Classical Tests Of General Relativity Research Articles

GLADE: Gravitational Light-Bending Astrometry Dual-Satellite Experiment

Light bending is one of the classical tests of general relativity and is a crucial aspect to be taken into account for accurate assessments of photon propagation. In particular, high-precision astrometry can constrain theoretical models of gravitation in the weak field limit applicable to the Sun neighborhood. We propose a concept for experimental determination of the light deflection close to the Sun in the 10−7 to 10−8 range, in a modern rendition of the 1919 experiment by Dyson, Eddington and Davidson, using formation flying to generate an artificial long-lasting eclipse. The technology is going to be demonstrated by the forthcoming ESA mission PROBA3. The experimental setup includes two units separated by 150 m and aligned to the mm level: an occulter and a small telescope (0.3 m diameter) with an annular field of view covering a region 0∘.7 from the Sun. The design is compatible with a space weather payload, merging several instruments for observation of the solar corona and environment. We discuss the measurement conditions and the expected performance.

Fundamental physics with a state-of-the-art optical clock in space

Recent advances in optical atomic clocks and optical time transfer have enabled new possibilities in precision metrology for both tests of fundamental physics and timing applications. Here we describe a space mission concept that would place a state-of-the-art optical atomic clock in an eccentric orbit around Earth. A high stability laser link would connect the relative time, range, and velocity of the orbiting spacecraft to earthbound stations. The primary goal for this mission would be to test the gravitational redshift, a classical test of general relativity, with a sensitivity 30 000 times beyond current limits. Additional science objectives include other tests of relativity, enhanced searches for dark matter and drifts in fundamental constants, and establishing a high accuracy international time/geodesic reference.

A test of general relativity with ESA’s JUICE mission

The ESA’s JUICE mission is planned for launch in April 2023. After a 8.3-year interplanetary cruise it will reach the Jovian system in mid 2031. The mission is devoted to the study of Jupiter and three of the Galilean moons (Europa, Callisto and Ganymede). The 3GM (Geodesy and Geophysics of Jupiter and the Galilean Moons) radio-science package onboard the spacecraft comprises a Ka-band Transponder (KaT) that will enable a highly stable two-way coherent Ka/Ka link to study the gravity fields of the three Jovian satellites and their internal structure, and an Ultra Stable Oscillator (USO) to probe the atmosphere of Jupiter and the ionospheres of the three moons. The KaT can be used together with the onboard Deep Space Transponder (DST), enabling a full multi-frequency radio link system capable to suppress the dispersive noise, due to solar plasma and ionospheric effects, at nearly all solar elongation angles. The cruise phase of the mission provides three opportunities to perform classical tests of general relativity by measuring the relativistic time-delay and the frequency shift experienced by radio signals during superior solar conjunctions. A similar experiment, performed by Cassini in 2002, provided the most accurate measurement of the post-Newtonian parameter γ so far, with an accuracy of 2.3×10-5. The MORE experiment onboard the ESA/JAXA BepiColombo mission to Mercury is expected to improve the result obtained by Cassini up to a factor of 10 while orbiting the planet. Less significant improvements are expected in the cruise phase. The advanced radio-tracking system of JUICE and the favorable dynamical environment experienced in the outer solar system make a repetition of the Cassini and BepiColombo cruise experiments quite significant. In this work, we show the results of numerical simulations of JUICE superior conjunction experiments. We have found that 3GM can estimate γ with an accuracy at the level of 4.8×10-7, which represents a constraint on the value of γ 50 times tighter than the one obtained by Cassini and about four times better than the expected result from BepiColombo at the end of the mission.

Solar system tests in Einstein–æther gravity

In the current paper we analyse the three classical tests of general relativity, namely, the precession of perihelion, deflection of light, and time delay in Einstein–æther gravity. Einstein–æther gravity has two static, spherically symmetric, charged black hole solutions corresponding to different constraints on its coupling constants c14 and c123. We investigate the aforementioned tests for both these solutions, graphically and analytically. We also tabulate our results and discuss the outcome, which is promising. We evaluate the results, when the coupling constants are varied over a vast range of values, both within the constraints set by the recent observational data, and also beyond, for a comparative study.

