Moving objects in retarded gravitational potentials of an expanding spherical shell/Brief historical review

Preface Classical approach Brief historical review Around 1900 The finiteness of the propagation speed of gravity and its influence on gravitational forces was originally published by the Austrian astronomer Josef von Hepperger (1855–1928) in 1888 in Vienna.Hepperger Josef von https://books.google.de/books?id=TT3PAAAAMAAJ&hl=de&pg=PP1#v=onepage&q&f=false Über die Fortpflanzungsgeschwindigkeit der Gravitation 1888 Wien K. K. Hof.-und Staatsdruckerei de The German physicist Paul Gerber (1854–1909) published 1898 his paper on "Die räumliche und zeitliche Ausbreitung der Gravitation", where he established that the perihelion precession of the planet Mercury is related to the propagation speed of gravity, which is quite close to that of electromagnetic radiation.Gerber Paul Mehmke R. Cantor M. Die räumliche und zeitliche Ausbreitung der Gravitation The spatial and temporal propagation of gravity https://de.wikisource.org/wiki/Die_räumliche_und_zeitliche_Ausbreitung_der_Gravitation Zeitschrift für Mathematik und Physik de Leipzig 43 93–104 Verlag B. G. Teubner 1898 His formula for the perihelion precession of the planet Mercury wasn't known to Albert Einstein (1879–1955), but six years after Paul Gerber's death, Einstein found an identical formula in his publication "Erklärung der Perihelbewegung des Merkur aus der allgemeinen Relativitätstheorie" (English: "Explanation of Mercury's perihelion motion from the general theory of relativity") by applying the laws of General Relativity.Einstein Albert Erklärung der Perihelbewegung des Merkur aus der Allgemeinen Relativitätstheorie Explanation of Mercury's perihelion motion from the general theory of relativity Sitzungsberichte der Preußischen Akademie der Wissenschaften 1915 831–839 However, the contemporary scientists couldn't reproduce the derivation of Paul Gerber for the formula, and furthermore, they stated that some of the prerequisites used by him were wrong. Shortly before his early death the German astronomer and physicist Karl Schwarzschild (1873–1916) published a paper on "Über das Gravitationsfeld einer Kugel aus inkompressibler Flüssigkeit nach der Einsteinschen Theorie" (English: "On the gravitational field of a sphere of incompressible fluid according to Einstein's theory"), where he described how to compute the smallest possible radius for a sphere with a given mass. He found the radius for a sphere with the mass of the sun to be three kilometres.Schwarzschild Karl Deutsche Akademie der Wissenschaften zu Berlin http://archive.org/details/sitzungsberichte1916deutsch Sitzungsberichte der Königlich Preussischen Akademie der Wissenschaften zu Berlin 424–434 1882 Berlin : Deutsche Akademie der Wissenschaften zu Berlin Smithsonian Libraries In recognition of his achievement, the corresponding radius is now called the Schwarzschild radius. It is interesting to notice that Schwarzschild also made important contributions to retarded potentials in electrodynamics already in 1903. According to the electrokinetic potential he claimed:Schwarzschild Karl 1903 Zwei Formen des Prinzips der kleinsten Action in der Elektronentheorie Two forms of the principle of least action in electron theory Nachrichten von der Königlichen Gesellschaft der Wissenschaften zu Göttingen, Mathematisch-Physikalische Klasse Göttingen Commissionsverlag der Dieterich'schen Universitätsbuchhandlung, Lüder Horstmann 3 127–128 Es sind in jedem Raumelement die Werte der Dichte und der Geschwindigkeit zu benutzen, welche dort zu einer um die Lichtzeit zurückliegenden Epoche galten. In each spatial element, the values of density and velocity are to be used, which were valid there at an epoch around light time ago. Big Bang The Belgian theologian and physicist George Lemaître (1894–1966) is regarded as the founder of the Big Bang theory. In 1931, he introduced the term "atome primitif" (English: "primordial atom") to describe the hot initial state of the universe. Already in 1927 he wrote as the second conclusion of his publication about "a homogeneous universe of constant mass and increasing radius, accounting for the radial velocity of extra-galactic nebulae" with reference to the investigations of