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Local Spacetime Dynamics, the Einstein-Straus Vacuole and the PIONEER Anomaly: a New Access to These Problems

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Local Spacetime Dynamics, the Einstein-Straus Vacuole and the PIONEER Anomaly: a New Access to These Problems Local Spacetime Dynamics, the Einstein-Straus Vacuole and the PIONEER Anomaly: A New Access to these Problems Hans-J¨org Fahr and Mark Siewert Argelander-Institut f¨ur Astronomie, Abt. Astrophysik, Auf dem H¨ugel 71, D-53121 Bonn, Germany Reprint requests to Prof. H.-J. F.; E-mail: [email protected] Z. Naturforsch. 62a, 117 – 126 (2007); received December 8, 2006 The question concerning the extent of the local spacetime has often been raised. At what circum- solar distance the well known Robertson-Walker spacetime of our expanding universe may become a valid approximation? Inside of that distance a local Schwarzschild metric, which permits to explain the Keplerian motions of planets within the frame of general relativity, must be applicable. We briefly analyze the historical answer to that question given by Einstein, Straus and their followers and show that till now this answer is unsatisfactory in many respects. We revisit the problem of local spacetime geometries in the light of their effects on local pho- ton propagation in view of the radiopropagation phenomena detected with the NASA spaceprobes PIONEER-10/11, waiting for a satisfying answer for several decades now. Comparing radiosignals outgoing from the earth to the probe and ingoing again from the probe to the receiver on earth do show anomalous frequency shifts which presently find no explanation by anomalous non-Newtonian decel- erations of these probes. Therefore we study cosmological conditions for the transfer of radiosignals between the earth and these distant probes based on time dependent local spacetime geometries. First we study the cosmological redshift of radiophotons during their propagation to the spaceprobe and show that this shift in fact explains the registered PIONEER phenomenon under the assumption that the full cosmological expansion of the universe also takes place locally. Though yielding the right magnitude, one finds that this assumption leads to a redshift instead of the observed blueshift. We then, however, show that theoretically motivated forms of time dependent local spacetime metrices in fact lead to a blueshift of the needed magnitude. The appropriate local space vacuole is charac- terized by a Schwarzschild metric of a central mass increasing with cosmic time. Though it is clear that further studies of this effect have to be carried out to give more credit and verification to this hypothetical result, nevertheless more careful hightech radiotracking of freely flying spaceprobes may do a usefull job in confirming a completely unexpected, but cosmologically highly relevant phenomenon. Key words: Cosmology; General Relativity; Local Systems. 1. Introduction Perhaps the most obvious argument against the vac- uole concept is the fact that its radius 1.1. The Problem of Local Spacetime Metrics 1/3 = 3M , Since more than sixty years there exists a solution rES (1) 4πρ0 for the general relativistic connection between grav- itationally bound systems, such as the solar system, for a present-day cosmic matter density ρm − and the freely expanding cosmological space. This so- 10 30 g/cm3 and typical solar masses M 1030 kg, lution is known as the Einstein-Straus vacuole (ES turns out to be much too large compared to the mean vacuole), since it was first studied by Einstein and distance between any of two neighbouring central Straus [1, 2] and their successors [3, 4]. While this masses, and the vacuoles created by, say, two neigh- result was widely accepted as an adequate solution bouring suns in the milky way inevitably overlap. And to the underlying problem, there are both observa- since the Einstein field equations are nonlinear, two tional, e. g. [5, 6], and theoretical, e. g. [7], hints to neighbouring vacuoles may not simply be linearly su- fundamental problems related to the Einstein-Straus perposed. Such an overlap also contradicts the initial metric. assumptions made in [1], where the vision occurred 0932–0784 / 07 / 0300–0117 $ 06.00 c 2007 Verlag der Zeitschrift f¨ur Naturforschung, T¨ubingen · http://znaturforsch.com 118 H.