We show that the Kerr-Schild ansatz can be extended from the metric to the tetrad, and then to teleparallel gravity where curvature vanishes but torsion does not. We derive the equations of motion for the Kerr-Schild null vector, and describe the solution for a rotating black hole in this framework. It is shown that the solution depends on the chosen tetrad in a non-trivial way if the spin connection is fixed to be the one of the flat background spacetime. We show furthermore that any Kerr-Schild solution with a flat background is also a solution of $f(\mathcal{T})$ gravity.
In the present work, the spin-coefficient formalism of Newman and Penrose is used to formulate geometric constraints for the existence of Kerr-Schild groups, i.e. continuous groups of generalized Kerr-Schild transformations. In addition, by characterizing the geometric structure of the deformed Einstein tensor of the generalized Kerr-Schild class, restrictions are imposed on the existence of apparent conservation laws in generic spacetimes, which are defined via considering special Kerr-Schild currents whose associated Kerr-Schild vector fields coincide with timelike Killing vector fields of p…
We study in some detail the "extended Kerr-Schild" formulation of general relativity, which decomposes the gauge-independent degrees of freedom of a generic metric into two arbitrary functions and the choice of a flat background tetrad. We recast Einstein's equations and spacetime curvatures in the extended Kerr-Schild form and discuss their properties, illustrated with simple examples.
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.
Specialising to the case of Kerr-Schild spacetimes, which include the Kerr black hole and gravitational wave solutions, we propose a modification of the Penrose quasi-local energy. The modification relies on the existence of a natural Minkowski background for Kerr-Schild spacetimes. We find that the modified surface integral reduces to a volume integral of the Einstein tensor, which has been proposed previously as an appropriate definition for quasi-local energy for Kerr-Schild backgrounds. Furthermore, in the special case that the Kerr-Schild null vector is normal to the surface of interest, …
The Newman-Janis (NJ) method is a prescription to derive the Kerr space-time from the Schwarzschild metric. The BTZ, Kerr and five-dimensional Myers-Perry (MP) black hole solutions have already been generated by different versions of the NJ method. However, it is not known how to generate the metric of higher-dimensional (d > 6) rotating black holes by this method. In this paper, we propose the simplest algorithm for generation of the five-dimensional MP metric with two arbitrary angular momenta by using the Kerr-Schild form of the metric and quaternions. Then, we present another new two-step …
The Newman-Janis algorithm and its generalizations can be used mathematically to generate rotating solutions from nonrotating spherically-symmetric solutions within general relativity. The energy-momentum tensors of these solutions may or may not represent the same physical system, in the sense of both being a perfect fluid, or an electromagnetic field, or a $Λ$-term, and so on. In a series of two papers, we compare the structure of the eigenvalues and eigenvectors of the rotating and nonrotating energy-momentum tensors (their Segre types) and look for the existence of equations of state relat…
We study Kerr-Schild-Kundt class of metrics in generic gravity theories with Maxwell's field. We prove that these metrics linearize and simplify the field equations of generic gravity theories with Maxwell's field.
Close limit evolution of Kerr-Schild type initial data for binary black holes
我们发展了Bishop {\em et al.}在黑洞彼此靠近的极限。我们提出了一个精确的解决方案的线性化的初始值问题的基础上，他们的建议，并利用最近推出的广义形式主义研究任意坐标系中的Schwarzschild黑洞的扰动执行的演变。通过对黑洞碰撞辐射能量和波形的分析，阐明了初始数据族中自由参数的意义。
The Kerr-Schild form provides a natural way of realizing the classical double copy that relates exact solutions in general relativity to exact solutions in gauge theory. In this paper, we examine the asymptotic structure of Kerr-Schild form. In Newman-Unti gauge, we find a generic solution space satisfying the Kerr-Schild form in series expansion around null infinity. The news function in the solution space is chiral and can not lead to a mass loss formula. A class of asymptotically flat complex pp-wave solutions in closed form is obtained from the solution space.
