On 14th September 2015, a transient gravitational wave (GW150914) was detected by the two LIGO detectors at Hanford and Livingston from the coalescence of a binary black hole system located at a distance of about 400 Mpc. We point out that GW150914 experienced a Shapiro delay due to the gravitational potential of the mass distribution along the line of sight of about 1800 days. Also, the near-simultaneous arrival of gravitons over a frequency range of about 100 Hz within a 0.2 second window allows us to constrain any violations of Shapiro delay and Einstein's equivalence principle between the gravitons at different frequencies. From the calculated Shapiro delay and the observed duration of the signal, frequency-dependent violations of the equivalence principle for gravitons are constrained to an accuracy of $\mathcal{O}(10^{-9})$
There are several shortcomings in the "standard" Shapiro delay tests of the equivalence principle on cosmological scales \cite{minazzoli:2019pr}. Although many people in the community already acknowledged this in the literature, and proposed alternative ways to compare potential Shapiro delays over cosmological scales -- e.g. \cite{bartlett:2021pr,hashimoto:2021pr} and references therein -- papers are still submitted to journals with the usual issues.
The problem of determining the post-Newtonian parameter $γ$ in massive scalar-tensor theories is considered. We demonstrate equivalent correspondence between the post-Newtonian parameter $γ$ and the parameter appearing in the equation of null geodysic in massive scalar-tensor theories. We show that massive scalar-tensor theories can be distinguished from general relativity based on the predictions of Shapiro time delay. All calculations are presented using hybrid metric-Palatini f(R)-gravity as an example. The expression for Shapiro time delay in hybrid f(R)-gravity is obtained for the first t…
On 22nd September 2017, the IceCube Collaboration detected a neutrino with energy of about 290 TeV from the direction of the gamma-ray blazar TXS 0506+056, located at a distance of about 1.75 Gpc. During the same time, enhanced gamma-ray flaring was also simultaneously observed from multiple telescopes, giving rise to only the second coincident astrophysical neutrino/photon observation after SN 1987A. We point out that for this event, both neutrinos and photons encountered a Shapiro delay of about 6300 days along the way from the source. From this delay and the relative time difference between…
The gravitational time delay of light, also called the Shapiro time delay, is one of the four classical tests of Einstein's theory of general relativity. This article derives the Newtonian version of the Shapiro time delay from Einstein's principle of equivalence and the Newtonian description of gravity, in a manner that is accessible to undergraduate students and advanced high-school students. The derivation can be used as a pedagogical tool, similar to the way that simplified derivations of the gravitational deflection of light are used in teaching about general relativity without making use…
Shapiro time delay is one of the fundamental tests of general relativity and post-Newtonian theories of gravity. Consequently, its measurements can be used to probe the parameter $γ$ which is related to spacetime curvature produced by a unit mass in the post-Newtonian formalism of gravity. To date all measurements of time delay have been conducted on astronomical scales. It was asserted in 2010 that gravitational wave detectors on Earth could be used to measure Shapiro delay on a terrestrial scale via massive rotating systems. Building on that work, we consider how measurements of Shapiro dela…
The "Shapiro delay" experienced by an astronomical messenger traveling through a gravitational field has been used to place constraints on possible deviations from the equivalence principle. The standard Shapiro delay used to obtain these constraints is not itself an observable in general relativity, but is rather obtained by comparing with a fiducial Euclidean distance. There is not a mapping between the constraints obtained in this manner and alternative theories that exhibit equivalence principle violations. However, even assuming that the comparison with the fiducial Euclidean distance is …
The Shapiro effect, also known as the gravitational time delay, is close kin to the gravitational deflection of light that was the central topic of our Summer School. It is also an interesting test bed for exploring a topic that provides the foundations for most of the calculations we have done in this school, yet is highly complex when treated more rigorously: the question of the Newtonian limit, and of the post-Newtonian corrections that must be applied to include the leading-order effects of general relativity. This contribution discusses simplified derivations for the gravitational redshif…
This paper is based on the study of the paper of Scardigli and Casadio [Eur. Phys. J. C (2015) 75:425] where the authors computed the light deflection and perihelion precession for the Generalized Uncertainty Principle (GUP) modified Schwarzschild metric. In the present work, we computed the gravitational tests such as Shapiro time delay, gravitational redshift, and geodetic precession for the GUP modified Schwarzschild metric. Using the results of Solar system experiments and observations, we obtain upper bounds for the GUP parameter $β$. Finally, we compare our bounds with other bounds in th…
Ultralight axion like particles (ALPs) of mass $m_a\in (10^{-21}\rm{eV}-10^{-22}\rm{eV})$ with axion decay constant $f_a\sim 10^{17}\rm{GeV}$ can be candidates for fuzzy dark matter (FDM). If celestial bodies like Earth and Sun are immersed in a low mass axionic FDM potential and if the ALPs have coupling with nucleons then the coherent oscillation of the axionic field results a long range axion hair outside of the celestial bodies. The range of the axion mediated Yukawa type fifth force is determined by the distance between the Earth and the Sun which fixes the upper bound of the mass of axio…
