Dynamical analysis of null geodesics in brane-world spacetimes

Abstract

In this work, we present an extensive dynamical analysis of the null geodesics in the spacetimes proposed by Casadio, Fabbri, and Mazzacurati (CFM), which model black holes and wormholes in a Randall-Sundrum brane. Geodesic stability is evaluated by Lyapunov and Jacobi criteria, with coinciding results. Semistable photon spheres are found in the geometries of interest. Bifurcations associated with the dynamical system are also investigated, characterizing a degenerated Bogdanov-Takens bifurcation. Our results suggest deep connections between the geometric characteristics of the CFM spacetimes and the dynamics of null geodesics in these backgrounds.

arXiv comment15 pages, 5 figures

References in corpus (32)

• Observation of Gravitational Waves from a Binary Black Hole Merger
• A Large Mass Hierarchy from a Small Extra Dimension
• An Alternative to Compactification
• First M87 Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole
• The Einstein Equations on the 3-Brane World
• Geodesic stability, Lyapunov exponents and quasinormal modes
• Brane-World Gravity
• Is the gravitational-wave ringdown a probe of the event horizon?
• The geometry of photon surfaces
• Black holes on the brane
• Testing the No-Hair Theorem with Observations in the Electromagnetic Spectrum: II. Black-Hole Images
• Radiative Models of Sgr A* from GRMHD Simulations
• Light rings as observational evidence for event horizons: long-lived modes, ergoregions and nonlinear instabilities of ultracompact objects
• Wormholes as Black Hole Foils
• New black holes in the brane-world?
• Regular rotating black holes and the weak energy condition
• A general class of braneworld wormholes
• On a general class of brane-world black holes
• Application of the Campbell-Magaard theorem to higher-dimensional physics
• Unstable circular null geodesics of static spherically symmetric black holes, Regge poles and quasinormal frequencies
• Lyapunov timescales and black hole binaries
• Horizons vs. singularities in spherically symmetric space-times
• Lux in obscuro: Photon Orbits of Extremal Black Holes Revisited
• Rotating black holes in a Randall-Sundrum brane with a cosmological constant
• Black holes and wormholes in AdS branes
• Wormholes in de Sitter branes
• Electromagnetic perturbations in new brane world scenarios
• Inertial forces and photon surfaces in arbitrary spacetimes
• Thermodynamics of quantum photon spheres
• Isotropic extensions of the vacuum solutions in general relativity
• Deformations of the vacuum solutions of general relativity subjected to linear constraints
• Einstein's Field Equations as a Fold Bifurcation

Cited by in corpus (5)

• On null geodesics and shadow of hairy black holes in Einstein-Maxwell-dilaton gravity
• Null geodesics and shadow of 4$D$ Einstein-Gauss-Bonnet black holes surrounded by quintessence
• Cosmological dynamics and bifurcation analysis of the general non-minimally coupled scalar field models
• Geodesic dynamics in brane-de Sitter wormholes
• Black holes and wormholes in Deser-Woodard gravity