Predictions Of General Relativity Research Articles

Uncertainty relations and precession of perihelion

We compute the corrections to the Schwarzschild metric necessary to reproduce the Hawking temperature derived from a Generalized Uncertainty Principle (GUP), so that the GUP deformation parameter is directly linked to the deformation of the metric. Using this modified Schwarzschild metric, we compute corrections to the standard General Relativistic predictions for the perihelion precession for planets in the solar system, and for binary pulsars. This analysis allows us to set bounds for the GUP deformation parameter from well-known astronomical measurements.

Erratum: Post-Newtonian, quasicircular binary inspirals in quadratic modified gravity [Phys. Rev. D85, 064022 (2012)

We consider a general class of quantum gravity-inspired, modified gravity theories, where the Einstein-Hilbert action is extended through the addition of all terms quadratic in the curvature tensor coupled to scalar fields with standard kinetic energy. This class of theories includes Einstein-Dilaton-Gauss-Bonnet and Chern-Simons modified gravity as special cases. We analytically derive and solve the coupled field equations in the post-Newtonian approximation, assuming a comparable-mass, spinning black hole binary source in a quasi-circular, weak-field/slow-motion orbit. We find that a naive subtraction of divergent piece associated with the point-particle approximation is ill-suited to represent compact objects in these theories. Instead, we model them by appropriate effective sources built so that known strong-field solutions are reproduced in the far-field limit. In doing so, we prove that black holes in Einstein-Dilaton-Gauss-Bonnet and Chern-Simons theory can have hair, while neutron stars have no scalar monopole charge, in diametrical opposition to results in scalar-tensor theories. We then employ techniques similar to the direct integration of the relaxed Einstein equations to obtain analytic expressions for the scalar field, metric perturbation, and the associated gravitational wave luminosity measured at infinity. We find that scalar field emission mainly dominates the energy flux budget, sourcing electric-type (even-parity) dipole scalar radiation and magnetic-type (odd-parity) quadrupole scalar radiation, correcting the General Relativistic prediction at relative -1PN and 2PN orders. Such modifications lead to corrections in the emitted gravitational waves that can be mapped to the parameterized post-Einsteinian framework. Such modifications could be strongly constrained with gravitational wave observations.

What is Time and What Causes Time?

The explanation of time” from a totally new perspective and discover the real cause of time is done will bring to light the reason behind many predictions of Special and General Relativity. By knowing what is time and what is its cause you will discover why time slows with motion and in gravity.

RCSLenS: testing gravitational physics through the cross-correlation of weak lensing and large-scale structure

The unknown nature of dark energy motivates continued cosmological tests of large-scale gravitational physics. We present a new consistency check based on the relative amplitude of non-relativistic galaxy peculiar motions, measured via redshift-space distortion, and the relativistic deflection of light by those same galaxies traced by galaxy-galaxy lensing. We take advantage of the latest generation of deep, overlapping imaging and spectroscopic datasets, combining the Red Cluster Sequence Lensing Survey (RCSLenS), the Canada-France-Hawaii Telescope Lensing Survey (CFHTLenS), the WiggleZ Dark Energy Survey and the Baryon Oscillation Spectroscopic Survey (BOSS). We quantify the results using the "gravitational slip" statistic E_G, which we estimate as 0.48 +/- 0.10 at z=0.32 and 0.30 +/- 0.07 at z=0.57, the latter constituting the highest redshift at which this quantity has been determined. These measurements are consistent with the predictions of General Relativity, for a perturbed Friedmann-Robertson-Walker metric in a Universe dominated by a cosmological constant, which are E_G = 0.41 and 0.36 at these respective redshifts. The combination of redshift-space distortion and gravitational lensing data from current and future galaxy surveys will offer increasingly stringent tests of fundamental cosmology.