Classical tests of general relativity II: looking to the past to understand the present

The objective of this second part of the work is to present heuristic derivations of the three classical tests of general relativity. These derivations are based on the Einstein equivalence principle and use Newtonian physics as a theoretical framework. The results obtained are close to Einstein’s original predictions. Historical and anecdotal aspects of the subject are also discussed.

Classical tests of general relativity I: looking to the past to understand the present

Einstein’s theory of general relativity (GR) provides the best available description of gravity. The recent detection of gravitational waves and the first picture of a black hole have provided spectacular confirmations of GR, as well as arousing substantial interest in topics related to gravitation. However, to understand present and future discoveries, it is convenient to look to the past, to the classical tests of GR, namely, the deflection of light by the Sun, the perihelion precession of Mercury, and the gravitational redshift of light. The objective of this work is to offer a non-technical introduction to the classical tests of GR. In this first part of the work, some basic concepts of relativity are introduced and the principle of equivalence is analysed. The second part of the article examines the classical tests.

Dilaton-Axion Black Hole under the Solar System Tests

In the present paper we study the static and spherically symmetric dilaton-axion black hole in the testing ground of the Solar system. We constrain the parameters of the string motivated dilaton-axion form of the classical tests of general relativity, viz., the perihelion precession of the planet Mercury and the deflection of light by the Sun. In this case we have two free parameters: the dilaton strength and the point of curvature singularity of black hole. We obtain the permissible range of these two parameters from theoretical analysis based on the model and later compare them with the observations.

Classical tests on a charged Weyl black hole: bending of light, Shapiro delay and Sagnac effect

In this paper, we apply the classical test of general relativity on a charged Weyl black hole, the exterior geometry of which is defined by altering the spherically symmetric solutions of the Weyl conformal theory of gravity. The tests are basically founded on scrutinizing the angular geodesics of light rays propagating in the gravitating system caused by the black hole. In this investigation, we bring detailed discussions about the bending of light, together with two other relativistic effects, known as the Shapiro and the Sagnac effects. We show that the results are in good conformity with the general relativistic effects, in addition to giving long-distance corrections caused by the cosmological nature of the background geometry under study.

Solar system tests in Rastall gravity

In this paper, we have investigated the classical tests of General Relativity like precession of perihelion, deflection of light and time delay by considering a phenomenological astrophysical object like Sun, as a neutral regular Hayward black hole in Rastall gravity. We have tabulated all our results for some appropriate values of the parameter [Formula: see text]. We have compared our values with [Formula: see text], which corresponds to the Schwarzschild case. Also the value of [Formula: see text] is of particular interest as it gives some promising results.

Gravitational lensing, precession of periapsis and time delay due to wormhole in quintessence polytropic spacetime

The classical tests of General Relativity, namely, precession of periapsis, deflection of light and time delay serve to establish observational evidence for the theory of general relativity, so they are considered for several spherically symmetric astrophysical objects. In this paper, we investigate a stationary, spherically symmetric wormhole supported by a quintessence polytropic energy satisfying a polytropic equation of state: [Formula: see text], where [Formula: see text] is the polytropic index and [Formula: see text] is a positive constant such that [Formula: see text]. The solution of such an equation admits the negative null energy, which is the key ingredient for sustaining traversable wormholes. Motivated by the above-mentioned classical tests, we perform similar studies to explore the range of polytropic index [Formula: see text] which gives us promising results. The advance of periapsis with respect to a test particle and angle of deflection is calculated graphically for those values of [Formula: see text] which cannot be obtained analytically. The time delay has also been calculated numerically and tabulated.

Gravity between Newton and Einstein

Statements about relativistic effects are often subtle. In this essay we will demonstrate that the three classical tests of general relativity, namely perihelion precession, deflection of light and gravitational redshift, are passed perfectly by an extension of Newtonian gravity that includes gravitational time dilation effects while retaining a non-relativistic causal structure. This non-relativistic gravity theory arises from a covariant large speed of light expansion of Einstein’s theory of gravity that does not assume weak fields and which admits an action principle.

