[Paper Review] Binary Systems as Test-beds of Gravity Theories

Thibault Damour|ArXiv.org|Apr 5, 2007

Pulsars and Gravitational Waves ResearchPhysics and Astronomy44 references21 citations

TL;DR

This paper presents a theoretical framework for using binary pulsars—especially compact binary systems with neutron stars or black holes—as high-precision test-beds for general relativity and alternative gravity theories. By employing a multi-chart approach to model strong-field and radiative effects in relativistic binaries, the study demonstrates that pulsar timing data constrain tensor-scalar gravity theories with precision comparable to solar-system experiments, and crucially, exclude a broad class of strong-field solutions inaccessible to solar-system tests.

ABSTRACT

We review the general relativistic theory of the motion, and of the timing, of binary systems containing compact objects (neutron stars or black holes). Then we indicate the various ways one can use binary pulsar data to test the strong-field and/or radiative aspects of General Relativity, and of general classes of alternative theories of relativistic gravity.

Motivation & Objective

• To develop a theoretical framework for interpreting binary pulsar observations as tests of general relativity and alternative gravity theories.
• To address the limitations of the traditional single-coordinate-chart approach in modeling strongly self-gravitating compact objects.
• To demonstrate that binary pulsar systems probe the strong-field and radiative regimes of gravity, which are inaccessible to solar-system experiments.
• To compare the probing power of binary pulsar data with solar-system tests in constraining two-parameter families of tensor-scalar gravity theories.
• To show that pulsar data can exclude strong-field solutions that remain compatible with solar-system constraints, highlighting their unique sensitivity to non-perturbative effects.

Proposed method

• Adopt a multi-chart approach using one global coordinate system and N local coordinate systems for each compact body to describe spacetime outside and near each object.
• Combine global post-Newtonian expansions with local strong-field solutions (e.g., Schwarzschild or Kerr metrics) for each body to model motion and gravitational wave emission.
• Use the timing of pulsar signals to measure orbital decay and relativistic effects such as gravitational wave damping, which depend on the speed of gravity and energy loss mechanisms.
• Apply the parameterized post-Newtonian (PPN) formalism and extensions to tensor-scalar gravity theories to compare predictions with observed orbital decay and Shapiro delay.
• Construct goodness-of-fit statistics (e.g., χ²) to compare theoretical predictions with observational data from pulsars like PSR J0737−3039 and PSR B1913+16.
• Map constraints in the (α₀, β₀) parameter space of tensor-mono-scalar theories by combining data from multiple pulsars and comparing with solar-system results.

Experimental results

Research questions

• RQ1 How can binary pulsar systems be used to test the strong-field and radiative aspects of general relativity and alternative gravity theories?
• RQ2 What are the limitations of the traditional single-coordinate-chart approach in modeling compact binary systems, and how does the multi-chart method overcome them?
• RQ3 To what extent do binary pulsar observations constrain tensor-scalar gravity theories compared to solar-system tests?
• RQ4 Why do binary pulsar data exclude a domain of strong-field solutions that remain compatible with solar-system experiments?
• RQ5 What role do non-perturbative strong-field effects play in distinguishing viable gravity theories from their alternatives?

Key findings

• Binary pulsar data constrain tensor-scalar gravity theories with precision comparable to most solar-system tests, excluding a broad class of strong-field solutions inaccessible to solar-system experiments.
• The double binary pulsar PSR J0737−3039 provides a unique probe of strong-field gravity, with its orbital decay and timing data offering high-precision tests of relativistic gravity.
• Pulsar constraints exclude a domain in the (α₀, β₀) parameter space of tensor-mono-scalar theories for β₀ < -4, a region compatible with all solar-system experiments—including the Cassini mission—due to the absence of strong-field effects in weak-field regimes.
• The global constraint from combining all pulsar data is approximately bounded by the sequence: PSR J1913+16, PSR J1141−6545, PSR J0737−3039, and back, indicating a consistent and tight constraint set.
• The Cassini solar-system experiment provides the tightest constraint on α₀² (|α₀| < 3.4×10⁻³), but pulsar data probe a qualitatively different regime by detecting non-perturbative strong-field effects when −β₀·c_A ≈ 1.
• General Relativity remains consistent with all current data, including both pulsar and solar-system tests, but the multi-chart framework enables future detection of deviations in strong-field or radiative regimes.