Testing gravity with EG: mapping theory onto observations

We present a complete derivation of the observationally motivated definition of the modified gravity statistic EG. Using this expression, we investigate how variations to theory and survey parameters may introduce uncertainty in the general relativistic prediction of EG. We forecast errors on EG for measurements using two combinations of upcoming surveys, and find that theoretical uncertainties may dominate for a futuristic measurement. Finally, we compute predictions of EG under modifications to general relativity in the quasistatic regime, and comment on the pros and cons of using EG to test gravity with future surveys.

Gravity Probe B data analysis: III. Estimation tools and analysis results

This paper provides detailed descriptions of the numerical estimation algorithms used to fit physics-based models to the data from the Gravity Probe B spacecraft, as well as the scientific results of the experiment, and the statistical and systematic uncertainties. The first paper in this series of three data analysis papers derives the mathematical expressions for the signals to be analyzed, and the second paper deals with science data acquisition and their preparation for the relativistic drift rate estimation. The data from each of the four gyroscopes are partitioned into six segments, each spanning several weeks to several months. These segments are first analyzed individually to check the validity of the mathematical models and the accuracy of the estimation routine by examining the consistency of the relativistic drift rate estimates from each of these 24 gyro-segments. Then, the drift rate estimates and uncertainties are calculated for each individual gyroscope and for the four gyroscopes combined. These results are presented and compared with each other and with the prediction of general relativity.

Proportional helium thrusters for Gravity Probe B

The Gravity Probe B (GP-B) satellite used electrostatically suspended gyroscopes to test two predictions of general relativity. Here, we describe the satellite’s proportional thrusters, which utilized boil-off helium gas for attitude and translation Control (ATC). The evolution of the design and its successful effect on orbit performance is reported.

The three-fold theoretical basis of the Gravity Probe B gyro precession calculation

The Gravity Probe B (GP-B) experiment is complete and the results are in agreement with the predictions of general relativity (GR) for both the geodetic precession, 6.6 arcsec yr−1 to about 0.3%, and the Lense–Thirring precession, 39 marcsec to about 19%. This note is concerned with the theoretical basis for the predictions. The predictions depend on three elements of gravity theory, firstly that macroscopic gravity is described by a metric theory such as GR, secondly that the Lense–Thirring metric provides an approximate description of the gravitational field of the spinning Earth, and thirdly that the spin axis of a gyroscope is parallel displaced in spacetime, which gives its equation of motion. We look at each of these three elements to show how each is solidly based on previous experiments and well-tested theory. The agreement of GP-B with theory strengthens our belief that all three elements are correct and increases our confidence in applying GR to astrophysical phenomena. Conversely, if GP-B had not verified the predictions a major theoretical quandary would have occurred.

The Gravity Probe B gyroscope

The Gravity Probe B (GP-B) gyroscope, a unique cryogenically operated mechanical sensor, was used on-orbit to independently test two predictions of general relativity (GR). Here, we describe the development and performance of the GP-B gyroscope, its geometry and fabrication, spin-up and vacuum approach, magnetic considerations, and static charge management. The history of electrically suspended gyroscopes puts the current work in context. Fabrication and ground testing of the GP-B gyroscope are detailed, followed by a review of on-orbit initialization, calibration, operation, and performance. We find that the performance was degraded relative to the mission goals, but was still sufficient to provide excellent new tests of GR. The degradation is partially due to the existence of gyroscope torques due to an unanticipated interaction between patch potentials on the rotor and the housing. We discuss these patch potentials and describe the effect of related torques on gyro drift. It was essential to include models for the effects due to the patch potentials in the complete data analysis model to yield determinations of the two GR effects.

The Gravity Probe B test of general relativity

The Gravity Probe B mission provided two new quantitative tests of Einstein’s theory of gravity, general relativity (GR), by cryogenic gyroscopes in Earth’s orbit. Data from four gyroscopes gave a geodetic drift-rate of −6601.8 ± 18.3 marc-s yr−1 and a frame-dragging of −37.2 ± 7.2 marc-s yr−1, to be compared with GR predictions of −6606.1 and −39.2 marc-s yr−1 (1 marc-s = 4.848 × 10−9 radians). The present paper introduces the science, engineering, data analysis, and heritage of Gravity Probe B, detailed in the accompanying 20 CQG papers.