Edwin Hubble (1889–1953) in 1926:Hubble Edwin 1926 Extra-galactic nebulae Astrophysical Journal Contributions from the Mount Wilson Observatory Mount Wilson, California, USA 64 I 321–369Lemaître Georges 1927 Un univers homogéne de masse constante et de rayon croissant, rendant compte de la vitesse radiale des nébuleuses extra-galactiques Annales de la société scientifique de Bruxelles 47 A 49–59Lemaître Georges 1931 Expansion of the universe, A homogeneous universe of constant mass and increasing radius accounting for the radial velocity of extra-galactic nebulae Monthly Notices of the Royal Astronomical Society 91 483–490 Le rayon de l'univers croit sans cesse depuis une valeur asymptotique pour The radius of the universe increases without limit from an asymptotic value for In 1933 the Swiss astronomer Fritz Zwicky (1898–1974) obeserved a gravitational anomaly in the Coma galaxy cluster, and he coined the term dark matter (in German: "dunkle Materie") for the cause of this anomaly.Fritz Zwicky Die Rotverschiebung von extragalaktischen Nebeln The red shift of extragalactic neubulae https://articles.adsabs.harvard.edu//full/1933AcHPh...6..110Z/0000110.000.html 1933 2024-06-11 articles.adsabs.harvard.edu In his book Relativity, Gravitation and World Structure of the year 1935 the British astrophysicist and mathematician Edward Arthur Milne (1896–1950) introduced the special-relativistic cosmological Milne model.Milne Edward Arthur Relativity, gravitation and world-structure Clarendon Press 1935 Oxford, Great Britain 291-294 en World picture on the simple kinematic model - Comparison with local Newtonian gravitation and dynamics - §§412-418 This model assumes an isotropic and for all time linearly expanding, but not homogeneous universe. It is independent of general theory of relativity, but nevertheless equivalent to a special case of the Friedmann–Lemaître–Robertson–Walker metric in the limit of zero energy density. The redshift is explained by the velocity caused by a hypothetical initial explosion of matter. The density of such a universe must be small in comparison to the critical density of the Friedmann equations that were published by Russian physicist and mathematician Alexander Friedmann (1888–1925) in 1924.Alexander Friedman Über die Krümmung des Raumes About the curvature of the space Zeitschrift für Physik 10 1922 1 377–386 10.1007/BF01332580 1922ZPhy...10..377F 125190902 de Decades later, the Milne model fell almost completely into oblivion, whereas the cosmological models based on the general theory of relativity as well as on a homogeneous universe gained more and more attention. Cosmic microwave background In 1953 the German astrophysicist Erwin Finlay-Freundlich (1885–1964) derived a blackbody temperature for intergalactic space of 2.3 Kelvin according to his theory of tired light.Finlay-Freundlich Erwin 1953 Über die Rotverschiebung der Spektrallinien On the redshift of spectral lines Nachrichten der Akademie der Wissenschaften in Göttingen Göttingen Vandenhoeck & Ruprecht 7 94–101 The German-British mathematician and physicist Max Born (1882–1970) immediately recommended taking the problem seriously and pursuing it further.Born Max 1953 Theoretische Bemerkungen zu Freundlichs Formel für die stellare Rotverschiebung Theoretical remarks to Freundlich's formula for the stellar redshift Nachrichten der Akademie der Wissenschaften in Göttingen Göttingen Vandenhoeck & Ruprecht 7 102–108 thumb|right|upright=1.5|Map of cosmic background radiation with artificial colours that show tiny temperature variations. In 1965 the cosmic microwave background (CMB) was discovered by US-American radio astronomers Arno Allan Penzias (1933–2024) and Robert Woodrow Wilson (born 1936).Penzias Arno Allan Wilson Robert Woodrow 1965 A Measurement of Excess Antenna Temperature at 4080 Mc/s The Astrophysical Journal 142 1 419–421 10.1086/148307 free It has a thermal black body spectrum at a very low temperature of about 2.7 Kelvin. Since the cosmic microwave background was mainly created in the visible area of the electromagnetic spectrum, it must have undergone a strong wavelength extension on its way to the observers. This can happen because of two main reasons: The origin of the radiation moves away from us very quickly, which will