Multipole analysis on gyroscopic precession in $f(R)$ gravity with irreducible Cartesian tensors

Abstract

In $f(R)$ gravity, the metric, presented in the form of the multipole expansion, for the external gravitational field of a spatially compact supported source up to $1/c^3$ order is provided, where $c$ is the velocity of light in vacuum. The metric consists of General Relativity-like part and $f(R)$ part, where the latter is the correction to the former in $f(R)$ gravity. At the leading pole order, the metric can reduce to that for a point-like or ball-like source. For the gyroscope moving around the source without experiencing any torque, the multipole expansions of its spin's angular velocities of gravitoelectric-type precession, gravitomagnetic-type precession, $f(R)$ precession, and Thomas precession are all derived. The first two types of precession are collectively called General Relativity-like precession, and the $f(R)$ precession is the correction in $f(R)$ gravity. At the leading pole order, these expansions can recover the results for the gyroscope moving around a point-like or ball-like source. If the gyroscope has a nonzero four-acceleration, its spin's total angular velocity of precession up to $1/c^3$ order in $f(R)$ gravity is the same as that in General Relativity.

arXiv comment18 pages;

References in corpus (26)

• Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant
• Measurements of Omega and Lambda from 42 High-Redshift Supernovae
• Observation of Gravitational Waves from a Binary Black Hole Merger
• First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Determination of Cosmological Parameters
• GW170817: Observation of Gravitational Waves from a Binary Neutron Star Inspiral
• Wilkinson Microwave Anisotropy Probe (WMAP) Three Year Results: Implications for Cosmology
• f(R) Theories Of Gravity
• Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models
• Type Ia Supernova Discoveries at z>1 From the Hubble Space Telescope: Evidence for Past Deceleration and Constraints on Dark Energy Evolution
• Multi-messenger Observations of a Binary Neutron Star Merger
• GW151226: Observation of Gravitational Waves from a 22-Solar-Mass Binary Black Hole Coalescence
• Modified Gravity Theories on a Nutshell: Inflation, Bounce and Late-time Evolution
• GW170104: Observation of a 50-Solar-Mass Binary Black Hole Coalescence at Redshift 0.2
• The Supernova Legacy Survey: Measurement of Omega_M, Omega_Lambda and w from the First Year Data Set
• GW170814: A Three-Detector Observation of Gravitational Waves from a Binary Black Hole Coalescence
• The 2dF Galaxy Redshift Survey: Power-spectrum analysis of the final dataset and cosmological implications
• Tests of general relativity with GW150914
• Gravity Probe B: Final Results of a Space Experiment to Test General Relativity
• Astrophysical Implications of the Binary Black-Hole Merger GW150914
• Dynamics of Inflation and Dark Energy from $F(R,\mathcal{G})$ Gravity
• On the 1/c Expansion of f(R) Gravity
• Perturbation of the metric around a spherical body from a nonminimal coupling between matter and curvature
• The most general fourth order theory of Gravity at low energy
• Energy Bounds in $f(R,G)$ Gravity with Anisotropic Background
• Gravitoelectromagnetism in metric f(R) and Brans-Dicke theories with a potential
• The gyroscopic frequency of metric $f(R)$ and generalised Brans-Dicke theories: constraints from Gravity Probe-B

Cited by in corpus (2)

• The gravitational field outside a spatially compact stationary source in a generic fourth-order theory of gravity
• Multipole analysis on stationary massive vector and symmetric tensor fields