Geometrization of Newtonian Dynamics

Riemann’s principle “force equals geometry” provided the basis for Einstein’s General Relativity - the geometric theory of gravitation. In this paper, we follow this principle to derive the dynamics for any conservative force. We introduce the relativity of spacetime : an object lives in its own spacetime, whose geometry is determined by all of the forces affecting it. We also introduce the Generalized Principle of Inertia which unifies Newton’s first and second laws and states that: An inanimate object moves freely, that is, with zero acceleration, in its own spacetime. We derive the metric of an object’s spacetime in two ways. The first way uses conservation of energy to derive a Newtonian metric. We reveal a physical deficiency of this metric (responsible for the inability of Newtonian dynamics to account for relativistic behavior), and remove it. The dynamics defined by the corrected Newtonian metric leads to a new Relativistic Newtonian Dynamics (RND) for both massive objects and massless particles moving in any static, conservative force field, not necessarily gravitational. In the case of the gravitational field of a static, spherically symmetric mass distribution, this metric turns out to be the Schwarzschild metric. This dynamics reduces in the weak field, low velocity limit to classical Newtonian dynamics and also exactly reproduces the classical tests of General Relativity. In the second way, we obtain the RND metric directly, without first obtaining a Newtonian metric. Instead of conservation of energy, we use conservation of angular momentum, a carefully defined Newtonian limit and Tangherlini’s condition. The non-static case is handled by applying Lorentz covariance to the static case.

New metrics of a spherically symmetric gravitational field passing classical tests of general relativity

A general form of a metric preserving all symmetries of a spherically symmetric gravitational field and angular momentum in spherical coordinates is obtained. Such metric may have . The Newtonian limit uniquely defines g00(r). Geodesic motion under such metric exactly reproduces the precession of a planetary orbit, periastron advance of a binary, deflection of light and Shapiro time delay if the determinant of the time-radial parts of the metric is –1. In this model, the total time for a radial round trip of light is as in the Schwarzschild model, but it allows for light rays to have different speeds propagating toward or from the massive object. The value of g01(r) could be obtained by measuring these speeds. If , the metric does not satisfy Einstein's field equations far from the source.

Relativity from the geometrization of Newtonian dynamics

Based on the Generalized Principle of Inertia, which states that: An inanimate object moves freely, that is, with zero acceleration, in its own spacetime, whose geometry is determined by all of the forces affecting it, we geometrize Newtonian dynamics for any conservative force. For an object moving in a spherically symmetric force field, using a variational principle, conservation of angular momentum and a classical limit, we construct a metric with respect to which the object's worldline is a geodesic. For the gravitational field of a static, spherically symmetric mass, this metric is the Schwarzschild metric. The resulting dynamics reduces in the weak-field, low-velocity limit to classical Newtonian dynamics and exactly reproduces the classical tests of general relativity. We propose a method to extend the theory to handle a gravitational field generated by several sources.

A geometric relativistic dynamics under any conservative force

Riemann’s principle “force equals geometry” provided the basis for Einstein’s General Relativity — the geometric theory of gravitation. In this paper, we follow this principle to derive the dynamics for any static, conservative force. The geometry of spacetime of a moving object is described by a metric obtained from the potential of the force field acting on it. We introduce a generalization of Newton’s First Law — the Generalized Principle of Inertia stating that: An inanimate object moves inertially, that is, with constant velocity, in its own spacetime whose geometry is determined by the forces affecting it. Classical Newtonian dynamics is treated within this framework, using a properly defined Newtonian metric with respect to an inertial lab frame. We reveal a physical deficiency of this metric (responsible for the inability of Newtonian dynamics to account for relativistic behavior), and remove it. The dynamics defined by the corrected Newtonian metric leads to a new Relativistic Newtonian Dynamics for both massive objects and massless particles moving in any static, conservative force field, not necessarily gravitational. This dynamics reduces in the weak field, low velocity limit to classical Newtonian dynamics and also exactly reproduces the classical tests of General Relativity, as well as the post-Keplerian precession of binaries.

