Gravitational Radiation Reaction Force Research Articles

Oscillations of Hypermassive Compact Stars with Gravitational Radiation and Viscosity

Abstract Binary neutron star mergers, such as the multimessenger GW170817 event, may produce hypermassive compact objects that are supported against collapse by the internal circulation of the fluid within the star. We compute their unstable modes of oscillations driven by gravitational-wave radiation and shear viscosity, modeling them as triaxial Riemann ellipsoids. We work in a perturbative regime, where the gravitational radiation-reaction force is taken into account at 2.5-post-Newtonian order and find unstable modes with dissipation timescales ≳1 ms that are relevant to the transient state of a hypermassive remnant of a merger. We show that the secular instabilities are dominated by gravitational-wave radiation. If the shear viscosity is included, it can increase the growth times or even stabilize the unstable modes, but it must have values several orders of magnitude larger than predicted for cold neutron stars.

Magnetic field amplification by the r-mode instability

We discuss the magnetic field enhancement by unstable r-modes (driven by the gravitational radiation reaction force) in rotating stars. In the absence of a magnetic field, gravitational radiation exponentially increases the r-mode amplitude α, and accelerates differential rotation (secular motion of fluid elements). For a magnetized star, differential rotation enhances the magnetic field energy. Rezzolla et al (2000–2001) argued that if the magnetic energy grows faster than the gravitational radiation reaction force pumps energy into the r-modes, then the r-mode instability is suppressed. Chugunov (2015) demonstrated that without gravitational radiation, differential rotation can be treated as a degree of freedom decoupled from the r-modes and controlled by the back reaction of the magnetic field. In particular, the magnetic field windup does not damp r-modes. Here we discuss the effect of the back reaction of the magnetic field on differential rotation of unstable r-modes, and show that it limits the generated magnetic field and the magnetic energy growth rate preventing suppression of the r-mode instability by magnetic windup at low saturation amplitudes, α ≪ 1, predicted by current models.

Nonchaotic evolution of triangular configuration due to gravitational radiation reaction in the three-body problem

Continuing work initiated in an earlier publication [H. Asada, Phys. Rev. D {\bf 80}, 064021 (2009)], the gravitational radiation reaction to Lagrange's equilateral triangular solution of the three-body problem is investigated in an analytic method. The previous work is based on the energy balance argument, which is sufficient for a two-body system because the number of degrees of freedom (the semimajor axis and the eccentricity in quasi-Keplerian cases, for instance) equals that of the constants of motion such as the total energy and the orbital angular momentum. In a system with three (or more) bodies, however, the number of degrees of freedom is more than that of the constants of motion. Therefore, the present paper discusses the evolution of the triangular system by directly treating the gravitational radiation reaction force to each body. The perturbed equations of motion are solved by using the Laplace transform technique. It is found that the triangular configuration is adiabatically shrinking and is kept in equilibrium by increasing the orbital frequency due to the radiation reaction if the mass ratios satisfy the Newtonian stability condition. Long-term stability involving the first post-Newtonian corrections is also discussed.

Differential rotation of the unstable nonlinearr-modes

At second order in perturbation theory, the $r$-modes of uniformly rotating stars include an axisymmetric part that can be identified with differential rotation of the background star. If one does not include radiation-reaction, the differential rotation is constant in time and has been computed by S\'a. It has a gauge dependence associated with the family of time-independent perturbations that add differential rotation to the unperturbed equilibrium star: For stars with a barotropic equation of state, one can add to the time-independent second-order solution arbitrary differential rotation that is stratified on cylinders (that is a function of distance $\varpi$ to the axis of rotation). We show here that the gravitational radiation-reaction force that drives the $r$-mode instability removes this gauge freedom: The expontially growing differential rotation of the unstable second-order $r$-mode is unique. We derive a general expression for this rotation law for Newtonian models and evaluate it explicitly for slowly rotating models with polytropic equations of state.

Incompleteness of General Relativity, Einstein's Errors, and Related Experiments-- American Physical Society March meeting, Z23 5, 2015 --

General relativity is incomplete since it does not include the gravitational radiation reaction force and the interaction of gravitation with charged particles. General relativity is confusing because Einstein's covariance principle is invalid in physics. Moreover, there is no bounded dynamic solution for the Einstein equation. Thus, Gullstrand is right and the 1993 Nobel Prize for Physics press release is incorrect. Moreover, awards to Christodoulou reflect the blind faith toward Einstein and accumulated errors in mathematics. Note that the Einstein equation with an electromagnetic wave source has no valid solution unless a photonic energy-stress tensor with an anti-gravitational coupling is added. Thus, the photonic energy includes gravitational energy. The existence of anti-gravity coupling implies that the energy conditions in space-time singularity theorems of Hawking and Penrose cannot be satisfied, and thus are irrelevant. Also, the positive mass theorem of Yau and Schoen is misleading, though considered as an achievement by the Fields Medal. E = mc2 is invalid for the electromagnetic energy alone. The discovery of the charge-mass interaction establishes the need for unification of electromagnetism and gravitation and would explain many puzzles. Experimental investigations for further results are important.

Gravitational radiation reaction along general orbits in the effective one-body formalism

We derive the gravitational radiation-reaction force modifying the Effective One Body (EOB) description of the conservative dynamics of binary systems. Our result is applicable to general orbits (elliptic or hyperbolic) and keeps terms of fractional second post-Newtonian order (but does not include tail effects). Our derivation of radiation-reaction is based on a new way of requiring energy and angular momentum balance. We give several applications of our results, notably the value of the (minimal) "Schott" contribution to the energy, the radial component of the radiation-reaction force, and the radiative contribution to the angle of scattering during hyperbolic encounters. We present also new results about the conservative relativistic dynamics of hyperbolic motions.

