Supplement to the scientific paper: Gravitational waves and dark energy. Can the discoveries in gravitational wave astronomy contribute to understanding the nature of space?
The analysis of LIGO/Virgo data shows that merging black holes exhibit significant rotation (Kerr metric). This work examines whether the Kerr-specific curvature of spacetime affects the hypothesis that mass losses are converted into spatial volume. It is demonstrated that while the effect is locally dominant, it becomes negligible on cosmological scales—the conversion factor dV=2πG⋅(light travel time)^2 remains valid.
Supplement to the scientific paper:
Can the discoveries in gravitational wave astronomy contribute to understanding the nature of space? [6]
1. Abstract
"The analysis of LIGO/Virgo data shows that merging black holes exhibit significant rotation (Kerr metric). This work examines whether the Kerr-specific curvature of spacetime affects the hypothesis that mass losses are converted into spatial volume. It is demonstrated that while the effect is locally dominant, it becomes negligible on cosmological scales—the conversion factor dV=2πG⋅(light travel time)^2 remains valid."
2. Introduction
"Gravitational wave astronomy, through observations by LIGO/Virgo, has confirmed that merging black holes typically rotate and must therefore be described by the Kerr metric—in contrast to the simplified Schwarzschild approximation. This supplement discusses the extent to which the Kerr-specific expansion of space influences the core thesis of this work, namely that mass is converted into spatial volume during the mergers of compact objects. Specifically, it analyzes why the Kerr effect, while causing a curvature increased by a factor of e (Eulers number) locally (e.g., at R=1 light-second), decays exponentially with distance. Thus, the original conclusion remains scale-invariant."
3. Kerr Metric vs. Schwarzschild Approximation
The original calculations were based on the Schwarzschild metric (non-rotating black holes), while LIGO/Virgo data show that merging compact objects exhibit significant rotation (Kerr metric) [1, 2]. For a maximally rotating Kerr black hole with a maximum spin parameter a=1, the local volume distortion compared to Euclidean space is:
(VKerr−Veukl)/(VSchw−Veukl)≈e (at R=1 light-second)
(where e is Euler's number, ≈2.718) [3, 4].
4. Scale Dependence of the Kerr Effect
The deviation decays exponentially with distance R:
Illustrations are not included in the reading sample
Illustrations are not included in the reading sample
For cosmic distances (R>10^-6 light-seconds), the correction term becomes negligible (<10^-5) [5].
5. Implications for the Hypothesis
The conversion factor
dV=2πG⋅(light travel time)^2(4.195×10−10 m3/kg s^2)
remains scale-invariant for cosmological volumes because:
- Kerr effects are confined to local regions R < 1 light-second
- The averaged curvature over large scales matches Schwarzschild predictions [5].
6. Acknowledgments “
„This work was developed with the assistance of an AI system (DeepSeek Chat) for refining mathematical notations, text structuring, and literature research. The interpretation of results and scientific reasoning remain solely the responsibility of the author.“
7. References
[1] LIGO Scientific Collaboration, Virgo Collaboration, and KAGRA Collaboration. 2022. Spin Measurements of Binary Black Hole Mergers in O3a. LIGO Document P2200027
[2] Abbott, B.P . et al. (LIGO, Virgo, and KAGRA Collaborations). 2021. Population Properties of Compact Objects from LIGO/Virgo O3a . Astrophysical Journal Letters 915 , L5. DOI:10.3847/2041-8213/ac082e.
[3] Kerr, R.P . 1963. Gravitational Field of a Spinning Mass. Physical Review Letters 11, 237–238. DOI:10.1103/PhysRevLett.11.237.
[4] Ohanian, H.C . 1976. The Kerr Metric: A Brief Review. American Journal of Physics 44, 1047–1055.
[5] Visser, M . 2007. The Kerr Spacetime: A Brief Introduction . (arXiv:0706.0622).
[6] Schöfnagl ,H.(2022): Gravitational waves and dark energy. Can the discoveries in gravitational wave astronomy contribute to understanding the nature of space? https://www.grin.com/document/1300057
[...]
Buy now
- Quote paper
- Herbert Schöfnagl (Author), 2025, Supplement to the scientific paper: Gravitational waves and dark energy. Can the discoveries in gravitational wave astronomy contribute to understanding the nature of space?, Munich, GRIN Verlag, https://www.grin.com/document/1574042