Solar system tests in constraining parameters of dyon black holes

In the present paper we examine the possibility of constraining dyon black holes based on the available observational data at the scale of the Solar system. For this we consider the classical tests of general relativity, viz., the perihelion precession of the planet Mercury and the deflection of light by the Sun. In connection to mathematical analysis we are considering static and spherically symmetric dyon black hole which carries both the electric and magnetic charge simultaneously, which are encoded it by the parameters lambda _0 and beta _0. We constrain these two parameters using the Solar system tests and obtain the permissible range from theoretical analysis based on our model and later on compare them with the available observational data.

Determination of angle of light deflection in higher-derivative gravity theories

Gravitational light deflection is known as one of three classical tests of general relativity and the angle of deflection may be computed explicitly using approximate or exact solutions describing the gravitational force generated from a point mass. In various generalized gravity theories, however, such explicit determination is often impossible due to the difficulty in obtaining an exact expression for the deflection angle. In this work, we present some highly effective globally convergent iterative methods to determine the angle of semiclassical gravitational deflection in higher- and infinite-derivative formalisms of quantum gravity theories. We also establish the universal properties that the deflection angle always stays below the classical Einstein angle and is a strictly decreasing function of the incident photon energy, in these formalisms.

Quadratic curvature terms and deformed Schwarzschild–de Sitter black hole analogues in the laboratory

Sound waves on a fluid stream, in a de Laval nozzle, are shown to correspond to quasinormal modes emitted by black holes that are physical solutions in a quadratic curvature gravity with cosmological constant. Sound waves patterns in transsonic regimes at a laboratory are employed here to provide experimental data regarding generalized theories of gravity, comprised by the exact de Sitter-like solution and a perturbative solution around the Schwarzschild–de Sitter standard solution as well. Using the classical tests of General Relativity to bound free parameters in these solutions, acoustic perturbations on fluid flows in nozzles are then regarded, to study quasinormal modes of these black holes solutions, providing deviations of the de Laval nozzle cross-sectional area, when compared to the Schwarzschild solution. The fluid sonic point in the nozzle, for sound waves in the fluid, is shown to implement the acoustic event horizon corresponding to quasinormal modes.

Probing topologically charged black holes on brane worlds in $$f(\mathrm {R})$$ f ( R ) bulk

The perihelion precession, the deflection of light and the radar echo delay are classical tests of General Relativity here used to probe brane-world topologically charged black holes in a f(R) bulk. Moreover, such tests are used to constrain the parameter that arises from the Shiromizu–Maeda–Sasaki procedure applied to a f(R) bulk. Observational data constrain the possible values of the tidal charge parameter and the effective cosmological constant in this context. We show that the observational/experimental data for both perihelion precession and radar echo delay make the black hole parameters to be more strict than the ones for the DMPR black hole. Moreover, the deflection of light constrains the tidal charge parameter similarly as the DMPR black holes, due to a peculiarity in the equation of motion.

Classroom reconstruction of the Schwarzschild metric

A promising way to introduce general relativity (GR) in the classroom is to study the physical implications of certain given metrics, such as the Schwarzschild one. This involves lower mathematical expenditure than an approach focusing on differential geometry in its full glory and permits to emphasize physical aspects before attacking the field equations. Even so, in terms of motivation, lacking justification of the metric employed may pose an obstacle. The paper discusses how to establish the weak-field limit of the Schwarzschild metric with a minimum of relatively simple physical assumptions, avoiding the field equations but admitting the determination of a single parameter from experiment. An attractive experimental candidate is the measurement of the perihelion precession of Mercury, because the result was already known before the completion of GR. It is shown how to determine the temporal and radial coefficients of the Schwarzschild metric to sufficiently high accuracy to obtain quantitative predictions for all the remaining classical tests of GR.