Gravity Probe B data analysis: I. Coordinate frames and analysis models

Gravity Probe B (GP-B) was a cryogenic, space-based experiment testing the geodetic and frame-dragging predictions of Einstein's theory of general relativity (GR) by means of gyroscopes in Earth orbit. This first of three data analysis papers reviews the GR predictions and details the models that provide the framework for the relativity analysis. In the second paper we describe the flight data and their preprocessing. The third paper covers the algorithms and software tools that fit the preprocessed flight data to the models to give the experimental results published in Everitt et al (2011 Phys. Rev. Lett. 106 221101–4).

Precision attitude control of the Gravity Probe B satellite

The Gravity Probe B satellite used ultra-precise gyroscopes in low Earth orbit to compare the orientation of the local inertial reference frame with that of distant space in order to test predictions of general relativity. The experiment required that the Gravity Probe B spacecraft have milliarcsecond-level attitude knowledge for the science measurement, and milliarcsecond-level control to minimize classical torques acting on the science gyroscopes. The primary sensor was a custom Cassegrainian telescope, which measured the pitch and yaw angles of the experiment package with respect to a guide star. The spacecraft rolled uniformly about the direction to the guide star, and the roll angle was measured by star trackers. Attitude control was performed with sixteen proportional thrusters that used boil-off from the experiment’s liquid Helium cryogen as propellant. This paper summarizes the attitude control system’s design and on-orbit performance.

Hydrogen Burning in Low Mass Stars Constrains Scalar-Tensor Theories of Gravity.

The most general scalar-tensor theories of gravity predict a weakening of the gravitational force inside astrophysical bodies. There is a minimum mass for hydrogen burning in stars that is set by the interplay of plasma physics and the theory of gravity. We calculate this for alternative theories of gravity and find that it is always significantly larger than the general relativity prediction. The observation of several low mass red dwarf stars therefore rules out a large class of scalar-tensor gravity theories and places strong constraints on the cosmological parameters appearing in the effective field theory of dark energy.

Testing general relativity on accelerators

Within the general theory of relativity, the curvature of spacetime is related to the energy and momentum of the present matter and radiation. One of the more specific predictions of general relativity is the deflection of light and particle trajectories in the gravitational field of massive objects. Bending angles for electromagnetic waves and light in particular were measured with a high precision. However, the effect of gravity on relativistic massive particles was never studied experimentally. Here we propose and analyze experiments devoted to that purpose. We demonstrate a high sensitivity of the laser Compton scattering at high energy accelerators to the effects of gravity. The main observable – maximal energy of the scattered photons – would experience a significant shift in the ambient gravitational field even for otherwise negligible violation of the equivalence principle. We confirm predictions of general relativity for ultrarelativistic electrons of energy of tens of GeV at a current level of resolution and expect our work to be a starting point of further high-precision studies on current and future accelerators, such as PETRA, European XFEL and ILC.

Gravitational tests of the generalized uncertainty principle

We compute the corrections to the Schwarzschild metric necessary to reproduce the Hawking temperature derived from a Generalized Uncertainty Principle (GUP), so that the GUP deformation parameter is directly linked to the deformation of the metric. Using this modified Schwarzschild metric, we compute corrections to the standard General Relativistic predictions for the light deflection and perihelion precession, both for planets in the solar system and for binary pulsars. This analysis allows us to set bounds for the GUP deformation parameter from well-known astronomical measurements.

Solution for a local straight cosmic string in the braneworld gravity

In this work we deal with the spacetime shaped by a straight cosmic string, emerging from local gauge theories, in the braneworld gravity context. We search for physical consequences of string features due to the modified gravitational scenario encoded in the projected gravitational equations. It is shown that cosmic strings in braneworld gravity may present significant differences when compared to the general relativity predictions since its linear density is modified and the deficit angle produced by the cosmic string is attenuated. Furthermore, the existence of cosmic strings in that scenario requires a strong restriction to the braneworld tension: $\lambda \geq 3 \times 10^{-17}$, in Planck units.

