Charged Axially Symmetric Solution and Energy in Teleparallel Theory Equivalent to General Relativity

Abstract

An exact charged solution with axial symmetry is obtained in the teleparallel equivalent of general relativity (TEGR). The associated metric has the structure function $G(\xi )=1-{\xi }^2-2mA{\xi }^3-q^2{A}^2{\xi }^4$. The fourth order nature of the structure function can make calculations cumbersome. Using a coordinate transformation we get a tetrad whose metric has the structure function in a factorisable form $(1-{\xi }^2)(1+r_{+}A\xi )(1+r_{-}A\xi )$ with $r_{\pm }$ as the horizons of Reissner-Nordstr$\ddot{o}$m space-time. This new form has the advantage that its roots are now trivial to write down. Then, we study the singularities of this space-time. Using another coordinate transformation, we obtain a tetrad field. Its associated metric yields the Reissner-Nordstr$\ddot{o}$m black hole. In Calculating the energy content of this tetrad field using the gravitational energy-momentum, we find that the resulting form depends on the radial coordinate! Using the regularized expression of the gravitational energy-momentum in the teleparallel equivalent of general relativity we get a consistent value for the energy.

15 pages, Latex

References in corpus (23)

• Quasilocal Energy and Conserved Charges Derived from the Gravitational Action
• Metric-Affine Gauge Theory of Gravity: Field Equations, Noether Identities, World Spinors, and Breaking of Dilation Invariance
• Gravitational Lorentz Force and the Description of the Gravitational Interaction
• Metric-affine approach to teleparallel gravity
• Energy and angular momentum of the gravitational field in the teleparallel geometry
• A new form of the C-metric
• Hamiltonian formulation of general relativity in the teleparallel geometry
• Energy-Momentum Complex in Møller's Tetrad Theory of Gravitation
• Hamiltonian structure of the teleparallel formulation of GR
• Stability of the Vacuum Non Singular Black Hole
• Lessons of spin and torsion: Reply to ``Consistent coupling to Dirac fields in teleparallelism"
• Energy of General Spherically Symmetric Solution in Tetrad Theory of Gravitation
• Energy-momentum current for coframe gravity
• Energy-momentum and angular momentum densities in gauge theories of gravity
• Gauge symmetries of the teleparallel theory of gravity
• The quadratic spinor Lagrangian is equivalent to the teleparallel theory
• Poincaré gauge theory of gravity
• The gravitational energy-momentum flux
• On the teleparallel limit of Poincare gauge theory
• Weak field reduction in teleparallel coframe gravity. Vacuum case
• Quasilocal Center-of-Mass for Teleparallel Gravity
• Sparling two-forms, the conformal factor and the gravitational energy density of the teleparallel equivalent of general relativity
• Energy of general 4-dimensional stationary axisymmetric spacetime in the teleparallel geometry

Cited by in corpus (18)

• Charged spherically symmetric black holes in $f(R)$ gravity and their stability analysis
• Exact Teleparallel Gravity of Binary Black Holes
• Charged rotating black holes coupled with nonlinear electrodynamics Maxwell field in the mimetic gravity
• Reconstruction of $f(T)$-gravity in the absence of matter
• Anisotropic compact stars in higher-order curvature theory
• On the energy of charged black holes in generalized dilaton-axion gravity
• On the energy of Hořava-Lifshitz black holes
• Rotating black hole in $f(R)$ theory
• Consistency between black hole and mimetic gravity -- Case of $(2+1)$-dimensional gravity
• The Hidden Flat Like Universe II: Quasi inverse power law inflation by $f(T)$ gravity
• Multi-horizons black hole solutions, photon sphere and perihelion shift in weak ghost-free Gauss-Bonnet theory of gravity
• Quadratic and cubic spherically symmetric black holes in the modified teleparallel equivalent of general relativity: Energy and thermodynamics
• Magnetic black holes in Weitzenböck geometry
• Energy Distribution for Non-commutative Radiating Schwarzschild Black Holes
• Distribution of Energy-Momentum in a Schwarzschild-Quintessence Space-time Geometry
• Charged spherically symmetric Taub-NUT black hole solutions in $f(R)$ gravity
• Energy-Momentum Localization for a Space-Time Geometry Exterior to a Black Hole in the Brane World
• Black holes solutions in power-law Maxwell-$f(T)$ gravity in diverse dimensions