Structure of the post-Newtonian expansion in general relativity

In the continuation of a preceding work, we derive a new expression for the metric in the near zone of an isolated matter system in post-Newtonian approximations of general relativity. The post-Newtonian metric, a solution of the field equations in harmonic coordinates, is formally valid up to any order, and is cast in the form of a particular solution of the wave equation, plus a specific homogeneous solution which ensures the asymptotic matching to the multipolar expansion of the gravitational field in the exterior of the system. The new form is suitable for practical computations of the gravitational radiation reaction forces in harmonic coordinates. It also provides some insights on the structure of the post-Newtonian expansion in general relativity and the radiation reaction terms therein.

Mergers of Neutron Star–Black Hole Binaries with Small Mass Ratios: Nucleosynthesis, Gamma‐Ray Bursts, and Electromagnetic Transients

We discuss simulations of the coalescence of black hole-neutron star binary systems with black hole masses between 14 and 20 M☉. The calculations use a three-dimensional smoothed particle hydrodynamics code, a temperature-dependent, nuclear equation of state, and a multiflavor neutrino scheme. General relativistic effects are mimicked using the Paczyński-Wiita pseudo-potential and gravitational radiation reaction forces. Unlike previous, purely Newtonian calculations, in none of the explored cases does episodic mass transfer occur. The neutron star is always completely disrupted after most of its mass has been transferred directly into the hole. For black hole masses between 14 and 16 M☉ an accretion disk forms; large parts of it, however, are inside the last stable orbit and therefore falling with large radial velocities into the hole. These disks are (opposite to the neutron star merger case) thin and—except for a spiral shock—essentially cold. For higher mass black holes (MBH ≥ 18 M☉) almost the entire neutron star disappears in the hole without forming an accretion disk. In these cases the surviving material is spun up by tidal torques and ejected as a half-ring of neutron-rich matter. None of the investigated systems is a promising gamma-ray burst (GRB) central engine. We find between 0.01 and 0.2 M☉ of the neutron star to be dynamically ejected. Like in a Type Ia supernova, the radioactive decay of this material powers a light curve with a peak luminosity of a few times 1044 ergs s-1. The maximum is reached about 3 days after the coalescence and is mainly visible in the optical/near-infrared band. The coalescence itself may produce a precursor pulse with a thermal spectrum of ~10 ms duration.

Optimizing the third-and-a-half post-Newtonian gravitational radiation-reaction force for numerical simulations

The gravitational radiation-reaction force acting on perfect fluids at $3.5$ post-Newtonian order is cast into a form which is directly applicable to numerical simulations. Extensive use is made of metric-coefficient changes induced by functional coordinate transformations, of the continuity equation, as well as of the equations of motion. We also present an expression appropriate for numerical simulations of the radiation field causing the worked out reaction force.

LIGO/VIRGO Searches for Gravitational Radiation in Hypernovae

A torus around a stellar-mass Kerr black hole can emit about 10% of the spin energy of a black hole in gravitational radiation, which is potentially associated with a gamma-ray burst (GRB). Wide tori may develop buckling modes by the Papaloizou-Pringle instability and gravitational radiation-reaction forces in the Burke-Thorne approximation. Gravitational-wave experiments may discover these emissions in a fraction of nearby supernovae. This provides a test for Kerr black holes and for GRB inner engines by a comparison with the deredshifted durations of long GRBs.

Regularization of Gravitational Radiation Reaction Force

Regularization of Gravitational Radiation Reaction Force

Gravitational radiation reaction and balance equations to post-Newtonian order

Gravitational radiation reaction forces and balance equations are investigated to 3/2 post-Newtonian (1.5PN) order beyond the quadrupole approximation, corresponding to the 4PN order in the equations of motion of an isolated system. By matching a post-Newtonian solution for the gravitational field inside the system to a post-Minkowskian solution (obtained in a previous work) for the gravitational field exterior to the system, we determine the 1PN relativistic corrections to the ``Newtonian'' radiation reaction potential of Burke and Thorne. The 1PN reaction potential involves both scalar and vectorial components, with the scalar component depending on the mass-type quadrupole and octupole moments of the system, and the vectorial component depending in particular on the current-type quadrupole moment. In the case of binary systems, the 1PN radiation reaction potential has been shown elsewhere to yield consistent results for the 3.5PN approximation in the binary's equations of motion. Adding up the effects of tails, the radiation reaction is then written to 1.5PN order. In this paper, we establish the validity to 1.5PN order, for general systems, of the balance equations relating the losses of energy, linear momentum, and angular momentum in the system to the corresponding fluxes in the radiation field far from the system.

Finite reduced hydrodynamic equations in the slow-motion approximation to general relativity. Part I. First post-Newtonian equations

The iteration procedure of Anderson and DeCanio (1975) for obtaining hydrodynamic equations in the slow-motion approximation to general relativity is modified at each iteration step. These improvements keep all expressions needed for the 2 1/2 post-Newtonian approximation (PNA) manifestly finite, but fail to prevent some divergent terms in the third and higher PNAs. In this Part I, the improvements to the iteration scheme are outlined, and the calculation is completed through the second iteration, yielding Newtonian-like hydrodynamic equations in the first PNA. Paper II will complete the calculation through the 2 1/2 PNA, allowing the calculation of the gravitational radiation reaction force, and making explicit the source of the divergences which occur in the higher PNAs.