-J. Fahr and M. Siewert · Local Spacetime Dynamics that the entire universe might be filled by such discrete residual decelerations, besides some 10 percent fluc- (non-overlapping) vacuoles. The present-day view is tuations, remained constant for all the ongoing PIO that smaller objects, such as suns and galaxies, are em- itineraries to larger distances, i. e. seemed to prove as bedded in the static spacetime of a much larger vac- being independent of the solar distance, orientation and uole (see, e. g. [8]), usually the vacuole of a larger time. structure, which is usually identified as the surround- A large number of proposals, how these anoma- ing galaxy cluster. However, inside a vacuole there is lous decelerations could be explained, have meanwhile no cosmological expansion, which would destroy the been made, see e. g. [16, 17] or [18]. These propos- perhaps best established and most trusted cosmologi- als mainly focus on classical and conservative physi- cal instrument, Hubbles redshift distance relation. In cal effects like friction forces with interplanetary dust other words, if gravitationally bound systems are em- grains, asymmetric thermal emission from the probe bedded in a vacuole of the Einstein-Straus type, then or an accelerated motion of the whole solar system in most cosmological objects should, in first approxima- the direction normal to the ecliptic. In addition, fur- tion, not be redshifted at all. ther deceleration effects were considered, such as the A more recent attempt to solve this problem is the helicity-rotation coupling of the spacecraft [19, 20] or inclusion of the cosmological constant Λ [9 – 11], an additional, general relativistic accelerations [21], al- additional cosmological parameter connected to the though they all turned out to be systematically too vacuum energy, which was invented and then rejected small and/or position dependent to explain the ob- by Einstein and which resurfaced only on account of served effect. More speculative reasons were also dis- more recent observations [12 – 14]. The cosmological cussed, like effects caused by dark matter or vacuum constant reduces the Einstein-Straus radius by a factor energy gravity contributions [11], but none of these of about 2 [5], which is by far not enough to abolish proposed explanations up to now could fit the observed the mentioned underlying problem. magnitude and the distance independence of the mea- sured anomalous deceleration. 1.2. Local Spacetime and the PIONEER Anomaly For this reason, more recently also purely cosmo- logical causes for the existing anomalous decelera- In this paper we let ourselves be challenged by tion have been added to the ongoing discussions, see the PIONEER anomaly (or PIONEER effect, subse- e. g. [22 – 26]. These cosmological reasons of the PIO quently abbreviated by PIO), which has been per- anomaly are all connected with the highly problem- ceived as one of the most important unsolved prob- atic question of how much the cosmological expansion lems in modern physics (see e. g. [15]). For at least of the universe may touch our local spacetime metrics two decades it is known that deep spaceprobes (most near the sun [7, 11, 27], which in turn is closely re- prominently the PIO-10 and -11 missions) seem to lated to the problem of the ES vacuole introduced in experience an anomalous deceleration towards the the first part of this section. One of the more promising sun [16, 17]. While other spaceprobes, such as Galileo ideas so far has been applied recently by Petry [24, 25], and Ulysses [17], also seem to observe this effect, the who seems to be able to explain the PIO anomaly in PIO spacecrafts are nevertheless the most appropriate terms of an additional frequency shift, which occurs ones for dynamical trajectory studies, since their spin on account of the time dilatation during the propaga- stabilization and their great distances to the earth re- tion of the photon. His ansatz is built on a variant grav- quire only a minimum of artificial earth-attitude reori- itational theory [28, 29], which, for weak gravitational entations. This permits very precise Newtonian accel- fields, becomes identical with Einstein’s general rel- eration estimates down to the level of 10−10 cm/s2. ativistic field equations [25]. We now adopt a mod- Since about 1980, when PIO-10 moved at solar dis- ification of the standard cosmological representation tances larger than 20 AU (astronomical units) and the which is trimmed to be “as close as possible” to the Newtonian solar gravitational pull dropped to levels standard model. We critically analyze several possible −8 2 of as ≤ 5 · 10 cm/s , the NASA Jet Propulsion Lab modifications of this ES concept, attempting to repro- (JPL) orbit determination program (ODP) found un- duce a pseudo-cosmological frequency shift of radio- modelled accelerations with a systematic residual level photons in a vacuole, which would be able to fix both −8 2 of aPIO −(8.74 ± 1.33) · 10 cm/s directed to- problems, the redshift of distant photons and the ob- wards the sun. Interestingly enough, the level of these served blueshift of the PIO spacecrafts. This attempt H.-J. Fahr and M. Siewert · Local Spacetime Dynamics 119 is motivated by the observational fact that the PIO Comparing this result with the PIO frequency shift (2), phenomenon, which is almost exclusively termed as we derive the relation anomalous deceleration, (which would turn out to be a t an illusion from this paper) is nicely represented by ∆ν = −ν PIO i = ν H t . (6) 0 c 0 0 i the cosmological quantity aPIO H0c,whereH0 de- notes the present-day Hubble constant, which is of the This finally leads to the time-, distance- and direction- order of 70 km/s/Mpc [14, 30].
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