Neutron interference in the gravitational field of a ring laser

The neutron split-beam interferometer has proven to be particularly useful in measuring Newtonian gravitational effects such as those studied by Colella, Overhauser, and Werner (COW). The development of the ring laser has led to numerous applications in many areas of physics including a recent general relativistic prediction of frame dragging in the gravitational field produced by the electromagnetic radiation in a ring laser. This paper introduces a new general technique based on a canonical transformation of the Dirac equation for the gravitational field of a general linearized spacetime. Using this technique it is shown that there is a phase shift in the interference of two neutron beams due to the frame-dragging nature of the gravitational field of a ring laser.

On claims that general relativity differs from Newtonian physics for self-gravitating dusts in the low velocity, weak field limit

Galaxy rotation curves are generally analyzed theoretically using Newtonian physics; however, two groups of authors have claimed that for self-gravitating dusts, general relativity (GR) makes significantly different predictions to Newtonian physics, even in the weak field, low velocity limit. One group has even gone so far as to claim that nonlinear general relativistic effects can explain flat galactic rotation curves without the need for cold dark matter. These claims seem to contradict the well-known fact that the weak field, low velocity, low pressure correspondence limit of GR is Newtonian gravity, as evidenced by solar system tests. Both groups of authors claim that their conclusions do not contradict this fact, with Cooperstock and Tieu arguing that the reason is that for the solar system, we have test particles orbiting a central gravitating body, whereas for a galaxy, each star is both an orbiting body and a contributor to the net gravitational field, and this supposedly makes a difference due to nonlinear general relativistic effects. Given the significance of these claims for analyses of the flat galactic rotation curve problem, this article compares the predictions of GR and Newtonian gravity for three cases of self-gravitating dusts for which the exact general relativistic solutions are known. These investigations reveal that GR and Newtonian gravity are in excellent agreement in the appropriate limits, thus supporting the conventional use of Newtonian physics to analyze galactic rotation curves. These analyses also reveal some sources of error in the referred to works.

Quantum viewpoint of quadratic f(R) gravity, constraints, vacuum-to-vacuum transition amplitude and particle content

We investigate, from a quantum viewpoint, the nature of the linearized quadratic \(f(R)=(R+aR^2)\)-gravity. To derive the explicit expression of the underlying propagator of the theory, the field is coupled to an external energy–momentum \(T^{\mu \nu }\), and an auxiliary field is introduced to deal with gauge constraints as done in gauge theories. In particular for a conserved \(T^{\mu \nu }\), we establish the gauge invariance of the vacuum-to-vacuum transition amplitude \(\langle 0_+|0_-\rangle \), and prove the necessary positivity condition \(|\langle 0_+|0_-\rangle |^2 0\), required by the quantum theory aspect of the treatment. An exact expression is then derived of the number of particles emitted, at a given energy, by a circularly oscillating Nambu string from which we may compare the relative number of the spin 0 massive particles emitted to the graviton number which turns up to give a clear cut departure from the general relativity prediction.

New results for electromagnetic quasinormal and quasibound modes of Kerr black holes

The perturbations of the Kerr metric and the miracle of their exact solutions play a critical role in the comparison of predictions of general relativity with astrophysical observations of compact massive objects. The differential equations governing the late-time ring-down of the perturbations of the Kerr metric, the Teukolsky Angular Equation and the Teukolsky Radial Equation, can be solved analytically in terms of confluent Heun functions. In this article, we solve numerically the spectral system formed by those exact solutions and we obtain the electromagnetic (EM) spectra of the Kerr black hole. Because of the novel direct way of imposing the boundary conditions, one is able to discern three different types of spectra: the well-known quasinormal modes (QNM), the symmetric with respect to the real axis quasibound modes (QBM) and a spurious spectrum who is radially unstable. This approach allows clearer justification of the term "spurious" spectrum, which may be important considering the recent interest in the spectra of the electromagnetic counterparts of events producing gravitational waves.