Periodic orbits in charged LQG black holes produce zoom-whirl gravitational waveforms detectable by future space-based observatories, with features depending on the fixed polymerization parameter.
Astrophysically relevant bound trajectories around a Kerr black hole
6 Pith papers cite this work, alongside 48 external citations. Polarity classification is still indexing.
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abstract
We derive alternate and new closed-form analytic solutions for the non-equatorial eccentric bound trajectories, $\{ \phi \left( r, \theta \right)$, $\ t \left( r, \theta \right),\ r \left( \theta \right) \}$, around a Kerr black hole by using the transformation $1/r=\mu \left(1+ e \cos \chi \right)$. The application of the solutions is straightforward and numerically fast. We obtain and implement translation relations between energy and angular momentum of the particle, ($E$, $L$), and eccentricity and inverse-latus rectum, ($e$, $\mu$), for a given spin, $a$, and Carter's constant, $Q$, to write the trajectory completely in the ($e$, $\mu$, $a$, $Q$) parameter space. The bound orbit conditions are obtained and implemented to select the allowed combination of parameters ($e$, $\mu$, $a$, $Q$). We also derive specialized formulae for spherical and separatrix orbits. A study of the non-equatorial analog of the previously studied equatorial separatrix orbits is carried out where a homoclinic orbit asymptotes to an energetically bound spherical orbit. Such orbits simultaneously represent an eccentric orbit and an unstable spherical orbit, both of which share the same $E$ and $L$ values. We present exact expressions for $e$ and $\mu$ as functions of the radius of the corresponding unstable spherical orbit, $r_s$, $a$, and $Q$, and their trajectories, for ($Q\neq0$) separatrix orbits; they are shown to reduce to the equatorial case. These formulae have applications to study the gravitational waveforms from EMRIs besides relativistic precession and phase space explorations. We obtain closed-form expressions of the fundamental frequencies of non-equatorial eccentric trajectories that are equivalent to the previously obtained quadrature forms and also numerically match with the equivalent formulae previously derived. We sketch several orbits and discuss their astrophysical applications.
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EFTGR black-hole periodic orbits follow the (z,w,v) taxonomy and emit zoom-whirl waveforms whose phase, not amplitude, is sensitive to the EFTGR coupling ϵ1.
Extends intrinsic curvature criteria for massive particle surfaces to stationary spacetimes and demonstrates application to black hole shadows in Kerr-family and Einstein-Maxwell-dilaton solutions.
The quantum parameter ξ in an asymptotically safe regular black hole shifts the innermost stable orbit, enhances whirl behavior in periodic geodesics, and produces amplitude-modulated millihertz gravitational-wave strains whose peak amplitude grows with ξ, placing them inside the sensitivity bands预计
Numerical study of timelike geodesics and millihertz gravitational waves from periodic orbits around a Schwarzschild black hole embedded in a (1,4,γ) Dehnen dark matter halo.
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Periodic orbits as probes of charged loop quantum gravity black holes through gravitational waves
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Deviations from γ=1 in the Zipoy-Voorhees metric shift the (z,w,v) classification of periodic orbits and induce phase shifts plus amplitude modulations in their gravitational-wave signals.
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Gravitational radiations from periodic orbits around a black hole in the effective field theory extension of general relativity
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Massive particle surfaces and black hole shadows from intrinsic curvature
Extends intrinsic curvature criteria for massive particle surfaces to stationary spacetimes and demonstrates application to black hole shadows in Kerr-family and Einstein-Maxwell-dilaton solutions.
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Probing Gravitational Wave Signatures from Periodic Orbits of Regular Black Holes in Asymptotically Safe Gravity
The quantum parameter ξ in an asymptotically safe regular black hole shifts the innermost stable orbit, enhances whirl behavior in periodic geodesics, and produces amplitude-modulated millihertz gravitational-wave strains whose peak amplitude grows with ξ, placing them inside the sensitivity bands预计
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Gravitational Wave Signatures of Schwarzschild Black Hole in a Generalized Dehnen-Type $(1,4,\gamma)$ Dark Matter Halo
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