cause an increase of the wavelength according to the Doppler effect described by Christian Doppler (1803–1853) in 1842.Doppler Christian 1842 Ueber das farbige Licht der Doppelsterne und einiger anderer Gestirne des Himmels. On the Coloured Light of the Double Stars and some other Celestial Bodies https://archive.org/details/ueberdasfarbigel00doppuoft/page/n9/mode/2up?view=theater Abhandlungen der Böhmischen Gesellschaft der Wissenschaften 5/2 465–485 There is a huge mass behind the origin of the radiation, which will cause an increase of the wavelength according to the gravitation and the relativity principle of Albert Einstein (1879–1955) of 1907.Einstein Albert 1907 Relativitätsprinzip und die aus demselben gezogenen Folgerungen On the Relativity Principle and the Conclusions Drawn from It http://www.soso.ch/wissen/hist/SRT/E-1907.pdf Jahrbuch der Radioaktivität 4 411–462 In addition, it is discussed that an expansion of the spacetime during the propagation time of a light wave also would increase its wavelength to the same extent. The redshift factor is defined as a relation between an emitted wavelength and an observed wavelength of electromagnetic radiation: The redshift of the cosmic microwave background was found to be in 2003, which is an extremely high value.C. L. Bennett, M. Halpern, G. Hinshaw, N. Jarosik, A. Kogut, M. Limon, S. S. Meyer, L. Page, D. N. Spergel, G. S. Tucker, E. Wollack, E. L. Wright, C. Barnes, M. R. Greason, R. S. Hill, E. Komatsu, M. R. Nolta, N. Odegard, H. V. Peirs, L. Verde, J. L. Weiland First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Preliminary Maps and Basic Results Astrophys. J. Suppl. 148 2003 1–27 10.1086/377253 free The age of the universe at the time this background radiation was created by hydrogen atoms has been estimated at around 379,000 years.2013-02-13 Microwave (WMAP) All-Sky Survey Guide Digital Universe Hayden Planetarium https://web.archive.org/web/20130213023246/http://www.haydenplanetarium.org/universe/duguide/exgg_wmap.php 2024-06-01 web.archive.org 21st century Observations of distant type Ia supernovae published by both the Supernova Cosmology Project as well as the High-Z Supernova Search Team in 1998 show that the relative expansion of the universe is accelerating. For the analysis the astronomers Saul Perlmutter, Brian P. Schmidt and Adam Riess were awarded the Nobel Prize in Physics in 2011.The Nobel Prize in Physics 2011 https://www.nobelprize.org/prizes/physics/2011/advanced-information/ 2024-03-16 NobelPrize.org en-US From 2001 to 2010 the NASA spacecraft Wilkinson Microwave Anisotropy Probe (WMAP) was investigating the cosmic microwave background. Its measurements led to the current Standard Model of Cosmology (Lambda cold dark matter, Lambda-CDM or ΛCDM model). According to this model the universe currently consists of less than 5 percent ordinary baryonic matter; about 24 percent cold dark matter (CDM) that interacts only weakly with ordinary matter and electromagnetic radiation; and more than 70 percent of dark energy that is used to explain the accelerated expansion of the universe.Francis Matthew 2013-03-21 First Planck results: the Universe is still weird and interesting https://arstechnica.com/science/2013/03/first-planck-results-the-universe-is-still-weird-and-interesting/ 2024-06-11 Ars Technica en-us These data were more or less confirmed by the Planck space observatory that was operated by the European Space Agency (ESA) from 2009 to 2013.ESA Science & Technology - From an almost perfect Universe to the best of both worlds https://sci.esa.int/web/planck/-/60499-from-an-almost-perfect-universe-to-the-best-of-both-worlds 2024-06-11 sci.esa.int In 2013 the Indian researcher Chandrakant Raju proposed to apply the retarded gravitation theory (RGT) to explain the flyby anomaly of spacecrafts in the gravitational field of the earth as well as the acceleration of masses in the retarded gravitational fields of spiral galaxies.Raju Chandrakant 2013-11-27 Retarded gravitation theory https://arxiv.org/pdf/1102.2945.pdf 2024-03-22 School of Mathematical Sciences, Universiti Sains Malaysia Penang, Malaysia en PDF 1102.2945 In 2016, researchers from the gravitational-wave observatory LIGO reported the first direct measurement of gravitational waves