[Paper Review] Relativistic Studies of Close Neutron Star Binaries

Grant J. Mathews, Pedro Marronetti+1 more|ArXiv.org|Oct 21, 1997

Pulsars and Gravitational Waves Research3 citations

TL;DR

This paper presents 3+1 dimensional general relativistic hydrodynamic simulations of close neutron star binaries using a conformally flat spatial 3-metric to solve the relativistic field equations. Key findings include relativistic compression and heating, near-zero spin relaxation, black hole formation, and lower-frequency orbital inspiral than predicted by post-Newtonian or weak-field models, with implications for gravitational wave detection.

ABSTRACT

We discuss (3+1) dimensional general relativistic hydrodynamic simulations of close neutron star binary systems. The relativistic field equations are solved at each time slice with a spatial 3-metric chosen to be conformally flat. Against this solution the hydrodynamic variables and gravitational radiation are allowed to respond. We have studied four physical processes which occur as the stars approach merger. These include: 1) the relaxation to a hydrodynamic state of almost no spin; 2) relativistically driven compression, heating, and neutrino emission; 3) collapse to two black holes; and 4) orbit inspiral occurring at a lower frequency than previously expected. We give a brief account of the physical origin of these effects and an explanation of why they do not appear in models based upon, 1PN hydrodynamics, a weak field multipole expansion, a tidal analysis, or a rigidly corotating velocity field. The implication of these results for gravity wave detectors is also discussed.

Motivation & Objective

• To model the late-stage dynamics of close neutron star binaries using full general relativistic hydrodynamics.
• To investigate physical processes such as compression, heating, and neutrino emission during the final approach to merger.
• To understand why previous models based on post-Newtonian, weak-field, or rigidly corotating approximations fail to capture key relativistic effects.
• To explore the implications of these simulations for gravitational wave detection, particularly in terms of waveforms and merger signatures.

Proposed method

• Employing (3+1) dimensional general relativistic hydrodynamics to simulate the evolution of neutron star binaries.
• Solving the relativistic field equations at each time step using a conformally flat spatial 3-metric to simplify the Einstein equations.
• Allowing hydrodynamic variables and gravitational radiation to dynamically respond to the evolving spacetime geometry.
• Tracking the evolution of the system through four key physical processes: spin relaxation, relativistic compression and heating, black hole collapse, and orbital inspiral.
• Comparing results against predictions from 1PN hydrodynamics, weak-field multipole expansions, tidal analyses, and rigidly corotating velocity fields.
• Using the simulation output to assess the detectability of gravitational waves from such systems.

Experimental results

Research questions

• RQ1 What physical processes emerge in close neutron star binaries when full general relativity is applied, beyond post-Newtonian or weak-field approximations?
• RQ2 Why do standard models fail to reproduce the observed dynamics such as spin relaxation and enhanced compression?
• RQ3 How does the orbital inspiral frequency in relativistic simulations compare to predictions from 1PN or weak-field models?
• RQ4 What role do neutrino emission and heating play in the final stages of binary neutron star coalescence?
• RQ5 How do the simulated waveforms and merger dynamics affect the detectability of gravitational waves by current and future detectors?

Key findings

• The simulations reveal a strong relaxation to a hydrodynamic state with almost no spin, contrary to assumptions in rigidly corotating models.
• Relativistic compression leads to significant heating and enhanced neutrino emission, effects absent in weak-field or 1PN treatments.
• In some cases, the system collapses directly into two black holes, a phenomenon not captured by non-relativistic or post-Newtonian models.
• The orbital inspiral occurs at a lower frequency than previously expected, indicating a deviation from standard post-Newtonian predictions.
• These effects arise due to the full nonlinearity of general relativity and are not describable by tidal analyses or multipole expansions.
• The results suggest that gravitational wave detectors must account for these relativistic effects to accurately identify signals from neutron star mergers.