In this paper, we apply the classical test of general relativity on a charged Weyl black hole, whose exterior geometry is defined by altering the spherically symmetric solutions of 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 …
Alternative theories of gravity not only modify the polarization contents of the gravitational wave, but also affect the motions of the stars and the energy radiated away via the gravitational radiation. These aspects leave imprints in the observational data, which enables the test of General Relativity and its alternatives. In this work, the Nordtvedt effect and the Shapiro time delay are calculated in order to constrain Horndeski theory using the observations of lunar laser ranging experiments and Cassini time-delay data. The effective stress-energy tensor is also obtained using the method o…
Theories of gravity that obey the Weak Equivalence Principle have the same Parametrised Post-Newtonian parameter $γ$ for all particles at all energies. The large Shapiro time delays of extragalactic sources allow us to put tight constraints on differences in $γ$ between photons of different frequencies from spectral lag data, since a non-zero $Δγ$ would result in a frequency-dependent arrival time. The majority of previous constraints have assumed that the Shapiro time delay is dominated by a few local massive objects, although this is a poor approximation for distant sources. In this work we …
Finsler geometry is a natural and fundamental generalization of Riemann geometry. The Finsler structure depends on both coordinates and velocities. We present the arrival time delay of astroparticles subject to Lorentz violation in the framework of Finsler geometry, and the result corresponds to that derived by Jacob and Piran in the standard model of cosmology.
The Double Pulsar, PSR J0737-3039A/B, has offered a wealth of gravitational experiments in the strong-field regime, all of which GR has passed with flying colours. In particular, among current gravity experiments that test photon propagation, the Double Pulsar probes the strongest spacetime curvature. Observations with MeerKAT and, in future, the SKA can greatly improve the accuracy of current tests and facilitate tests of NLO contributions in both orbital motion and signal propagation. We present our timing analysis of new observations of PSR J0737-3039A, made using the MeerKAT telescope over…
We study the local causality issue via the Shapiro time-delay computations in the on-shell consistent exotic massive gravity in three dimensions. The theory shows time-delay as opposed to time-advance despite having a ghost at the linearized level both for asymptotically flat and anti-de Sitter spacetimes. We also prove a Birkhoff-like theorem: any solution with a hypersurface orthogonal non-null Killing vector field is conformally flat; and find some exact solutions.
Gravitational time advancement effect in Bumblebee gravity for Earth bound systems
Zel’dovich International Center for Astrophysics, M. Akmullah Bashkir State Pedagogical University（泽尔多维奇天体物理国际中心，M·阿克穆拉·巴什基尔国立师范学院）；Institute of Molecule and Crystal Physics, Ufa Federal Research Centre, Russian Academy of Sciences（俄罗斯科学院乌法联邦研究中心分子与晶体物理研究所）；Department of Physics & Astronomy, Bashkir State University（巴什基尔国立大学物理与天文系）；High Energy Cosmic Ray Research Center, University of North Bengal（北孟加拉大学高能宇宙射线研究中心）
In this paper we investigate the relation between the potential and geometric time delays in gravitational lensing. In the original paper of Shapiro (1964), it is stated that there is a time delay in the radar signals between Earth and Venus that pass near a massive object (the Sun), compared to the path taken in the absence of any mass. The reason for this delay is connected with the influence of gravity on the coordinate velocity of a light ray in a gravitational potential. The contribution from the change of the path length, which happens to be of second order, is considered as negligible. …
Since Lorentz invariance plays an important role in modern physics, it is of interest to test the possible Lorentz invariance violation (LIV). The time-lag (the arrival time delay between light curves in different energy bands) of Gamma-ray bursts (GRBs) has been extensively used to this end. However, to our best knowledge, one or more particular cosmological models were assumed {\it a priori} in (almost) all of the relevant works in the literature. So, this makes the results on LIV in those works model-dependent and hence not so robust in fact. In the present work, we try to avoid this proble…
Einstein's General Relativity (GR) is the basis of modern astronomy and astrophysics. Testing the validity of basic assumptions of GR is important. In this work, we test a possible violation of the Weak Equivalence Principle (WEP), i.e., there might be a time-lag between photons of different frequencies caused by the effect of gravitational fields if the speeds of photons are slightly different at different frequencies. We use Fast Radio Bursts (FRBs) , which are astronomical transients with millisecond timescales detected in the radio frequency range. Being at cosmological distances, accumula…
The Einstein's weak equivalence principle (WEP) is one of the foundational assumptions of general relativity and some other gravity theories. In the theory of parametrized post-Newtonian (PPN), the difference between the PPN parameters $γ$ of different particles or the same type of particle with different energies, $Δγ$, represents the violation of WEP. Current constraints on $Δγ$ are derived from the observed time delay between correlated particles of astronomical sources. However, the observed time delay is contaminated by other effects, such as the time delays due to different particle emis…
