The aim of this paper is to test whether gravitational waves could contribute to dark energy. It is tested how the change of the space curvature due to mass loss during the fusion of compact objects like black holes affects the space geometry. The result shows a correlation between mass loss on the one hand and space growth and time on the other (volume = mass ×light travel time^2). The calculated factor 4,195 × 10^(-10) m^3/kg, s^2 is very close to the value 2× ×G (gravitational constant).
Title: Can the discoveries in gravitational wave astronomy contribute to understanding the nature of space?
Abstracts:
The aim of this paper is to test whether gravitational waves could contribute to dark energy. It is tested how the change of the space curvature due to mass loss during the fusion of compact objects like black holes affects the space geometry. The result shows a correlation between mass loss on the one hand and space growth and time on the other (volume = mass ×light travel time^2). The calculated factor 4,195 × m^3/kg, s^2 is very close to the value 2×𝛑×G (gravitational constant).
Introduction:
As shown by findings in the last few years (LIGO, VIRGO, etc.), when compact objects such as black holes or neutron stars merge, mass losses occur as a result of the differences in angular momentum before and after the merger of these objects (Loss of rotational mass differences) 1 2 3. These mass losses during the merging of two black holes are typically on a scale of approximately 5% of the sum of the total masses. With regard to the merging of neutron stars, this figure appears to be on a scale of approximately 1% 3. The general theory of relativity states that a mass bends the space around it. The result is an increase in the radial distance due to the presence of a mass, compared to a sphere of the same surface, without the presence of a mass. The increase (Delta s) is approximately (1-((2*G*M/(c^2*r))) ^-0.54 (this does, however, only apply outside the Schwarzschild radius Rs =2*G*M/c^2)
It follows those spaces with increased radial distance (due to masses present), compared to massless spaces with the same surface, have a larger volume. If it is assumed that the space consists of quanta of constant volumes or for other reasons has a plastic but largely incompressible behavior 5 6, the surface of the space affected should therefore increase in the event of a loss of mass. Thereby, the radius would also increase depending on the loss of mass per time unit and cause an expansion of the surrounding space.
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Calculation:
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The volume change due to mass loss is therefore V- Veukl.
This volume change is now divided by the mass (kg) and the light travel time (s) of the respective radius.
This calculation results in a constant value of 4,195* /kg over several orders of space and mass. This value is very close to the value of
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Agreement with observation:
Is the hypothesis compatible with the current knowledge about the universe?
By means of a simulation it can be checked whether this hypothesis can deliver a plausible picture of our universe, if for the age of the universe 13.8 billion years and for the time-dependent mass transformation Mt (kg/0.138 billion years) the relation Mt=10^49*t^-6.5335 (t billion years) is assumed, the simulation delivers (with an initial mass - energy of 8.3*10^54 kg a Hubble constant of 70 km/s-Mpc. Today's mass conversion would have a value of 100 solar masses per year, the universe would have a radius of 47.51 billion light years, a density of 9.21*10^-27kg/m^3 and a residual mass (matter + dark matter) of 3.5*10^54 kg. According to this, 57.79% of the originally existing mass - energy would have been converted into space until today. If now is assumed that the true value of the Hubble constant lies between the values 68 and 73 km/s-Mpc and the mass transformation rate lies today between 1 and 1,000 solar masses per year, the simulation results in a possible size of the universe of a radius between 46.94 to 47.9 billion light-years, a density between 8.68 and 10*10^-27 kg/m^3 13 and a transformation rate of 55.7 to 59.23%.
Verification by future observations
With the measurements of gravitational wave events in the next years, it should be possible to statistically evaluate the mass conversion rate for different distances (time horizons). This would allow the following predictions of this hypothesis to be tested.
1) The mass loss rate increases with increasing distance .
2) The present mass loss rate is between 1 and 1,000 solar masses per year.
3) The curve of the increase of the mass loss rate has a similar shape as described before.
