General Relativistic Phenomena Research Articles

On the high accuracy to test dragging of inertial frames with the LARES 2 space experiment

In this paper we treat some aspects of the LARES 2 space experiment to test the general relativistic phenomenon of dragging of inertial frames, or frame-dragging, in particular we discuss some aspects of its relative accuracy which can approach one part in a thousand. We then, once again respond to the criticisms of the author of a recent paper about the accuracy in the measurement of frame-dragging with LARES 2. The claims of such a paper are not reproducible in any independent analyses. Indeed, it claims that the accuracy in the test of frame-dragging, which can be reached by the LARES 2 space experiment, is several orders of magnitude larger than previously estimated in a number of papers. Here we show that such a paper is based on a number of significant misunderstandings and conceptual mistakes. Furthermore, it is puzzling to observe that previous papers by the same author contained completely opposite statements about the accuracy which can be reached using two satellites with supplementary inclinations, such as in the LARES 2 space experiment, and in general with laser-ranged satellites.

Polarized signatures of orbiting hot spots: Special relativity impact and probe of spacetime curvature

Context. The Galactic Center supermassive black hole is well known to exhibit transient peaks of flux density on a daily basis across the spectrum. Recent infrared and millimeter observations have strengthened the case for the association between these flares and circular orbital motion in the vicinity of the event horizon. The strongly polarized synchrotron radiation associated with these events leads to specific observables called QU loops, that is, looping motion in the Stokes QU plane of linear polarization. These patterns have been observed by the Submillimeter Array, VLTI/GRAVITY, and ALMA. Aims. We want to deepen the understanding of the QU loops associated with orbiting hot spots. To this end, we computed such loops in Minkowski and Schwarzschild spacetimes in order to determine which aspects of the observed patterns are due to special- or general-relativistic phenomena. Methods. We considered a parcel of energized plasma in circular motion in Minkowski spacetime and in Keplerian orbit in the Schwarzschild spacetime. We computed, using the GYOTO ray-tracing code, the polarized radiative transfer associated with this orbiting hot spot and derived the evolution of the flux density, astrometry, and Stokes Q and U parameters. Results. We show that QU loops in Minkowski spacetime at low or moderate inclination i ≲ 45° (where i = 0° is a face-on view) share all the qualitative features of Schwarzschild QU loops. There exist QU loops for all setups considered (including for the face-on view and vertical magnetic field), there may be one or two QU loops per orbital period for a vertical magnetic field configuration, and there are always two QU loops in case of a toroidal magnetic field. The simplicity of Minkowski spacetime is a key asset for allowing us to provide analytical formulas that explain the details of this behavior. Moreover, we analyzed the flux variation of the hot spot and show that it is dictated either by the angular dependence of the radiative transfer coefficients or by relativistic beaming. In the former case, this can lead to extreme flux ratios, even at a moderate inclination. Finally, we highlight the increasing mirror asymmetry of the Schwarzschild QU track with increasing inclination and show that this behavior is a specific Schwarzschild feature caused by light bending. Conclusions. Although special-relativistic effects have not been extensively discussed in this context, they are a crucial part in generating the observed QU loops. However, general-relativistic light bending leads to a specific observable feature encoded in the asymmetry of the observed loops, and this feature might allow the spacetime curvature to be quantified.

Einstein's relativity falsified: I. The factor γ can take values larger than √2, which requires a speed of light < c in moving inertial frames

Considering that an Einstein clock can travel at a speed no greater than c, from the principle of relativity, a kinematic time dilation factor can be derived whose value cannot be greater than <mml:math display="inline"> <mml:msqrt> <mml:mn>2</mml:mn> </mml:msqrt> </mml:math> . In fact, however, the kinematic time dilation factor γ can approach an infinite value. This discrepancy demonstrates that the derivation of the kinematic time dilation factor γ in Einstein's special relativity (SR) cannot be physically justified by the principle of relativity, and that it is not physically possible that the speed of light is constant in any frame of reference. The mathematical method of Einstein's SR, which I refer to as the “mathematical method of relativity,” allows the calculation of constant physical values from different quantities of any physical unit and is thus scientifically worthless. Accordingly, it is not surprising that it is possible to predict so-called general relativistic phenomena, e.g., the phenomena observed at the binary pulsar PSR B1913 + 16, just by applying Kepler's second law and simple quantum physical considerations [R. G. Ziefle, Phys. Essays 33, 99 (2020)]. A careful interpretation of interferometer experiments on Earth clearly shows that there is in fact no need for artificial time acceleration by length contraction. However, today's physicists seem to be lost in mathematics. The aim of this paper is to contribute to a physical theory of relativity that does not require mathematical tricks, such as time acceleration (length contraction), space-time curvature, and other mathematical tricks that follow from Einstein's mathematical methods and uphold the illusion that the belief in a constant speed of light c in any frame of reference is physically justified.