generated by the collision of two black holes (gravitational wave event GW150914).LIGO Scientific Collaboration and Virgo Collaboration Abbott B. P. Abbott R. Abbott T. D. Abernathy M. R. Acernese F. Ackley K. Adams C. Adams T. Addesso P. Adhikari R. X. Adya V. B. Affeldt C. Agathos M. Agatsuma K. 2016-02-11 Observation of Gravitational Waves from a Binary Black Hole Merger https://link.aps.org/doi/10.1103/PhysRevLett.116.061102 Physical Review Letters 116 6 061102 10.1103/PhysRevLett.116.061102 Already in 2017 the Nobel Prize in Physics was awarded for the first direct observation of gravitational waves.The Nobel Prize in Physics 2017 https://www.nobelprize.org/prizes/physics/2017/advanced-information/ 2024-03-16 NobelPrize.org en-US On 17th August 2017 a merging binary neutron star was observed independently and simultaneously by the Advanced LIGO and Virgo detectors (gravitational wave event GW170817) and the Fermi Gamma-ray Burst Monitor as well as the Anticoincidence Shield for the Spectrometer for the International Gamma-Ray Astrophysics Laboratory (gamma ray burst event GRB 170817A).LIGO Scientific Collaboration Virgo Collaboration Monitor Fermi Gamma-Ray Burst INTEGRAL 2017-10-20 Gravitational Waves and Gamma-rays from a Binary Neutron Star Merger: GW170817 and GRB 170817A http://arxiv.org/abs/1710.05834 The Astrophysical Journal Letters 848 2 L13 10.3847/2041-8213/aa920c 2041-8205 These observations prove that the propagation velocity of gravitational waves must be extremely close to that of electromagnetic waves. The velocities of the solar system, of the Milky Way or the Local Group’s motion relative to the cosmic microwave background (CMB) frame indicate an anisotropy of the universe observed from the solar system. This anisotropy contradicts the cosmological principle, and is not taken into account in the ΛCDM model. Nevertheless, the results of the Planck mission from 2018 clearly show that there is a CMB anisotropy, which can be described by a dipole with an amplitude of around 3.36 Millikelvin. This dipole is interpreted as the result of a Doppler effect due to the movement of the solar system in relation to the source of the CMB: the solar system is moving with a velocity of 370 kilometres per second and the Local Group is moving with a velocity of more than 600 kilometres per second, which is around two parts per million of the speed of light.Aghanim N. Akrami Y. Arroja F. Ashdown M. Aumont J. Baccigalupi C. Ballardini M. Banday A. J. Barreiro R. B. Bartolo N. Basak S. Battye R. Benabed K. Bernard J.-P. Bersanelli M. 2020-09-01 Planck 2018 results – I. Overview and the cosmological legacy of Planck – 29. Cosmic Microwave Background https://www.aanda.org/articles/aa/abs/2020/09/aa33880-18/aa33880-18.html Astronomy & Astrophysics en 641 2–3 10.1051/0004-6361/201833880 0004-6361 thumb|right|JADES-GS-z14-0 taken with the Near-Infrared Spectrograph of the James Webb Space Telescope. In January 2024 the very young and very far galaxis JADES-GS-z14-0 was found with the Near-Infrared Spectrograph (NIRSpec) of the James Webb Space Telescope (JWST). This galaxy assumed to be in a state 290 million years after the big bang. Its redshift measured with the well-known Lyman alpha break at a wavelength about 1.8 micrometres has a value of a good 14, which is a very high value for an astronomical object, but much lower than that of the cosmic microwave background.2024-05-30 Stefano Carniani, Kevin Hainline NASA’s James Webb Space Telescope Finds Most Distant Known Galaxy https://webbtelescope.org/contents/early-highlights/nasas-james-webb-space-telescope-finds-most-distant-known-galaxy webbtelescope.org The high redshift cannot be explained by the ΛCDM model. In March 2025 it was published that the galaxy JADES-GS-z14-0 indicates oxygen in its electromagnetic spectrum at 7.7 micrometres, which according to the ΛCDM model should not be present at the time of the universe.Helton Jakob M. Rieke George H. Alberts Stacey Wu Zihao Eisenstein Daniel J. Hainline Kevin N. Carniani Stefano Ji Zhiyuan Baker William M. Bhatawdekar Rachana Bunker Andrew J. Cargile Phillip A. Charlot Stéphane Chevallard Jacopo D’Eugenio Francesco 2025-05-07 Photometric detection at 7.7 μm of a galaxy beyond redshift 14 with JWST/MIRI