Slow-rotating black holes with potential in dynamical Chern-Simons modified gravitational theory

Abstract

The Chern-Simons amended gravity theory appears as a low-energy effective theory of string theory. The effective theory includes an anomaly-cancelation correction to the Einstein-Hilbert action. The Chern-Simons expression consists of the product $\phi R\tilde{R}$ of the Pontryagin density $R\tilde{R}$ with a scalar field $\phi$, where the latter is considered as a background field (dynamical construction or non-dynamical construction). Many different solutions to Einstein's general relativity continue to be valid in the amended theories. The Kerr metric is, however, considered an exceptional case that raised a search for rotating black hole solutions. We generalize the solution presented in Phys. Rev. D \textbf{77}, 064007 (2008) by allowing the potential $V$ to have a non-vanishing value and we discuss three different cases of the potential, that is, $V=const.$, $V\propto \phi$, and $V\propto {\phi }^2$ cases. The present study presents, for the first time, novel solutions prescribing rotating black holes in the frame of the dynamical formulation of the Chern-Simons gravity, where we include a potential and generalize the previously derived solutions. We derive the solutions in the slow-rotation limit, where we write the parameter of the slow-rotation expansion by $\epsilon$. These solutions are axisymmetric and stationary and they give a distortion of the Kerr solution by a dipole scalar field. Moreover, we investigate that the rectification to the metric behaves in the inverse of the fourth order of radial distance from the center of the black hole when $V\propto \phi$. This suggests that any meaningful limits from the weak-field experiments could be passed.

20 pages, 2 figures, will appear in JCAP

References in corpus (38)

• Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models
• A Metric for Rapidly Spinning Black Holes Suitable for Strong-Field Tests of the No-Hair Theorem
• Dynamical Chern-Simons Modified Gravity I: Spinning Black Holes in the Slow-Rotation Approximation
• Rotating Black Holes in Dilatonic Einstein-Gauss-Bonnet Theory
• Using LISA EMRI sources to test off-Kerr deviations in the geometry of massive black holes
• Testing the general relativistic ''no-hair'' theorems using the galactic center black hole SgrA*
• Testing the black hole "no-hair" hypothesis
• Slowly-Rotating Black Holes in Einstein-Dilaton-Gauss-Bonnet Gravity: Quadratic Order in Spin Solutions
• The 4D Einstein-Gauss-Bonnet Theory of Gravity: A Review
• The effects of Chern-Simons gravity on bodies orbiting the Earth
• Observable Properties of Orbits in Exact Bumpy Spacetimes
• Anisotropic compact stars in $f(R)$ gravity
• How do Black Holes Spin in Chern-Simons Modified Gravity?
• Parity breaking signatures from a Chern-Simons coupling during inflation: the case of non-Gaussian gravitational waves
• Quasi-normal modes of rotating black holes in Einstein-dilaton Gauss-Bonnet gravity: the first order in rotation
• Peccei--Quinn mechanism in gravity and the nature of the Barbero--Immirzi parameter
• A new PPN parameter to test Chern-Simons gravity
• Perturbations of Schwarzschild Black Holes in Chern-Simons Modified Gravity
• Non-Local Gravity Cosmology: an Overview
• Parametrized Post-Newtonian Expansion of Chern-Simons Gravity
• Topological Interpretation of Barbero-Immirzi Parameter
• Beyond Einstein's General Relativity: Hybrid metric-Palatini gravity and curvature-matter couplings
• Non-trivial black hole solutions in $f(R)$ gravitational theory
• Energy and momentum of a spherically symmetric dilaton frame as regularized by teleparallel gravity
• Quasinormal modes of Schwarzschild black holes in projective invariant Chern-Simons modified gravity
• Does a black hole rotate in Chern-Simons modified gravity?
• Dirichlet boundary value problem for Chern-Simons modified gravity
• Fundamental Symmetries and Spacetime Geometries in Gauge Theories of Gravity: Prospects for Unified Field Theories
• Einstein-Cartan formulation of Chern-Simons Lorentz-violating Gravity
• Stability of rotating black holes in Einstein dilaton Gauss-Bonnet gravity
• Scalar field excited around a rapidly rotating black hole in Chern-Simons modified gravity
• On the causality aspects of the dynamical Chern-Simons modified gravity
• A possible topological interpretation of the Barbero-Immirzi parameter
• Axion induced angular momentum reversal in Kerr-like black holes
• Phase transitions of black strings in dynamical Chern-Simons modified gravity
• First-order perturbations of Gödel-type metrics in non-dynamical Chern-Simons modified gravity
• Gravitational waves propagation in nondynamical Chern-Simons gravity
• Scalarization of Chern-Simons Kerr Black Hole Solutions and Wormholes

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