Dynamical evolution of the resistive thick accretion Tori around a Schwarzschild black hole

ABSTRACT To study time-dependent phenomena of plasma surrounding a non-rotating black hole with a dipolar magnetic field, we have developed a fully set of 3 + 1 formalism of generalized general relativistic magnetohydrodynamic equations. The general relativistic phenomena, in particular, have been investigated with respect to the Ohm law. Magnetofluid is supposed to flow in three directions and forms a thick disc structure around the central black hole. All physical quantities of the system are functions of three variables: radial distance r, polar angle θ, and time t. The radial, meridional, and time behaviours of all these quantities have been investigated. It has been shown that the electrical conductivity of the fluid is not constant and may be both positive and negative depending on the values of some free parameters. The initially purely rotating non-magnetized plasma in the presence of an external magnetic field gives rise to an azimuthal current density and a charge density measured by the comoving observer. This current generates an electromagnetic field inside the disc which has both poloidal and toroidal components. The dipolar magnetic field lines of the central black hole is able to penetrate the plasma disc, due to the presence of a finite resistivity for the plasma. The accreting plasma pushes them outwards and makes them parallel to the rotation axis of the disc in the meridional plane.

The LARES 2 satellite, general relativity and fundamental physics

LARES 2, successfully launched on July 13, 2022, is a new generation laser-ranged satellite. LARES is an acronym for LAser RElativity Satellite. The first LARES satellite was successfully launched on February 13, 2012 with the ESA-ASI-AVIO launch vehicle VEGA. LARES 2 was injected with extremely high precision onto a high-altitude orbit at about 5900 km altitude with the new ESA-ASI-AVIO launch vehicle VEGA C. Laser-ranged satellites have many applications, including to test Einstein’s theory of general relativity. The main general relativistic phenomenon that LARES 2 will test with high accuracy is the dragging of inertial frames, or frame-dragging. It will also test other aspects and principles of fundamental physics and general relativity, such as the weak equivalence principle at the foundation of viable gravitational theories. Frame-dragging is the name Einstein himself gave in 1913 to an intriguing phenomenon of general relativity which implies that a current of mass-energy, such as the rotation of a body, will generate spacetime curvature. Frame-dragging has a key role in high energy astrophysics, e.g., in the generation of gravitational waves by the collision of two black holes to form a rotating black hole. Frame-dragging by the rotating Earth was measured to a few percent accuracy by combining the data of the satellites LARES, LAGEOS and LAGEOS 2 (Ciufolini et al. in Eur Phys J C 79:872, 2019). LARES 2, thanks to its extremely high injection precision, is projected to improve the test of frame-dragging by at least an order of magnitude. LARES 2 has also relevant applications in space geodesy and geodynamics, e.g., in the study of the shape of the Earth and in the determination of the International Terrestrial Reference Frame (ITRF) by improving the determination of the Earth center of mass and by contributing to a better determination of its rotation axis.

Absurd: Einstein’s special relativity (SR) causes an inconstant speed of light, claiming to explain the consequences of a constant speed c

Einstein was led astray by a physically incorrect calculation by Michelson and Morley in the context of the Michelson‐Morley experiment. For the light beam in the horizontal light path, their calculation yields the claim that [(1 − v/c) × c] + [(1 + v/c) × c] = 2[(1 − v2/c2) × c]. This is incorrect and mathematically increases the horizontal light path 2d 0 by the factor [(1 + v2/c2)], which Einstein’s theory of special relativity corrects by introducing the time dilation factor γ and the length contraction factor 1/γ. When we calculate correctly, the mathematical increase in the length of horizontal light path no longer happens and Einstein’s mathematical corrections of the horizontal light path imply an inconstancy of the speed of light. This means that Einstein’s special relativity is just a mathematical correction of a physical calculation error, not a true physical theory, and it was thus pure chance that Einstein found the physically real kinematic time dilation factor γ. The null result of the Michelson‐Morley experiment, along with the kinematic and gravitational time dilation, must instead be explained by a constant value for the speed c of light with respect to the gravitational potentials of predominant gravitational fields, resulting from the principles of minimum energy and energy conservation. On this basis, it becomes possible to predict so-called general relativistic phenomena, e.g., the precession of Mercury’s perihelion or the phenomena observed in the binary pulsar PSR B1913 + 16, just by applying Kepler’s second law and simple quantum physical considerations. [R. G. Ziefle, Phys. Essays 33, 99 (2020)].