Discussion:
The hypothesis presented in this work for the explanation of the dark energy is a further alternative explanation attempt, to the hypotheses presented so far. (Cosmological constant, dynamic model like quintessence, brane model, string theory etc..11). The cosmological constant introduces a negative pressure which is interpreted mostly as vacuum energy (vacuum fluctuation). However, the calculation does not agree with the observation! (The dynamic models are based on the arbitrary introduction of a not constant density term (a not derivable constant/potential) 11. The brane model and the string theory introduce a five- or multi-dimensional manifold (string theory 10 space dimensions of it 6 extremely small). These extra dimensions are difficult to not detectable and so far, no evidence for the existence for extra dimensions has been found 11. The presented hypothesis does not contradict the current understanding of the composition of the universe from mass and energy. It is also not in contradiction with the propagation of gravitational waves. The presented hypothesis postulates an accelerated expansion of the universe and is only conclusive for an open (hyperbolic) universe.
Parameters:
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References
1. LIGO Scientific Collaboration, Virgo Collaboration and KAGRA Collaboration Data Releases/Gravitational wave open science center/Event list/1.8.2022 (https://www.gw-openscience.org/eventapi/html/allevents/)
2. Davide Gerosa,Cecilia Maria Fabbri, Ulrich Sperhake/The irreducible mass of LIGO's black holes/arxiv/2022 (https://arxiv.org/search/grqc?searchtype=author&query=Fabbri%2C+C+M)
3. R. Abbott et al 2021 ApJL 915 L5/ Observation of Gravitational Waves from Two Neutron Star–Black Hole Coalescences (https://iopscience.iop.org/article/10.3847/2041-8213/ac082e)
4. Franz Embacher ,Fakultät für Physik der Universität Wien, Maßstäbe und Längen und Raumkrümmung im Gravitationsfeld, Seminar an der Pädagogischen Hochschule Oberösterreich Linz, 3. 12. 2014 (http://homepage.univie.ac.at/franz.embacher/Rel/artMassstaebe/start.htm)
5. Smolin,Lee.”Towards a theory of spacetime structure at very short distances.”Nuclear Physiks B 160.2 (1979):253-263
6. Peebles, P. J. E. and Ratra, Bharat, The cosmological constant and dark energy Rev. Mod. Phys.,75,2,559-606,2003 (https://link.aps.org/doi/10.1103/RevModPhys.75.559
7. G. Rosi and F. Sorrentino and L. Cacciapuoti and M. Prevedelli and G. M. Tino, Precision measurement of the Newtonian gravitational constant using cold atoms, 2014,10.1038/nature13433, volume = {510}, number = {7506}, @article{RevModPhys.75.559,
8. Cladwell,R.R.,and Eric V.Linder.”Limits of quintessence.”pysikal review letters 95.14 (2005):141301.
9. Ghaffari,S.et al.”Tsallis holographik dark energy in the brane cosmology.“Physics of the Dark Universe 23 (2019):1000246.99
10. Viorel Laurentiu Cartas, The Elasticity of Quantum Spacetime Fabric, Geometry, Integrability and Quantization, Proceedings Series, 2018: 105-114 (2018) (https://doi.org/10.7546/giq-19-2018-105-114)
11. Florian Herrmann, Dunkle Energie, Seminarvortrag im Institut für Theoretische Physik Universität Münster, Fachbereich 11: Physik,2014 Münster ,( https://www.uni-muenster.de/Physik.TP/archive/typo3/fileadmin/lehre/teilchen/ws1314/DunkleEnergie.pdf)
12. 1lPanck-Kollaboration; Aghanim, N.; Akrami, Y.; Ashdown, M.; Aumont, J.; Bacgalupi, C.; Ballardini, M.; Banday, AJ; Barreiro, RB; Bartolo, N.; Basak, S. (September 2020). "Planck 2018 Ergebnisse: VI. Kosmologische Parameter" . Astronomie & Astrophysik . 641 : A6. arXiv : 1807.06209 . Bibcode : 2020A&A...641A...6P . doi : 10.1051/0004-6361/201833910 . ISSN 0004-6361 . S2CID 119335614 .
13. Dimitar Todorov Valev,Bulgarian Academy of Sciences ,Estimations of total mass and energy of the observable universe March 2014,Physics International 5(1):15-20 DOI:10.3844/pisp.2014.15.20
14. LIGO.org/science/publication-O2BBH Pop/Binary Black Hole Population properties inferred from O1 and O2.
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- Quote paper
- Herbert Schöfnagl (Author), 2022, Gravitational waves and dark energy. Can the discoveries in gravitational wave astronomy contribute to understanding the nature of space?, Munich, GRIN Verlag, https://www.hausarbeiten.de/document/1300057
