Jun 8, 2018 - The LIGO discovery of gravitational waves is the most important ... Sir Isaac Newton discovered gravitational field attached to bodies.
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Numerical Relativity beyond General Relativity
CENTRO CIENCIAS BENASQUE
Benasque, Spain, June 3-9, 2018
How well does the relativistic two-body problem approximates the LIGO BBH merger events? Plamen Fiziev TCPA Foundation, Sofia University, Bulgaria and BLTP, JINR, Dubna 8th of June, 2018
The LIGO discovery of gravitational waves is the most important experimental discovery in gravity after sir Isaac Newton: Sir Isaac Newton discovered gravitational field attached to bodies. LIGO discovered gravitational field spreading in space freely and detached from bodies. Now, most important is the real opportunity to examine experimentally the theoretical assumptions, as well as to look for new developments and unexpected physical phenomena.
The LIGO data: GW150914 ???
and their interpretation ???
10−21
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The best fit taking into account the spin precession
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The First LIGO Open Data Workshop March 2018
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NR describes mereger only of naked BH. ???How well does the relativistic two-body problem approximate the LIGO BBH merger events ???
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Remarks about GR BH hypothesis: 1. We have never seen a “naked” BH like :
2. The NR produces also “naked” BH which essentially defers form observed astrophysical BH:
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NR “necked” BBH
versus observed astrophysical BH
PROBLEM: Why we have to presuppose that in the LIGO REAL EVENTS “NAKED BH” take part ??? How well does this approximate the LIGO BBH merger events ??? Note that in the Nature we obviously have more then TWO BODIES and the two-body-problem with regular motion is only THE FIRST APPROXIMATION even for the Hydrogen atom!
STF, Gauss window, σ =150 :
Hanford
H1: 3441 Points = 0.26 s
Livingston L1: 3441 Points =0.26 s
𝟏𝟎−𝟐𝟏
BH – NR STF Gauss -sigma-150 , 3441 points:
Numerical Errors at low frequencies
Residuals: A pure noise or an indication of irregular motion ?
Some part of physical GWB-information can be found in the residuals: B. P. Abbott et al., An improved analysis of GW150914 using a fully spin-precessing waveform model, LIGO-P1600048, arXiv:1606.01210.
Deterministic chaos ? Some authors announced a significant correlation between residuals of Hanford and Livingston detectors for GW150914, GW151226 and GW170104, after one introduces corresponding lags . The existence of that correlations seem strange, if we suppose the residuals to present pure noise: Journal of Cosmology and Astroparticle Physics, Issue 08, article id. 013 (2017). My idea is to explain the above correlations with presence of matter around mergering BBH which causes irregular motion and corresponding chaotic fraction in the gravitational waves signal from the source. Such natural explanation requires to extend the numerical investigation of the BBH merger to the problem in presence of matter. In the simplest case one is forced to solve relativistic three body problem in full GR – much more complicated problem than the two-body one.
The MAIN HYPOTHESES in the present talk: The simplest second approximation for the models of
REAL LIGO EVENTS of BBH merger shall be THE THREE BODY gravitational problem, thus taking into account presence of some matter
Some astronomical facts and 3BS-3d-solutions: • • •
N=7
Known 612 stars with multiplicity 3 to 7, half of them within 100 pc from the Sun; 700 visual triple stars within 200 pc from the Sun. In 82% of triple stars the close subsystem is related to the primary of a wide pair. Algol triple system:
http://www.scholarpedia.org/article/Three_body_problem
Some known 3b solutions:
Dynamical chaos in restricted 3b problem
Move: https://youtu.be/SEe49T3G6SQ Restricted three body problem Chaotic behavior of a planet in the gravitational field of two stars with different masses moving on constant circular orbits
EFFECTIVE ONE BODY APPROACH TO THE THREE BODY COLLINEAR PROBLEM PPF and Ts. Ya. Fizieva , Few-Body Systems 2, 71-80 (1987) PPF, Lett. In Math.Phys., 12, 1986, p.267
Hyper-spherical coordinates: SCM
A total separation of 2BC and 3BC
(Eccentricity = 1)
PF (1987): https://www.researchgate.net/publication/307208487_Investigation_of_the_integrability_of_the_classical_threebody_problem?showFulltext=1&linkId=57c4658d08ae32a03dad4111
Trajectories without recombination
Trajectories with recombination
Tree particle resonance
A 3b numerical example:
Gravitational waves from collinear classical three body problem PPF arXiv:1609.026
ℎ× = 0
, for E = const
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Some numerical trajectories
Numerical trajectories with clear irregular behavior
and
the Gabor transform of their gravitational waves
Deterministic chaos
Just a comparison:
H1 data
L1 data
Pure binary system
Deterministic chaos
The best 2BNR NR2B template
3B Newton system
Some concluding remarks: For a real explanation of observed GW we need: 1) To consider the back reaction of the emission of GW on the 3BS motion (at least in PN approximation). 2) To make our 3b consideration relativistic. 3) The next step in the study of GW must be a full numerical-relativity-treatment of the 3BS. 4) Corresponding 3BS templates are needed.
LIGO
Let’s believe to reach an understanding of the GW at least at the level of our understanding of the water waves
Thank you for your attention