General-relativistic precession in a black-hole binary.

The general-relativistic phenomenon of spin-induced orbital precession has not yet been observed in strong-field gravity. Gravitational-wave observations of binary black holes (BBHs) are prime candidates, as we expect the astrophysical binary population to contain precessing binaries1,2. Imprints of precession have been investigated in several signals3-5, but no definitive identification of orbital precession has been reported in any of the 84 BBH observations so far5-7 by the Advanced LIGO and Virgo detectors8,9. Here we report the measurement of strong-field precession in the LIGO-Virgo-Kagra gravitational-wave signal GW200129. The binary's orbit precesses at a rate ten orders of magnitude faster than previous weak-field measurements from binary pulsars10-13. We also find that the primary black hole is probably highly spinning. According to current binary population estimates, a GW200129-like signal is extremely unlikely, and therefore presents a direct challenge to many current binary-formation models.

Evidence for subdominant multipole moments and precession in merging black-hole-binaries from GWTC-2.1

The LIGO--Virgo--KAGRA collaborations (LVK) produced a catalogue containing gravitational-wave (GW) observations from the first half of the third GW observing run (O3a). This catalogue, GWTC-2.1, includes for the first time a number of \emph{exceptional} GW candidates produced from merging black-hole-binaries with unequivocally unequal component masses. Since subdominant multipole moments and spin-induced orbital precession are more likely to leave measurable imprints on the emitted GW from unequal component mass binaries, these general relativistic phenomena may now be measurable. Indeed, both GW190412 and GW190814 have already shown conclusive evidence for subdominant multipole moments. This provides valuable insights into the dynamics of the binary. We calculate the evidence for subdominant multipole moments and spin-induced orbital precession for all merging black-hole-binaries in GWTC-2.1 that were observed during O3a and show that (a) no gravitational-wave candidate has measurable higher order multipole content beyond $\ell = 3$, (b) in addition to the confident subdominant multipole measurements in GW190412 and GW190814, GW190519\_153544 and GW190929\_012149 show marginal evidence for the $(\ell, |m|) = (3, 3)$ subdominant multipole, (c) GW190521 may have measurable subdominant multipole content and (d) GW190412 may show evidence for spin-induced orbital precession.

Gravitational Wave Signatures of Black Hole Quasinormal Mode Instability.

Black hole (BH) spectroscopy has emerged as a powerful approach to extracting spacetime information from gravitational wave (GW) observed signals. Yet, quasinormal mode (QNM) spectral instability under small scale perturbations has been recently shown to be a common classical general relativistic phenomenon [J. L. Jaramillo et al., Phys. Rev. X 11, 031003 (2021)PRXHAE2160-330810.1103/PhysRevX.11.031003]. This requires assessing its impact on the BH QNM spectrum, in particular on BH QNM overtone frequencies. We conclude (i)perturbed BH QNM overtones are indeed potentially observable in the GW waveform, providing information on small-scale environment BH physics, and (ii)their detection poses a challenging data analysis problem of singular interest for LISA astrophysics. We adopt a twofold approach, combining theoretical results from scattering theory with a fine-tuned data analysis on a highly accurate numerical GW ringdown signal. The former introduces a set of effective parameters (partially relying on a BH Weyl law) to characterize QNM instability physics. The latter provides a proof of principle demonstrating that the QNM spectral instability is indeed accessible in the time-domain GW waveform, though certainly requiring large signal-to-noise ratios. Particular attention is devoted to discussing the patterns of isospectrality loss under QNM instability, since the disentanglement between axial and polar GW parities may already occur within the near-future detection range.

Newtonian quantum gravity and the derivation of the gravitational constant G and its fluctuations

The theory of gravity “Newtonian quantum gravity” (NQG) is an ingeniously simple theory, because it precisely predicts so-called “general relativistic phenomena,” as, for example, that observed at the binary pulsar PSR B1913 + 16, by just applying Kepler’s second law on quantized gravitational fields. It is an irony of fate that the unsuspecting relativistic physicists still have to effort with the tensor calculations of an imaginary four-dimensional space-time. Everybody can understand that a mass that moves through space must meet more “gravitational quanta” emitted by a certain mass, if it moves faster than if it moves slower or rests against a certain mass, which must cause additional gravitational effects that must be added to the results of Newton's theory of gravity. However, today's physicists cannot recognize this because they are caught in Einstein's relativistic thinking and as general relativity can coincidentally also predict these quantum effects by a mathematically defined four-dimensional curvature of space-time. Advanced NQG is also able to derive the gravitational constant G and explains why G must fluctuate. The “string theory” tries to unify quantum physics with general relativity, but as the so-called “general relativistic” phenomena are quantum physical effects, it cannot be a realistic theory. The “energy wave theory” is lead to absurdity by the author.

