Deflection of light by a rotating black hole surrounded by “quintessence”

We present a detailed analysis of a rotating black hole surrounded by “quintessence.” This solution represents a fluid with a constant equation of state, [Formula: see text], which can for example describe an effective warm dark matter fluid around a black hole. We clarify the conditions for the existence of such a solution and study its structure by analyzing the existence of horizons as well as the extremal case. We show that the deflection angle produced by the black hole depends on the parameters [Formula: see text] which need to obey the condition [Formula: see text] because of the weak energy condition, where [Formula: see text] is an additional parameter describing the hair of the black hole. In this context, we found that for [Formula: see text] (consistent with warm dark matter) and [Formula: see text], the deviation angle is larger than that in the Kerr space–time for direct and retrograde orbits. We also derive an exact solution in the case of [Formula: see text].

Kerr–Bolt black hole entropy and soft hair

Recently it has been speculated that a set of infinitesimal [Formula: see text] diffeomorphisms exist which act nontrivially on the horizon of some black holes such as Kerr and Kerr–Newman black holes.[Formula: see text] Having applied this symmetry in covariant phase space formalism, one can obtain Virasoro charges as surface integrals on the horizon. Kerr–Bolt space–time is well known for its asymptotically topology and has been studied widely in recent years. In this work, we are interested to find conserved charge associated to the Virasoro symmetry of Kerr–Bolt geometry using covariant phase space formalism. We will show right and left central charge are [Formula: see text], respectively. Our results also show good agreement with Kerr space–time in the limiting behavior.

Spinning cosmic strings in conformal gravity

We investigate the space–time of a spinning cosmic string in conformal invariant gravity, where the interior consists of a gauged scalar field. We find exact solutions of the exterior of a stationary spinning cosmic string, where we write the metric as [Formula: see text], with [Formula: see text] a dilaton field which contains all the scale dependences. The “unphysical” metric [Formula: see text] is related to the [Formula: see text]-dimensional Kerr space–time. The equation for the angular momentum [Formula: see text] decouples, for the vacuum situation as well as for global strings, from the other field equations and delivers a kind of spin-mass relation. For the most realistic solution, [Formula: see text] falls off as [Formula: see text] and [Formula: see text] close to the core. The space–time is Ricci flat. The formation of closed timelike curves can be pushed to space infinity for suitable values of the parameters and the violation of the weak energy condition can be avoided. For the interior, a numerical solution is found. This solution can easily be matched at the boundary on the exterior exact solution by special choice of the parameters of the string. This example shows the power of conformal invariance to bridge the gap between general relativity and quantum field theory.

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.

Wave Optics in the Kerr Space-Time Taking the Spin-Helicity Interaction into Account

We apply an algebraically special solution of the Maxwell equations in the Kerr space-time, which we specify as outgoing in the Chandrasekhar meaning, to obtain the wave vectors of right- and left-polarized waves and prove that the nullity condition of field invariants yield the non-nullity of wave vectors and that the wave vector is not geodesic. We also show how these are related to the analysis of radiation in the Kerr space-time, provided by Starobinskii and Teukolsky.

Applied holography of the AdS5–Kerr space–time

Asymptotically anti-de Sitter–Kerr black holes (we focus here on the five-dimensional case) are associated holographically with matter at conformal infinity which has a nonzero angular momentum density. It is natural to attempt to associate this angular momentum with the recently discovered vorticity of the plasmas produced in peripheral heavy-ion collisions. We assume that an AdS5–Kerr black hole with angular momentum to mass ratio [Formula: see text] is dual to boundary matter with an angular momentum density to energy density ratio also equal to [Formula: see text]. With this assumption, we find that, for collisions corresponding to a given value of [Formula: see text], there is a maximal possible angular velocity (well below the maximal value permitted by causality) for such matter at infinity, and that this value is in approximate agreement with the experimentally reported value of the average plasma vorticity produced in typical peripheral collisions of heavy ions.

On Quantization of a Slowly Rotating Kerr Black Hole in Teleparallel Gravity

In this article we calculate the total angular momentum for Kerr space-time for slow rotations in the context of teleparallel gravity. In order to analyze the role of such a quantity, we apply Weyl quantization method to obtain a quantum equation for the z-component of the angular momentum density, and for the squared angular momentum density as well. We present an approximate solution using the Adomian decomposition method (AM), which reveals a discrete characteristic for angular momentum.