Short timescale variability is often associated with a black hole system. The consequence of an electromagnetic outflow suddenly generated near a Kerr black hole is considered assuming that it is described by a solution of a force-free field with a null electric current. We compute charged particle acceleration induced by the burst field. The interaction between the particle and the field is characterized by a large dimensionless number. We show that the particle is instantaneously accelerated to the relativistic regime by the field with a very large amplitude. The typical maximum energy attained by a proton for an event near a super massive black hole is $E_{\rm max} \sim 100$ TeV, which is enough observed high-energy flares.
The null geodesic equation in the Kerr spacetime can be expressed as a set of integral equations involving certain potentials. We classify the roots of these potentials and express the integrals in manifestly real Legendre elliptic form. We then solve the equations using Jacobi elliptic functions, providing the complete set of null geodesics of the Kerr exterior as explicit parameterized curves.
The exact metric of a moving Kerr black hole with an arbitrary constant velocity is derived in Kerr-Schild coordinates. We then calculate the null equatorial gravitational deflection caused by a radially moving Kerr source up to the second post-Minkowskian order, acting as an application of the weak field limit of the metric. The bending angle of light is found to be consistent with the result given in the previous works.
A three-dimensional light-like foliation of a spacetime geometry is one particular way of studying its light cone structure and has important applications in numerical relativity. In this paper, we execute such a foliation for the Kerr-Newman-AdS black hole geometry and compare it with the lightlike foliations of the Kerr-AdS and Kerr-Newman black holes. We derive the equations that govern this slicing and study their properties. In particular, we find that these null hypersurfaces develop caustics inside the inner horizon of the Kerr-Newman-AdS black hole, in strong contrast to the Kerr-AdS c…
For many purposes, a three-dimensional foliation of spacetime is more advantageous to understanding its light cone structure. We derive the equations describing such foliations for the Kerr geometry with non-zero cosmological constant, and show that they reduce to null hypersurfaces in vacuum (anti-)de Sitter spacetime in the limit of zero mass. Furthermore, we find that these null hypersurfaces are free of caustics everywhere for $r>0$. Our construction has applications in numerical studies of rotating black holes, and in defining Kruskal coordinates for rotating black holes with non-zero cos…
We examine the singularities of the wave fronts of null geodesics from point sources in the Kerr Metric. We find that the wave fronts develop a tube like structure that collapses non-symmetrically, leading to cusp features in the wave front singularities. As the wave front advances, the cusps trace out an astroidal shaped caustic tube, which had been discovered previously using lens mapping and geodesic deviation methods. Thus, the wave front approach in this study helps to complete a picture of caustics and gravitational lensing in the Kerr geometry.
We consider null geodesics in the exterior region of a subextremal Kerr spacetime. We show that most well-known fundamental properties of null geodesics can be represented on one plot. In particular, one can see immediately that the ergoregion and trapping are separated in phase space. Furthermore, we show that from the point of view of any timelike observer outside of the black hole, trapping can be understood as a smooth set of spacelike directions on the celestial sphere of the observer. Finally, we discuss some applications of these insights.
Characterization of (asymptotically) Kerr-de Sitter-like spacetimes at null infinity
本文研究了具有正宇宙学常数$Λ$的爱因斯坦真空场方程的解$(\mathcal{M}, g)$，该方程允许一个光滑的零无穷$\mathcal{J}^-$ à la Penrose和一个Killing矢量场，其相关的Mars-Simon张量（MST）为零.这项工作的主要目的是提供一个表征这些时空的柯西数据$\mathcal{J}^-$。在此过程中，我们还研究了MST不消失的时空。在这种情况下，其定义中存在由标量函数$Q$捕获的模糊性。我们分析了不同选择的$Q$的MST的属性。在这样做的时候，我们导致的“渐近克尔-德西特类时空”的定义，我们也在$\mathcal{J}^-$的渐近数据方面的特点。
We analyze the stability of circular geodesics for timelike as well as null geodesics of the Kerr BH spacetime with rotation parameter on the equatorial plane by Lyapunov stability analysis. Also, we verify the results of stability by presenting the phase portrait for both timelike and null geodesics. Further, by reviewing the Kosambi-Cartan-Chern (KCC) theory, we analyze the Jacobi stability for Kerr spacetime and present a comparative study of the methods used for stability analysis of geodesics.
The Landau-Lifshitz decomposition of spacetime, or (1+3)-split, determines the three-dimensional velocity and acceleration as measured by static observers. We use these quantities to analyze the geodesic particles in Schwarzschild and Kerr spacetimes. We show that in both cases there is no room for a positive acceleration (repulsion). We also compute the escape and terminal speeds. The escape speed in the case of a static black hole coincides with the Newton result. For the Kerr spacetime, the escape speed depends on the polar angle, showing that a particle needs less energy to escape in the d…
The no-hair theorem can be tested in the strong gravity regime by using the top-bottom approach and the bottom-top approach. The non-Kerr spacetime of the later approach is an ideal framework to do the tests in the region very close to the black holes. In this work, we propose a non-Kerr black hole metric (and its charged extension) that is accelerating as well. These new objects are studied for their basic properties and thermodynamics.
Geodesic motion has significant characteristics of space-time. We calculate the principle Lyapunov exponent (LE), which is the inverse of the instability timescale associated with this geodesics and Kolmogorov-Senai (KS) entropy for our rotating Kerr-Kiselev (KK) black hole. We have investigate the existence of stable/unstable equatorial circular orbits via LE and KS entropy for time-like and null circular geodesics. We have shown that both LE and KS entropy can be written in terms of the radial equation of innermost stable circular orbit (ISCO) for time-like circular orbit. Also, we computed …
We discuss the generalization of the Kerr-Schild (KS) formalism for general relativity and double field theory (DFT) to the heterotic DFT and supergravity. We first introduce a heterotic KS ansatz by introducing a pair of null O(d,d+G) generalized tangent vectors. The pair of null vectors are represented by a pair of d-dimensional vector fields, and one of the vector fields is not a null vector. This implies that the null property of the usual KS formalism, which plays a crucial role in linearizing the field equations, can be partially relaxed in a consistent way. We show that the equations of…
An atom falling freely into a Kerr black hole in a Boulware-like vacuum is shown to emit radiation with a Planck spectrum at the Hawking temperature. For a cloud of falling atoms with random initial times, the radiation is thermal. The existence of this radiation is due to the acceleration of the vacuum field modes with respect to the falling atom. Its properties can be traced to the dominant role of conformal quantum mechanics (CQM) in the neighborhood of the event horizon. We display this effect for a scalar field, though the acceleration radiation has a universal conformal behavior that is …
The Minkowski background intrinsic to the Kerr-Schild version of the Kerr metric provides a definition of a boosted spinning black hole. There are two Kerr-Schild versions corresponding to ingoing or outgoing principal null directions. The two corresponding Minkowski backgrounds and their associated boosts differ drastically. This has an important implication for the gravitational memory effect. A prior analysis of the transition of a non-spinning Schwarzschild black hole to a boosted state showed that the memory effect in the nonlinear regime agrees with the linearised result based upon the r…
