Janis Newman Algorithm Research Articles

Generating rotating black hole solutions by using the Cayley–Dickson construction

This paper exploits the power of the Cayley–Dickson algebra to generate stationary rotating black hole solutions in one fell swoop. Specifically, we derive the nine-dimensional Myers–Perry solution with four independent angular momenta by using the Janis–Newman algorithm and Giampieri’s simplification method, exploiting the octonion algebra. A general formula relating the dimension of the Cayley–Dickson algebra with the maximum number of angular momenta in each dimension is derived. Finally, we discuss the cut-off dimension for using the Cayley–Dickson construction along with the Janis–Newman algorithm for producing the rotating solutions.

Rotating black holes in cubic gravity

Using on-shell amplitude methods, we derive a rotating black hole solution in a generic theory of Einstein gravity with additional terms cubic in the Riemann tensor. We give an explicit expression for the metric in Einsteinian Cubic Gravity (ECG) and low energy effective string theory, which correctly reproduces the previously discovered solutions in the zero angular-momentum limit. We show that at first order in the coupling, the classical potential can be written to all orders in spin as a differential operator acting on the non-rotating potential, and we comment on the relation to the Janis-Newman algorithm. Furthermore, we derive the classical impulse and scattering angle for such a black hole and comment on the phenomenological interest of such quantities.

Kerr-Newman from minimal coupling

We show that at 1PN all four-dimensional black hole solutions in asymptotically flat spacetimes can be derived from leading singularities involving minimally coupled three-particle amplitudes. Furthermore, we show that the rotating solutions can be derived from their non-rotating counterparts by a spin-factor deformation of the relevant minimally coupled amplitudes. To show this, we compute the tree-level and one-loop leading singularities for a heavy charged source with generic spin s. We compute the metrics both with and without a spin factor and show that we get both the Kerr-Newman and Reissner- Nordström solutions respectively. We then go on to compute the impulse imparted to the probe particle in the infinite spin limit and show that the spin factor induces a complex deformation of the impact parameter, as was recently observed for Kerr black holes in [1]. We interpret these observations as being the on-shell avatar of the Janis-Newman algorithm for charged black holes.

Electromagnetic self-force in curved spacetime: New insights from the Janis-Newman algorithm

We present an original approach to compute the electromagnetic self-force acting on a static charge in Kerr spacetime. Our approach is based on an improved version of the Janis-Newman algorithm and extends its range of applicability. It leads to a closed expression which generalizes the existing one and, since it does not involve the electromagnetic potential, it simplifies the calculation of the self-force.

Janis–Newman Algorithm: Generating Rotating and NUT Charged Black Holes

In this review we present the most general form of the Janis–Newman algorithm. This extension allows generating configurations which contain all bosonic fields with spin less than or equal to two (real and complex scalar fields, gauge fields, metric field) and with five of the six parameters of the Plebański–Demiański metric (mass, electric charge, magnetic charge, NUT charge and angular momentum). Several examples are included to illustrate the algorithm. We also discuss the extension of the algorithm to other dimensions.

Deciphering and generalizing Demiański–Janis–Newman algorithm

In the case of vanishing cosmological constant, Demia\'nski has shown that the Janis-Newman algorithm can be generalized in order to include a NUT charge and another parameter $c$, in addition to the angular momentum. Moreover it was proved that only a NUT charge can be added for non-vanishing cosmological constant. However despite the fact that the form of the coordinate transformations was obtained, it was not explained how to perform the complexification on the metric function, and the procedure does not follow directly from the usual Janis-Newman rules. The goal of our paper is threefold: explain the hidden assumptions of Demia\'nski's analysis, generalize the computations to topological horizons (spherical and hyperbolic) and to charged solutions, and explain how to perform the complexification of the function. In particular we present a new solution which is an extension of the Demia\'nski metric to hyperbolic horizons. These different results open the door to applications in (gauged) supergravity since they allow for a systematic application of the Demia\'nski-Janis-Newman algorithm.

Janis–Newman algorithm for supergravity black holes

We summarize the recent generalization of the Janis–Newman algorithm in view of its application to (gauged) supergravity. In particular this includes an extension of the algorithm to gauge fields and complex scalar fields, to topological horizons, to dyonic and NUT charges.

Five-dimensional Janis–Newman algorithm

The Janis–Newman algorithm has been shown to be successful in finding new stationary solutions of four-dimensional gravity. Attempts for a generalization to higher dimensions have already been found for the restricted cases with only one angular momentum. In this paper we propose an extension of this algorithm to five-dimensions with two angular momenta—using the prescription of Giampieri—through two specific examples, that are the Myers–Perry and BMPV black holes. We also discuss possible enlargements of our prescriptions to other dimensions and maximal number of angular momenta, and show how dimensions higher than six appear to be much more challenging to treat within this framework. Nonetheless this general algorithm provides a unification of the formulation in of the Janis–Newman algorithm, from which several examples are exposed, including the BTZ black hole.

Supergravity, complex parameters and the Janis–Newman algorithm

The Demiański–Janis–Newman (DJN) algorithm is an original solution generating technique. For a long time it has been limited to producing rotating solutions, restricted to the case of a metric and real scalar fields, despite the fact that Demiański extended it to include more parameters such as a NUT charge. Recently two independent prescriptions have been given for extending the algorithm to gauge fields and thus electrically charged configurations. In this paper we aim to end setting up the algorithm by providing a missing but important piece, which is how the transformation is applied to complex scalar fields. We illustrate our proposal through several examples taken from N = 2 supergravity, including the stationary BPS solutions from Behrndt et al and Senʼs axion–dilaton rotating black hole. Moreover we discuss solutions that include pairs of complex parameters, such as the mass and the NUT charge, or the electric and magnetic charges, and we explain how to perform the algorithm in this context (with the example of Kerr–Newman–Taub–NUT and dyonic Kerr–Newman black holes). The final formulation of the DJN algorithm can possibly handle solutions with five of the six Plebański–Demiański parameters along with any type of bosonic fields with spin less than two (exemplified with the stationary Israel–Wilson–Perjes solutions). This provides all the necessary tools for applications to general matter-coupled gravity and to (gauged) supergravity.

Janis–Newman algorithm: simplifications and gauge field transformation

The Janis-Newman algorithm is an old but very powerful tool to generate rotating solutions from static ones through a set of complex coordinate transformations. Several solutions have been derived in this way, including solutions with gauge fields. However, the transformation of the latter was so far always postulated as an ad hoc result. In this paper we propose a generalization of the procedure, extending it to the transformation of the gauge field. We also present a simplification of the algorithm due to G. Giampieri. We illustrate our prescription on the Kerr-Newman solution.