When will we observe binary black holes precessing?

After eleven gravitational-wave detections from compact-binary mergers, we are yet to observe the striking general-relativistic phenomenon of orbital precession. Measurements of precession would provide valuable insights into the distribution of black-hole spins, and therefore into astrophysical binary formation mechanisms. Using our recent two-harmonic approximation of precessing-binary signals~\cite{Fairhurst:2019_2harm}, we introduce the ``precession signal-to-noise ratio'', $\rho_p$. We demonstrate that this can be used to clearly identify whether precession was measured in an observation (by comparison with both current detections and simulated signals), and can immediately quantify the measurability of precession in a given signal, which currently requires computationally expensive parameter-estimation studies. $\rho_p$ has numerous potential applications to signal searches, source-property measurements, and population studies. We give one example: assuming one possible astrophysical spin distribution, we predict that precession has a one in $\sim 25$ chance of being observed in any detection.

Newtonian quantum gravity

Newtonian Quantum Gravity (NQG) unifies quantum physics with Newton's theory of gravity and calculates the so-called “general relativistic” phenomena more precisely and in a much simpler way than General Relativity, whose complicated theoretical construct is no longer needed. Newton's theory of gravity is less accurate than Albert Einstein's theory of general relativity. Famous examples are the precise predictions of General Relativity at binary pulsars. This is the reason why relativistic physicists claim that there can be no doubt that Einstein's theory of relativity correctly describes our physical reality. With the example of the famous “Hulse-Taylor binary” (also known as PSR 1913 + 16 or PSR B1913 + 16), the author proves that the so-called “general relativistic phenomena” observed at this binary solar system can be calculated without having any knowledge on relativistic physics. According to philosophical and epistemological criteria, this should not be possible, if Einstein's theory of relativity indeed described our physical reality. Einstein obviously merely developed an alternative method to calculate these phenomena without quantum physics. The reason was that in those days quantum physics was not yet generally taken into account. It is not the first time that a lack of knowledge of the underlying physical phenomena has to be compensated by complicated mathematics. Einstein's theory of general relativity indirectly already includes additional quantum physical effects of gravitation. This is the reason why it cannot be possible to unite Einstein's theory of general relativity with quantum physics, unless one uses “mathematical tricks” that make the additional quantum physical effects disappear again in the end.

A new laser-ranged satellite for General Relativity and space geodesy: I. An introduction to the LARES2 space experiment

We introduce the LARES 2 space experiment recently approved by the Italian Space Agency (ASI). The LARES 2 satellite is planned for launch in 2019 with the new VEGA C launch vehicle of ASI, ESA and ELV. The orbital analysis of LARES 2 experiment will be carried out by our international science team of experts in General Relativity, theoretical physics, space geodesy and aerospace engineering. The main objectives of the LARES 2 experiment are gravitational and fundamental physics, including accurate measurements of General Relativity, in particular a test of frame-dragging aimed at achieving an accuracy of a few parts in a thousand, i.e., aimed at improving by about an order of magnitude the present state-of-the-art and forthcoming tests of this general relativistic phenomenon. LARES 2 will also achieve determinations in space geodesy. LARES 2 is an improved version of the LAGEOS 3 experiment, proposed in 1984 to measure frame-dragging and analyzed in 1989 by a joint ASI and NASA study.

Phenomenology of the Lense-Thirring effect in the Solar System: Measurement of frame-dragging with laser ranged satellites

In this paper we respond to the criticisms of “Phenomenology of the Lense-Thirring effect in the Solar System” by Iorio et al. about the general relativistic phenomena of gravitomagnetism and frame-dragging. The claims of the paper by Iorio et al. are not reproducible in any of our independent analyses.

GENERALIZED GENERAL RELATIVISTIC MAGNETOHYDRODYNAMIC EQUATIONS AND DISTINCTIVE PLASMA DYNAMICS AROUND ROTATING BLACK HOLES

To study phenomena of plasmas around rotating black holes, we have derived a set of 3+1 formalism of generalized general relativistic magnetohydrodynamic (GRMHD) equations. Especially, we investigated general relativistic phenomena with respect to the Ohm's law. We confirmed the electromotive force due to the gravitation, centrifugal force, and frame-dragging effect in plasmas near the black holes. These effects are significant only in the local small-scale phenomena compared to the scale of astrophysical objects. We discuss the possibility of magnetic reconnection, which is triggered by one of these effects in a small-scale region and influences the plasmas globally. We clarify the conditions of applicability of the generalized GRMHD, standard resistive GRMHD, and ideal GRMHD for plasmas in black hole magnetospheres.

