scholarly journals Horizon radiation reaction forces

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Walter D. Goldberger ◽  
Ira Z. Rothstein
Keyword(s):  
Black Hole ◽  
Equations Of Motion ◽  
Finite Size ◽  
Radiation Reaction ◽  
Effective Field ◽  
Compact Objects ◽  
Finite Size Effect ◽  
Binary Black Holes ◽  
Dissipative Effects ◽  
Reaction Forces

Abstract Using Effective Field Theory (EFT) methods, we compute the effects of horizon dissipation on the gravitational interactions of relativistic binary black hole systems. We assume that the dynamics is perturbative, i.e it admits an expansion in powers of Newton’s constant (post-Minkowskian, or PM, approximation). As applications, we compute corrections to the scattering angle in a black hole collision due to dissipative effects to leading PM order, as well as the post-Newtonian (PN) corrections to the equations of motion of binary black holes in non-relativistic orbits, which represents the leading order finite size effect in the equations of motion. The methods developed here are also applicable to the case of more general compact objects, eg. neutron stars, where the magnitude of the dissipative effects depends on non-gravitational physics (e.g, the equation of state for nuclear matter).

scholarly journals Spin effects in the effective field theory approach to Post-Minkowskian conservative dynamics

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
Zhengwen Liu ◽  
Rafael A. Porto ◽  
Zixin Yang
Keyword(s):  
Field Theory ◽  
Effective Field Theory ◽  
Scattering Problem ◽  
Finite Size ◽  
Effective Field ◽  
Compact Objects ◽  
Scattering Data ◽  
Theory Approach ◽  
Spin Effects ◽  
Radial Action

Abstract Building upon the worldline effective field theory (EFT) formalism for spinning bodies developed for the Post-Newtonian regime, we generalize the EFT approach to Post-Minkowskian (PM) dynamics to include rotational degrees of freedom in a manifestly covariant framework. We introduce a systematic procedure to compute the total change in momentum and spin in the gravitational scattering of compact objects. For the special case of spins aligned with the orbital angular momentum, we show how to construct the radial action for elliptic-like orbits using the Boundary-to-Bound correspondence. As a paradigmatic example, we solve the scattering problem to next-to-leading PM order with linear and bilinear spin effects and arbitrary initial conditions, incorporating for the first time finite-size corrections. We obtain the aligned-spin radial action from the resulting scattering data, and derive the periastron advance and binding energy for circular orbits. We also provide the (square of the) center-of-mass momentum to $$ \mathcal{O}\left({G}^2\right) $$ O G 2 , which may be used to reconstruct a Hamiltonian. Our results are in perfect agreement with the existent literature, while at the same time extend the knowledge of the PM dynamics of compact binaries at quadratic order in spins.

The two-body problem and radiative losses

2018 ◽  
Author(s):  
Nathalie Deruelle ◽  
Jean-Philippe Uzan
Keyword(s):  
Mechanical Energy ◽  
Equations Of Motion ◽  
Reaction Force ◽  
Radiation Reaction ◽  
Compact Objects ◽  
Einstein Equations ◽  
Two Body Problem ◽  
System P ◽  
Radiative Losses ◽  
Radiation Reaction Force

This chapter begins by finding the field created by compact objects in the post-linear approximation of general relativity. The second quadrupole formula is then completely proven. Next, the chapter finds the equations of motion of the bodies in the field which they create to second order in the perturbations, assuming that their velocities are small. It shows that, to correctly describe the radiation reaction at 2.5 PN order, it will prove necessary to iterate Einstein equations a third time. This leads the discussion to the equations of motion, which generalize to order 1/c5 the EIH equations of order 1/c⁲. Finally, the chapter studies the effect of the radiation reaction force on the sources, and shows that there is an energy balance at 2.5 PN order between the energy radiated to infinity and the mechanical energy lost by the system.

scholarly journals Strong-field gravitational-wave emission in Schwarzschild and Kerr geometries: some general considerations

2018 ◽  
Vol 168 ◽  
pp. 02006 ◽  
Author(s):  
J.F. Rodríguez ◽  
J.A. Rueda ◽  
R. Ruffini
Keyword(s):  
Black Hole ◽  
Test Particle ◽  
Strong Field ◽  
Reaction Force ◽  
Dynamical Evolution ◽  
Radiation Reaction ◽  
Compact Objects ◽  
Einstein Equations ◽  
Smooth Transition ◽  
Wave Emission

We have used the perturbations of the exact solutions of the Einstein equations to estimate the relativistic wave emission of a test particle orbiting around a black hole. We show how the hamiltonian equations of motion of a test particle augmented with the radiation-reaction force can establish a priori constraints on the possible phenomena occurring in the merger of compact objects. The dynamical evolution consists of a helicoidal sequence of quasi-circular orbits, induced by the radiation-reaction and the background spacetime. Near the innermost stable circular orbit the evolution is followed by a smooth transition and finally plunges geodesically into the black hole horizon. This analysis gives physical insight of the merger of two equal masses objects.

