Equivalence Principle for Massive Bodies. II. Theory

1968/05/25 by Kenneth Nordtvedt · 396 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Brans–Dicke theory #Classical mechanics #Cosmology and Gravitation Theories #Einstein #Equivalence principle (geometric) #Geometry #Gravitation #Gravitational acceleration #Gravitational field #Mathematical physics #Mathematics #Order (exchange) #Physics #Quantum mechanics #Relativity and Gravitational Theory #Scalar (mathematics) #Space (punctuation) #Space time #Spacetime #Theoretical physics

paper · doi:10.1103/physrev.169.1017

published in Physical Review 169(5), 1017-1025 (American Institute of Physics)

openalex publication_date 1968/05/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29

Abstract

The acceleration of a massive body in an external field for general space-time geometrical gravitational theories is obtained. The condition on the metric is such that \fracm_gm_i=1 is obtained, and we reobtain the result that \fracm_gm_i=1 in Einstein's theory for massive objects with time-independent internal structure. But it is shown that a measurement of \fracm_gm_i for astronomical bodies would measure space-time metric components which have not been measured in other gravitational experiments. In the scalar-tensor gravitational theory due to Brans and Dicke, it is shown that \fracm_gm_i differs from 1 by a term of the order of the massive body's gravitational self-energy divided by its total energy.

Cited by

• Towards a causal effective thermodynamics of scalar-tensor gravity
• Post-Newtonian Global Conservation Laws in the Presence of Sensitive Bodies
• Numerical evaluation of the exact post-Newtonian parameters in Brans-Dicke and entangled relativity theories
• Gravitational Anomalies in the Solar System?
• Tests of General Relativity with Einstein Telescope
• The thermal view of singularity-free scalar-tensor spacetimes
• The thermal view of f(R) cosmology
• Inertia in Friedmann Universes with variable G G and Λ \varLambda
• Black Hole and Neutron Star Binaries: Theoretical Challenges
• Gravitational wave probes of particle dark matter: a review
• Constraining the Cosmological Evolution of Post-Newtonian Parameters with Gravitational Wave Signals from Compact Binary Inspirals
• Chern-Simons Modified General Relativity
• The Confrontation between General Relativity and Experiment
• On the Infeasibility of Low-Energy Warp Drive via Metamaterial Gravitational Coupling
• In-depth analysis of violations of the (strong) equivalence principle in scalarized Einstein-Gauss-Bonnet theories
• Laser Ranging to the Moon, Mars and Beyond
• Gravitational-wave tests of general relativity with ground-based detectors and pulsar-timing arrays
• Black hole interiors in the thermal view of scalar-tensor gravity
• Collapse to black holes in Brans-Dicke theory. II. Comparison with general relativity
• Violation of the Equivalence Principle in Modified Theories of Gravity
• Signals for Lorentz violation in post-Newtonian gravity
• Newtonian limit off(R)gravity
• Proposal for a geophysical search for dilatonic waves
• On the Possibility of Testing the Weak Equivalence Principle with Artificial Earth Satellites
• Testing gravity to second post-Newtonian order: A field-theory approach
• Parametrized post-Newtonian limit of fourth-order theories of gravity
• Chern-Simons modified gravity as a torsion theory and its interaction with fermions
• Asymptotic behavior of cosmological models in scalar-tensor theories of gravity
• On the possibility of measuring the solar oblateness and some relativistic effects from planetary ranging
• Lorentz violation with an antisymmetric tensor
• Orbital Motions and the Conservation-Law/Preferred-Frame α3 Parameter
• SPACE-BASED RESEARCH IN FUNDAMENTAL PHYSICS AND QUANTUM TECHNOLOGIES
• Gravity, Lorentz violation, and the standard model
• The Confrontation between General Relativity and Experiment
• Nuclear Heterodyne Interferometry for Gravitational Spectroscopy
• LUNAR LASER RANGING TESTS OF THE EQUIVALENCE PRINCIPLE WITH THE EARTH AND MOON
• (Pseudo)issue of the conformal frame revisited
• The laser astrometric test of relativity mission
• Screening and Absorption of Gravitation in Pre-Relativistic and Relativistic Theories
• EFFECTS OF STANDARD AND MODIFIED GRAVITY ON INTERPLANETARY RANGES
• Quasilocal mass in scalar–tensor gravity: spherical symmetry
• Radioscience simulations in general relativity and in alternative theories of gravity
• New limits on the violation of local position invariance of gravity
• The new lunar ephemeris INPOP17a and its application to fundamental physics
• PERSPECTIVES ON MEASURING THE PPN PARAMETERS β AND γ IN EARTH'S GRAVITATIONAL FIELD TO HIGH ACCURACY WITH CHAMP/GRACE MODELS
• Orbital effects on time delay interferometry for TianQin
• Tests of relativistic gravity in space
• Weak equivalence principle for self-gravitating bodies: A sieve for purely metric theories of gravity
• Averaging inhomogeneities in scalar–tensor cosmology
• Observational constraints on the completeness of space near astrophysical objects
• Gauge-invariant approach to the parametrized post-Newtonian formalism
• Secular effects of ultralight dark matter on binary pulsars
• Breakdown of the initial value formulation of scalar-tensor gravity and its physical meaning
• IMPROVING LLR TESTS OF GRAVITATIONAL THEORY
• Making the transition from Newton to Einstein: Chandrasekhar’s work on the post-Newtonian approximation and radiation reaction
• The Pioneer Anomaly. [europepmc]
• Tests of Gravity Using Lunar Laser Ranging. [europepmc]
• The Confrontation between General Relativity and Experiment. [europepmc]
• Gravitational-Wave Tests of General Relativity with Ground-Based Detectors and Pulsar-Timing Arrays. [europepmc]
• The Confrontation between General Relativity and Experiment. [europepmc]
• The Confrontation between General Relativity and Experiment. [europepmc]
• Solar system expansion and strong equivalence principle as seen by the NASA MESSENGER mission. [europepmc]
• Past-directed scalar field gradients and scalar-tensor thermodynamics. [europepmc]
• More on the first-order thermodynamics of scalar-tensor and Horndeski gravity. [europepmc]
• The Tolman-Ehrenfest criterion of thermal equilibrium in scalar-tensor gravity. [europepmc]
• Non-geodesic timelike observers and the ultralocal limit. [europepmc]

Related

• A new relativity principle for bodies in different gravitational potentials
• A novel violation of the equivalence principle
• New Astrophysical Tests from the Einstein's Equivalence Principle and Gravitational Experiments
• Conflict between the Gravitational Field Energy and the Experiments
• Fundamental Disagreements of Experiments with Theories on Gravitation and Cosmology