https://www.nature.com/articles/s41550-025-02503-z Nature Astronomy en 9 5 729–740 10.1038/s41550-025-02503-z 2397-3366 In February 2024, a study explained the anomalies in the rotation curves of more than hundred spiral galaxies of different types from the SPARC (Spitzer Photometry and Accurate Rotation Curves) Galaxy collection taken with the Spitzer Space Telescope, by accounting for retarded gravitational potentials of baryonic matter that is accreted by the galaxies, and without taking into account any dark matter or modifying general relativity.Glass Yuval Zimmerman Tomer Yahalom Asher 2024-02-20 Retarded Gravity in Disk Galaxies https://www.preprints.org/manuscript/202402.1088/v1 Symmetry en 16 4 387 10.3390/sym16040387 2073-8994Wagman Michal Lawrence Paul Horwitz Asher Yahalom Retardation theory of eleven galaxies Physica Scripta en 99 10 2024-09-01 1402-4896 10.1088/1402-4896/ad6c8d https://iopscience.iop.org/article/10.1088/1402-4896/ad6c8d 2025-06-07 In December 2025 it was confirmed that the gamma ray burst GRB 250314A with a redshift of 7.3 is linked to a supernova during the era of re-ionisation around 730 million years after Big Bang. The gamma ray burst was detected in March 2025 by the Space-based multi-band astronomical Variable Objects Monitor (VOM), and its afterglow was observed by the James Webb Space Telescope (JWST).Levan A. J. Schneider B. Floc’h E. Le Brammer G. Tanvir N. R. Malesani D. B. Martin-Carrillo A. Rossi A. Saccardi A. Sneppen A. Vergani S. D. An J. Atteia J.-L. Bauer F. E. Buat V. 2025-12-01 JWST reveals a supernova following a gamma-ray burst at z ≃ 7.3 https://www.aanda.org/articles/aa/abs/2025/12/aa56581-25/aa56581-25.html Astronomy & Astrophysics en 704 L8 10.1051/0004-6361/202556581 0004-6361Cordier B. Wei J. Y. Tanvir N. R. Vergani S. D. Malesani D. B. Fynbo J. P. U. Postigo A. de Ugarte Saccardi A. Daigne F. Atteia J.-L. Godet O. Götz D. Qiu Y. L. Schanne S. Xin L. P. 2025-12-01 SVOM GRB 250314A at z ≃ 7.3: An exploding star in the era of re-ionization https://www.aanda.org/articles/aa/abs/2025/12/aa56580-25/aa56580-25.html Astronomy & Astrophysics en 704 L7 10.1051/0004-6361/202556580 0004-6361 This discovery poses another very serious challenge to the ΛCDM model, as according to this model, events that produce heavy elements, such as supernovae, cannot have occurred in this early phase of the universe. In April 2026 Andreas Malcherek published his book on "Gravitation und Elektromagnetismus – Eine Alternative zur allgemeinen Relativitätstheorie" ("Gravity and Electromagnetism – An Alternative to the General Theory of Relativity", an English version of this book is supposed to be published later). He has developed a new theory of gravity that builds on the basic work of Oliver HeavisideOliver Heaviside: A gravitational and electromagnetic analogy, The Electrician, vol.31, pp. 281–282 (part I), p. 359 (part II), 1893 and Oleg D. Jefimenko.Oleg D. Jefimenko: Causality, electromagnetic induction, and gravitation : a different approach to the theory of electromagnetic and gravitational fields, Electret Scientific Co., Star City, West Virginia, 1992 It passes all tests of general relativity and provides new insights into its astrophysical applications without requiring the use of dark matter or dark energy. Instead, the theory uses gravitomagnetic field equations with retarded gravitational potentials in Minkowski spacetime to formulate a relativistic theory of gravitomagnetism.Andreas Malcherek: Gravitation und Elektromagnetismus – Eine Alternative zur allgemeinen Relativitätstheorie, Springer Vieweg, Wiesbaden, April 2026, DOI 978-3-658-49807-8, Softcover ISBN 978-3-658-49806-1 thumb|right|Image of MoM-BH*-1 taken by the James Webb Space Telescope (JWST). In August 2026, images taken by the James Webb Space Telescope (JWST) in the constellation Cetus revealed a candidate for a quasi-star, designated MoM-BH*-1, which has a mass of more than one million solar masses and, with a redshift of almost eight, poses yet another major challenge to the ΛCDM model.Naidu Rohan P. etal A gas-enshrouded and gas-reddened black hole at cosmic dawn Nature Springer Science and Business Media LLC 656 8127 2026-08-12 0028-0836 10.1038/s41586-026-10846-4 329–333 42587117 13468124 2026Natur.656..329N en References