Five-dimensional Einstein-Maxwell-Chern-Simons equations are investigated in the framework of an extended Kerr-Schild strategy to search for black holes solutions. The fulfillment of Einstein equations constrains the Chern-Simons coupling constant to a value determined by the trace of the energy-momentum tensor of the electromagnetic configuration.
The Newman-Janis trick is a procedure, (not even really an ansatz), for obtaining the Kerr spacetime from the Schwarzschild spacetime. This 50 year old trick continues to generate heated discussion and debate even to this day. Most of the debate focusses on whether the Newman-Janis procedure can be upgraded to the status of an algorithm, or even an inspired ansatz, or is it just a random trick of no deep physical significance. (That the Newman-Janis procedure very quickly led to the discovery of the Kerr-Newman spacetime is a point very much in its favour.) In the current article we will not a…
We construct the classical double copy formalism for M-theory. This extends the current state of the art by including the three form potential of eleven dimensional supergravity along with the metric. The key for this extension is to construct a Kerr-Schild type Ansatz for exceptional field theory. This Kerr-Schild Ansatz then allows us to find the solutions of charged objects such as the membrane from a set of single copy fields. The exceptional field theory formalism then automatically produces the IIB Kerr-Schild ansatz allowing the construction of the single copy for the fields of IIB supe…
We define (non-Einsteinian) universal metrics as the metrics that solve the source-free covariant field equations of generic gravity theories. Here, extending the rather scarce family of universal metrics known in the literature, we show that the Kerr-Schild--Kundt class of metrics are universal. Besides being interesting on their own, these metrics can provide consistent backgrounds for quantum field theory at extremely high energies.
We extend the standard Kerr-Schild solution generating method to higher order scalar tensor theories that are shift-invariant for the scalar field. Certain degeneracy conditions, crucial for the absence of Ostrogradski ghosts, are found to be required for the validity of the Kerr-Schild ansatz while on the other hand, theories with no parity symmetry are excluded from the solution generating method. The extended Kerr-Schild symmetry turns out to be a very useful tool to easily construct black hole solutions from simple seed configurations. In particular, the generating method developed is adap…
In this work we explore the consequences of considering from the very beginning the stationary and axisymmetric properties of the Kerr black hole as one attempts to derive this solution through the Kerr-Schild ansatz. The first consequence is kinematical and is based on a new stationary and axisymmetric version of the Kerr theorem that yields to the precise shear-free and geodesic null congruence of flat spacetime characterizing the Kerr solution. A straightforward advantage of this strategy is that now the parameter $a$ appears naturally as associated to the conserved angular momentum of the …
We propose an adaptation of the Kerr-Schild method by implementing the correspondence relations (mapping) between Ricci-based Gravity (RBG) and General Relativity (GR). Basically, we generate GR known solutions from a canonical metric with a well-defined form and then obtain the configuration of this solution for the Gravity f(R). The new method allows us to perturb the metric associated with GR with a null geodetic vector, but instead of taking us to a new solution described by Einstein's gravitational sector, it allows us to configure this solution in an RBG.
Relativistic dynamical friction in Kerr-Schild coordinates
Institut de Ciències del Cosmos (ICC), Universitat de Barcelona（巴塞罗那大学宇宙科学研究所）；Institute for Particle Physics Phenomenology Department of Physics, Durham University（杜伦大学粒子物理现象学系）；School of Mathematical Sciences, Queen Mary University of London（伦敦大学玛丽女王学院数学科学学院）
The Kerr-Schild version of the Schwarzschild metric contains a Minkowski background which provides a definition of a boosted black hole. There are two Kerr-Schild versions corresponding to ingoing or outgoing principle null directions. We show that the two corresponding Minkowski backgrounds and their associated boosts have an unexpected difference. We analyze this difference and discuss the implications in the nonlinear regime for the gravitational memory effect resulting from the ejection of massive particles from an isolated system. We show that the nonlinear effect agrees with the lineariz…
