationary and axisymmetric mixed-symmetry Killing tensor exists on the Kerr geometry. We discuss the implications for the motion of spinning particles on Kerr spacetime where the quasi-constants of motion are shown not to be in complete involution.

On the discrete version of the Kerr geometry

In this paper, a Kerr-type solution in the Regge calculus is considered. It is assumed that the discrete general relativity, the Regge calculus, is quantized within the path integral approach. The only consequence of this approach used here is the existence of a length scale at which edge lengths are loosely fixed, as considered in our earlier paper. In addition, we previously considered the Regge action on a simplicial manifold on which the vertices are coordinatized and the corresponding piecewise constant metric is introduced, and found that for the simplest periodic simplicial structure and in the leading order over metric variations between four-simplices, this reduces to a finite-difference form of the Hilbert–Einstein action. The problem of solving the corresponding discrete Einstein equations (classical) with a length scale (having a quantum nature) arises as the problem of determining the optimal background metric for the perturbative expansion generated by the functional integral. Using a one-complex-function ansatz for the metric, which reduces to the Kerr–Schild metric in the continuum, we find a discrete metric that approximates the continuum one at large distances and is nonsingular on the (earlier) singularity ring. The effective curvature [Formula: see text], including where [Formula: see text] (gravity sources), is analyzed with a focus on the vicinity of the singularity ring.

Black holes lessons from multipole ratios

We explain in detail how to calculate the gravitational mass and angular momentum multipoles of the most general non-extremal four-dimensional black hole with four magnetic and four electric charges. We also calculate these multipoles for generic supersymmetric four-dimensional microstate geometries and multi-center solutions. Both for Kerr black holes and BPS black holes many of these multipoles vanish. However, if one embeds these black holes in String Theory and slightly deforms them, one can calculate an infinite set of ratios of vanishing multipoles which remain finite as the deformation is taken away, and whose values are independent of the direction of deformation. For supersymmetric black holes, we can also compute these ratios by taking the scaling limit of multi-center solutions, and for certain black holes the ratios computed using the two methods agree spectacularly. For the Kerr black hole, these ratios pose strong constraints on the parameterization of possible deviations away from the Kerr geometry that should be tested by future gravitational wave interferometers.

Kerr metric Killing bundles

We provide a complete characterization of the metric Killing bundles (or metric bundles) of the Kerr geometry. Metric bundles can be generally defined for axially symmetric spacetimes with Killing horizons and, for the case of Kerr geometries, are sets of black holes (BHs) or black holes and naked singularities (NSs) geometries. Each metric of a bundle has an equal limiting photon (orbital) frequency, which defines the bundle and coincides with the frequency of a Killing horizon in the extended plane. In this plane each bundle is represented as a curve tangent to the curve that represents the horizons, which thus emerge as the envelope surfaces of the metric bundles. We show that the horizons frequency can be used to establish a connection between BHs and NSs, providing an alternative representation of such spacetimes in the extended plane and an alternative definition of the BH horizons. We introduce the concept of inner horizon confinement and horizons replicas and study the possibility of detecting their frequencies. We study the bundle characteristic frequencies constraining the inner horizon confinement in the outer region of the plane i.e. the possibility of detect frequency related to the inner horizon, and the horizons replicas, structures which may be detectable for example from the emission spectra of BHs spacetimes. With the replicas we prove the existence of photon orbits with equal orbital frequency of the horizons. It is shown that such observations can be performed close to the rotation axis of the Kerr geometry, depending on the BH spin. We argue that these results could be used to further investigate black holes and their thermodynamic properties.

Constraining LQG Graph with Light Surfaces: Properties of BH Thermodynamics for Mini-Super-Space, Semi-Classical Polymeric BH

This work participates in the research for potential areas of observational evidence of quantum effects on geometry in a black hole astrophysical context. We consider properties of a family of loop quantum corrected regular black hole (BHs) solutions and their horizons, focusing on the geometry symmetries. We study here a recently developed model, where the geometry is determined by a metric quantum modification outside the horizon. This is a regular static spherical solution of mini-super-space BH metric with Loop Quantum Gravity (LQG) corrections. The solutions are characterized delineating certain polymeric functions on the basis of the properties of the horizons and the emergence of a singularity in the limiting case of the Schwarzschild geometry. We discuss particular metric solutions on the base of the parameters of the polymeric model related to similar properties of structures, the metric Killing bundles (or metric bundles MBs), related to the BH horizons’ properties. A comparison with the Reissner–Norström geometry and the Kerr geometry with which analogies exist from the point of their respective MBs properties is done. The analysis provides a way to recognize these geometries and detect their main distinctive phenomenological evidence of LQG origin on the basis of the detection of stationary/static observers and the properties of light-like orbits within the analysis of the (conformal invariant) MBs related to the (local) causal structure. This approach could be applied in other quantum corrected BH solutions, constraining the characteristics of the underlining LQG-graph, as the minimal loop area, through the analysis of the null-like orbits and photons detection. The study of light surfaces associated with a diversified and wide range of BH phenomenology and grounding MBs definition provides a channel to search for possible astrophysical evidence. The main BHs thermodynamic characteristics are studied as luminosity, surface gravity, and temperature. Ultimately, the application of this method to this spherically symmetric approximate solution provides us with a way to clarify some formal aspects of MBs, in the presence of static, spherical symmetric spacetimes.

Efficient gravitational lens optical scalars calculation of black holes with angular momentum

ABSTRACT We provide new very simple and compact expressions for the efficient calculation of gravitational lens optical scalars for Kerr space–time, which are exact along any null geodesic. These new results are obtained recurring to well-known results on geodesic motion that exploit obvious and hidden symmetries of Kerr space–time and contrast with the rather long and cumbersome expressions previously reported in the literature, providing a helpful improvement for the sake of an efficient integration of the geodesic deviation equation on Kerr geometry. We also introduce a prescription for the observer frame that captures a new notion of centre of the black hole, which can be used for any position of the observer, including those near the black hole. We compare the efficient calculation of weak lens optical scalars with the exact equations, finding an excellent agreement.

Effect of turbulent pressure on the origin of low-frequency quasi-periodic oscillations in rotating black holes

ABSTRACT Quasi-periodic oscillation (QPO), particularly of low frequency (LF), is a very obvious feature of outbursting black hole candidates. The association of QPOs in a specific spectral state and their transition with states make them a key ingredient in understanding the underlying physical processes that produce them. Observations have revealed that generally, in the hard spectral state of the outburst, the size of the Compton cloud is relatively bigger, which produces low-frequency QPOs (LFQPOs). In progressive days increased cooling shrinks the area of the cloud, the inner edge of the disc comes close to the black holes, and produces higher frequency QPOs. However, rotating black holes with higher spin values are likely to produce LFQPOs even if their inner edge of the disc is closer to the hole. Here, for the first time, we address the issue, solving hydrodynamic flow equations in the presence of qualitative turbulent pressure and cooling in pseudo-Kerr geometry. Increasing turbulence slackens the infalling flow, thus the infall time becomes longer, producing LFQPOs. Our study discovers that the effect of turbulence modifies LFQPOs value significantly, by a factor of a few lower throughout the angular momentum distribution of the flow. We find a strong correlation between the turbulence and the spin parameter of the hole. Finally, we discuss the observed results in light of the present solution.