scholarly journals Black holes in active galactic nuclei

2009 ◽  
Vol 5 (S261) ◽  
pp. 260-268
Author(s):  
M. J. Valtonen ◽  
S. Mikkola ◽  
D. Merritt ◽  
A. Gopakumar ◽  
H. J. Lehto ◽  
...  
Keyword(s):  
Black Holes ◽  
General Relativity ◽  
Black Hole ◽  
Strong Field ◽  
Equations Of Motion ◽  
Binary Black Holes ◽  
Time Dynamic ◽  
Black Hole Spacetime ◽  
First Time ◽  
Black Hole Masses

AbstractSupermassive black holes are common in centers of galaxies. Among the active galaxies, quasars are the most extreme, and their black hole masses range as high as to 6⋅1010M⊙. Binary black holes are of special interest but so far OJ287 is the only confirmed case with known orbital elements. In OJ287, the binary nature is confirmed by periodic radiation pulses. The period is twelve years with two pulses per period. The last four pulses have been correctly predicted with the accuracy of few weeks, the latest in 2007 with the accuracy of one day. This accuracy is high enough that one may test the higher order terms in the Post Newtonian approximation to General Relativity. The precession rate per period is 39°.1 ± 0°.1, by far the largest rate in any known binary, and the (1.83 ± 0.01)⋅1010M⊙primary is among the dozen biggest black holes known. We will discuss the various Post Newtonian terms and their effect on the orbit solution. The over 100 year data base of optical variations in OJ287 puts limits on these terms and thus tests the ability of Einstein's General Relativity to describe, for the first time, dynamic binary black hole spacetime in the strong field regime. The quadrupole-moment contributions to the equations of motion allows us to constrain the ‘no-hair’ parameter to be 1.0 ± 0.3 which supports the black hole no-hair theorem within the achievable precision.

scholarly journals Gravitational cubic-in-spin interaction at the next-to-leading post-Newtonian order

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Michèle Levi ◽  
Stavros Mougiakakos ◽  
Mariana Vieira
Keyword(s):  
Degrees Of Freedom ◽  
Finite Size ◽  
Effective Field ◽  
Compact Objects ◽  
Spin Interaction ◽  
General Observation ◽  
Compact Binaries ◽  
Compact Binary ◽  
New Type ◽  
Rotational Degrees Of Freedom

Abstract In this work we derive for the first time the complete gravitational cubic-in-spin effective action at the next-to-leading order in the post-Newtonian (PN) expansion for the interaction of generic compact binaries via the effective field theory for gravitating spinning objects, which we extend in this work. This sector, which enters at the fourth and a half PN (4.5PN) order for rapidly-rotating compact objects, completes finite-size effects up to this PN order, and is the first sector completed beyond the current state of the art for generic compact binary dynamics at the 4PN order. At this order in spins with gravitational nonlinearities we have to take into account additional terms, which arise from a new type of worldline couplings, due to the fact that at this order the Tulczyjew gauge for the rotational degrees of freedom, which involves the linear momentum, can no longer be approximated only in terms of the four-velocity. One of the main motivations for us to tackle this sector is also to see what happens when we go to a sector, which corresponds to the gravitational Compton scattering with quantum spins larger than one, and maybe possibly also get an insight on the inability to uniquely fix its amplitude from factorization when spins larger than two are involved. A general observation that we can clearly make already is that even-parity sectors in the order of the spin are easier to handle than odd ones. In the quantum context this corresponds to the greater ease of dealing with bosons compared to fermions.

The two-body problem: an effective-one-body approach

2018 ◽  
Author(s):  
Nathalie Deruelle ◽  
Jean-Philippe Uzan
Keyword(s):  
Body Problem ◽  
Equations Of Motion ◽  
Reaction Force ◽  
Kerr Black Hole ◽  
Radiation Reaction ◽  
Spherically Symmetric ◽  
Geodesic Motion ◽  
Two Body Problem ◽  
Symmetric Spacetime ◽  
Radiation Reaction Force

This chapter presents the basics of the ‘effective-one-body’ approach to the two-body problem in general relativity. It also shows that the 2PN equations of motion can be mapped. This can be done by means of an appropriate canonical transformation, to a geodesic motion in a static, spherically symmetric spacetime, thus considerably simplifying the dynamics. Then, including the 2.5PN radiation reaction force in the (resummed) equations of motion, this chapter provides the waveform during the inspiral, merger, and ringdown phases of the coalescence of two non-spinning black holes into a final Kerr black hole. The chapter also comments on the current developments of this approach, which is instrumental in building the libraries of waveform templates that are needed to analyze the data collected by the current gravitational wave detectors.