The principle of relativity and inertial dragging

Mach’s principle and the principle of relativity have been discussed by Hartman and Nissim-Sabat. Several phenomena were said to violate the principle of relativity as applied to rotating motion. These claims have recently been contested by Bhadra and Das. However, neither set of authors allowed for the general relativistic phenomenon of inertial dragging, and no calculation was offered to substantiate their claims. I discuss the possible validity of the principle of relativity for rotating motion within the context of the general theory of relativity and discuss the significance of inertial dragging in this connection. Although my main points are of a qualitative nature, I also provide the necessary calculations to demonstrate how these points arise as consequences of the general theory of relativity.

Gravimagnetism, causality, and aberration of gravity in the gravitational light-ray deflection experiments

Experimental verification of the existence of gravimagnetic fields generated by currents of matter is important for a complete understanding and formulation of gravitational physics. Although the rotational (intrinsic) gravimagnetic field has been extensively studied and is now being measured by the Gravity Probe B, the extrinsic gravimagnetic field generated by the translational current of matter is less well studied. The present paper uses the post-Newtonian parametrized Einstein and light geodesics equations to show that the extrinsic gravimagnetic field generated by the translational current of matter can be measured by observing the relativistic time delay and/or light deflection caused by the moving mass. We prove that the extrinsic gravimagnetic field is generated by the relativistic effect of the aberration of the gravity force caused by the Lorentz transformation of the metric tensor and the Levi–Civita connection. We show that the Lorentz transformation of the gravity field variables is equivalent to the technique of the retarded Lienard–Wiechert gravitational potentials predicting that a light particle is deflected by gravitational field of a moving body from its retarded position so that both general-relativistic phenomena—the aberration and the retardation of gravity—are tightly connected and observing the aberration of gravity proves that gravity has a causal nature. We explain in this framework the 2002 deflection experiment of a quasar by Jupiter where the aberration of gravity from its orbital motion was measured with accuracy 20%. We describe a theory of VLBI experiment to measure the gravitational deflection of radio waves from a quasar by the Sun, as viewed by a moving observer from the geocentric frame, to improve the measurement accuracy of the aberration of gravity to a few percent.

Observational evidences for black-hole existence

Summary. — About forty years ago it was predicted that black holes can be detected as sources of X-ray radiation. Later distortions of spectral lines (Fe Kαline, in particular) for X-ray radiation emitted from the innermost parts of accretion disks were studied. In 1995 these features of Fe Kα-line were discovered with the Japanese ASCA satellite in MCG 6-30-15. Other X-ray missions such as RXTE, XMM-Newton, Chandra, etc. re-discovered features of Fe Kα-lines and other X-ray lines as well. Attempts to fit spectral line shapes lead to conclusions that sometimes the profiles should correspond to radiating regions which are located in the innermost parts of accretion disks where contributions of general relativistic phenomena are extremely important. As an illustration we consider a radiating annulus model to clarify claims about different spectral line profiles. We discuss properties of highly inclined disks and analyze the possibility to evaluate magnetic fields near black-hole horizons.

Is Space Really Expanding? A Counterexample

In all Friedman models, the cosmological redshift is widely interpreted as a consequence of the general-relativistic phenomenon of expansion of space. Other commonly believed consequences of this phenomenon are superluminal recession velocities of distant galaxies, and the distance to the particle horizon greater than ct (where t is the age of the Universe), in apparent conflict with special relativity. Here, we study a particular Friedman model: empty universe. This model exhibits both cosmological redshift, superluminal velocities and infinite distance to the horizon. However, we show that the cosmological redshift is there simply a relativistic Doppler shift. Moreover, apparently superluminal velocities and ‘acausal’ distance to the horizon are in fact a direct consequence of special-relativistic phenomenon of time dilation, as well as of the adopted definition of distance in cosmology. There is no conflict with special relativity, whatsoever. In

Status of numerical relativity

I describe the current status of numerical relativity from my personal point of view. Here, I focus mainly on explaining the numerical implementations necessary for simulating general relativistic phenomena such as the merger of compact binaries and stellar collapse, emphasizing the well-developed current status of such implementations that enable simulations for several astrophysical phenomena. Some of our latest results for simulation of binary neutron star mergers are briefly presented.