Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userOn the radiation gauge for spin-1 perturbations in Kerr-Newman spacetime
143
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
We extend previous work [arXiv:1908.09095] to the case of Maxwells equations with a source. Our work shows how to construct a retarded vector potential for the Maxwell field on the Kerr-Newman background in a radiation gauge. As in our previous work, the vector potential has a reconstructed term obtained from a Hertz potential solving Teukolskys equation with a source, and a correction term which is obtainable by a simple integration along outgoing principal null rays. The singularity structure of our vector potential is discussed in the case of a point particle source.
rate research
Read More
The Carter tensor is a Killing tensor of the Kerr-Newman spacetime, and its existence implies the separability of the wave equation. Nevertheless, the Carter operator is known to commute with the DAlembertian only in the case of a Ricci-flat metric. We show that, even though the Kerr-Newman spacetime satisfies the non-vacuum Einstein-Maxwell equations, its curvature and electromagnetic tensors satisfy peculiar properties which imply that the Carter operator still commutes with the wave equation. This feature allows to adapt to Kerr-Newman the physical-space analysis of the wave equation in Kerr by Andersson-Blue, which avoids frequency decomposition of the solution by precisely making use of the commutation with the Carter operator. We also extend the mathematical framework of physical-space analysis to the case of the Einstein-Maxwell equations on Kerr-Newman spacetime, representing coupled electromagnetic-gravitational perturbations of the rotating charged black hole. The physical-space analysis is crucial in this setting as the coupling of spin-1 and spin-2 fields in the axially symmetric background prevents the separation in modes as observed by Chandrasekhar, and therefore represents an important step towards an analytical proof of the stability of the Kerr-Newman black hole.
By introducing a specific etheric-like vector in the Dirac equation with Lorentz Invariance Violation (LIV) in the curved spacetime, an improved method for quantum tunneling radiation of fermions is proposed. As an example, we apply this new method to a charged axisymmetric Kerr-Newman black hole. Firstly, considering LIV theory, we derive a modified dynamical equation of fermion with spin 1/2 in the Kerr-Newman black hole spacetime. Then we solve the equation and find the increase or decrease of black holes Hawking temperature and entropy are related to constants $a$ and $c$ of the Dirac equation with LIV in the curved spacetime. As $c$ is positive, the new Hawking temperature is about $ frac{sqrt{1+2a+2cmk_r^2}}{sqrt{1+2a}}$ times higher than that without modification, but the entropy will decrease. We also make a brief discussion for the case of high spin fermions.
We derive the second-order post-Minkowskian solution for the small-deflection motion of test particles in the external field of the Kerr-Newman black hole via an iterative method. The analytical results are exhibited in the coordinate system constituted by the particles initial velocity unit vector, impact vector, and their cross-product. The achieved formulas explicitly give the dependences of the particles trajectory and velocity on the time once their initial position and velocity are specified, and can be applied not only to a massive particle, but also to a photon as well.
We consider the axisymmetric, linear perturbations of Kerr-Newman black holes, allowing for arbitrarily large (but subextremal) angular momentum and electric charge. By exploiting the famous Carter-Robinson identities, developed previously for the proofs of (stationary) black hole uniqueness results, we construct a positive-definite energy functional for these perturbations and establish its conservation for a class of (coupled, gravitational and electromagnetic) solutions to the linearized field equations. Our analysis utilizes the familiar (Hamiltonian) reduction of the field equations (for axisymmetric geometries) to a system of wave map fields coupled to a 2+1-dimensional Lorentzian metric on the relevant quotient 3-manifold. The propagating `dynamical degrees of freedom of this system are entirely captured by the wave map fields, which take their values in a four dimensional, negatively curved (complex hyperbolic) Riemannian target space whereas the base-space Lorentzian metric is entirely determined, in our setup, by elliptic constraints and gauge conditions.
Since its introduction in 1962, the Newman-Penrose formalism has been widely used in analytical and numerical studies of Einsteins equations, like for example for the Teukolsky master equation, or as a powerful wave extraction tool in numerical relativity. Despite the many applications, Einsteins equations in the Newman-Penrose formalism appear complicated and not easily applicable to general studies of spacetimes, mainly because physical and gauge degrees of freedom are mixed in a nontrivial way. In this paper we approach the whole formalism with the goal of expressing the spin coefficients as functions of tetrad invariants once a particular tetrad is chosen. We show that it is possible to do so, and give for the first time a general recipe for the task, as well as an indication of the quantities and identities that are required.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