scholarly journals Numerical methods for General Relativistic particles

2018 ◽  
Vol 14 (S342) ◽  
pp. 19-23
Author(s):  
Fabio Bacchini ◽  
Bart Ripperda ◽  
Alexander Y. Chen ◽  
Lorenzo Sironi
Keyword(s):  
Numerical Methods ◽  
Gravitational Lensing ◽  
Complex Dynamics ◽  
Equations Of Motion ◽  
Numerical Algorithms ◽  
Relativistic Effects ◽  
Compact Objects ◽  
Light Rays ◽  
Massive Particles ◽  
External Forces

AbstractWe present recent developments on numerical algorithms for computing photon and particle trajectories in the surrounding of compact objects. Strong gravity around neutron stars or black holes causes relativistic effects on the motion of massive particles and distorts light rays due to gravitational lensing. Efficient numerical methods are required for solving the equations of motion and compute i) the black hole shadow obtained by tracing light rays from the object to a distant observer, and ii) obtain information on the dynamics of the plasma at the microscopic scale. Here, we present generalized algorithms capable of simulating ensembles of photons or massive particles in any spacetime, with the option of including external forces. The coupling of these tools with GRMHD simulations is the key point for obtaining insight on the complex dynamics of accretion disks and jets and for comparing simulations with upcoming observational results from the Event Horizon Telescope.

scholarly journals An explicit construction of the dimension-9 operator basis in the standard model effective field theory

2020 ◽  
Vol 2020 (11) ◽  
Author(s):  
Yi Liao ◽  
Xiao-Dong Ma
Keyword(s):  
Field Theory ◽  
Standard Model ◽  
Effective Field Theory ◽  
Equations Of Motion ◽  
Baryon Number ◽  
Explicit Construction ◽  
Effective Field ◽  
Starting Point ◽  
The Standard Model ◽  
Symmetry Relations

Abstract We investigate systematically dimension-9 operators in the standard model effective field theory which contains only standard model fields and respects its gauge symmetry. With the help of the Hilbert series approach to classifying operators according to their lepton and baryon numbers and their field contents, we construct the basis of operators explicitly. We remove redundant operators by employing various kinematic and algebraic relations including integration by parts, equations of motion, Schouten identities, Dirac matrix and Fierz identities, and Bianchi identities. We confirm counting of independent operators by analyzing their flavor symmetry relations. All operators violate lepton or baryon number or both, and are thus non-Hermitian. Including Hermitian conjugated operators there are $$ {\left.384\right|}_{\Delta B=0}^{\Delta L=\pm 2}+{\left.10\right|}_{\Delta B=\pm 2}^{\Delta L=0}+{\left.4\right|}_{\Delta B=\pm 1}^{\Delta L=\pm 3}+{\left.236\right|}_{\Delta B=\pm 1}^{\Delta L=\mp 1} $$ 384 Δ B = 0 Δ L = ± 2 + 10 Δ B = ± 2 Δ L = 0 + 4 Δ B = ± 1 Δ L = ± 3 + 236 Δ B = ± 1 Δ L = ∓ 1 operators without referring to fermion generations, and $$ {\left.44874\right|}_{\Delta B=0}^{\Delta L=\pm 2}+{\left.2862\right|}_{\Delta B=\pm 2}^{\Delta L=0}+{\left.486\right|}_{\Delta B=\pm 1}^{\Delta L=\pm 3}+{\left.42234\right|}_{\Delta B=\mp 1}^{\Delta L=\pm 1} $$ 44874 Δ B = 0 Δ L = ± 2 + 2862 Δ B = ± 2 Δ L = 0 + 486 Δ B = ± 1 Δ L = ± 3 + 42234 Δ B = ∓ 1 Δ L = ± 1 operators when three generations of fermions are referred to, where ∆L, ∆B denote the net lepton and baryon numbers of the operators. Our result provides a starting point for consistent phenomenological studies associated with dimension-9 operators.

Analytical Modelling of the Dynamics of the Four-Bar Mechanism: A Comparison of Some Methods

2018 ◽  
Author(s):  
J. P. Meijaard ◽  
V. van der Wijk
Keyword(s):  
Virtual Work ◽  
Equations Of Motion ◽  
Differential Algebraic Equations ◽  
Force Balance ◽  
Dynamic Force ◽  
Algebraic Equations ◽  
Principle Of Virtual Work ◽  
Principal Vector ◽  
Reaction Forces ◽  
Principal Points

Some thoughts about different ways of formulating the equations of motion of a four-bar mechanism are communicated. Four analytic methods to derive the equations of motion are compared. In the first method, Lagrange’s equations in the traditional form are used, and in a second method, the principle of virtual work is used, which leads to equivalent equations. In the third method, the loop is opened, principal points and a principal vector linkage are introduced, and the equations are formulated in terms of these principal vectors, which leads, with the introduced reaction forces, to a system of differential-algebraic equations. In the fourth method, equivalent masses are introduced, which leads to a simpler system of principal points and principal vectors. By considering the links as pseudorigid bodies that can have a uniform planar dilatation, a compact form of the equations of motion is obtained. The conditions for dynamic force balance become almost trivial. Also the equations for the resulting reaction moment are considered for all four methods.

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