The Weiss variational principle in mechanics and classical field theory is a variational principle which allows displacements of the boundary. We review the Weiss variation in mechanics and classical field theory, and present a novel geometric derivation of the Weiss variation for the gravitational action: the Einstein-Hilbert action plus the Gibbons-Hawking-York boundary term. In particular, we use the first and second variation of area formulas (we present a derivation accessible to physicists in an appendix) to interpret and vary the Gibbons-Hawking-York boundary term. The Weiss variation for the gravitational action is in principle known to the Relativity community, but the variation of area approach formalizes the derivation, and facilitates the discussion of time evolution in General Relativity. A potentially useful feature of the formalism presented in this article is that it avoids an explicit 3+1 decomposition in the bulk spacetime.
The Weiss variation of the Einstein-Hilbert action with an appropriate boundary term has been studied for general boundary surfaces; the boundary surfaces can be spacelike, timelike, or null. To achieve this we introduce an auxiliary reference connection and find that the resulting Weiss variation yields the Einstein equations as expected, with additional boundary contributions. Among these boundary contributions, we obtain the dynamical variable and the associated conjugate momentum, irrespective of the spacelike, timelike or, null nature of the boundary surface. We also arrive at the general…
A method of calculation for the variational derivatives for gravitational actions in the pseudo-Riemannian case is proposed as a practical variant of the first order formalism with constraints. The method is then used to derive the metric field equations for a generic $f(R)$ model.
We derive formulae for the time variation of the gravitational ``constant'' and of the fine structure ``constant'' in various models with extra dimensions and analyze their consistency with the observational data.
Our main aim in this paper is to promote the coframe variational method as a unified approach to derive field equations for any given gravitational action containing the algebraic functions of the scalars constructed from the Riemann curvature tensor and its contractions. We are able to derive a master equation which expresses the variational derivatives of the generalized gravitational actions in terms of the variational derivatives of its constituent curvature scalars. Using the Lagrange multiplier method relative to an orthonormal coframe, we investigate the variational procedures for modif…
In the framework of 10-dimensional "Friedmann-Calabi-Yau" cosmology of superstring origin we show that the time variation of either Newton's gravitational constant or Yang-Mills one is unavoidable in the present epoch.
As one knows, strong discrepancies are found between the different precise measurements of the gravitational constant carried out in Earth-based laboratories. While the precision are increasing in different laboratories and with various methods, these measurements are even more and more discordant. We have shown since 2002 that an improved 5D Kaluza-Klein (KK) theory may provide a satisfactory explanation to these discrepancies by referring to the geomagnetic field as a possible cause. Here we take advantage of different precise measurements performed at the same location but at different epoc…
We consider a cosmological model with a variable gravitational constant, G, based on a scalar-tensor theory. Using the recent observational data for the Hubble diagram of type Ia supernovae (SNeIa) we find a phenomenological expression describing the variation of G. The corresponding variation of the fine structure constant αwithin multidimensional theories is also computed and is shown not to support known constraints on Δα/ α.
The Machian cosmological solution satisfying $ϕ=O(ρ/ω)$ for the perfect-fluid with negative pressure is discussed. When the coefficient of the equation of state $γ\to -1/3$, the gravitational constant approaches to constant. If we assume the present mass density $ρ_{0}\sim ρ_{c}$ (critical density), the parameter $ε$ ($γ=(ε-1)/3$) has a value of order $10^{-3}$ to support the present gravitational constant. The closed model is valid for $ω<-3/2ε$ and exhibits the slow accelerating expansion. We understand why the coupling parameter $| ω|$ is so large ($ω\sim -10^{3}$). The time-variation of th…
A D-dimensional gravitational model with Gauss-Bonnet term is considered. When ansatz with diagonal cosmological type metrics is adopted, we find solutions with exponential dependence of scale factors (with respect to "synchronous-like" variable) which describe an exponential expansion of "our" 3-dimensional factor-space and obey the observational constraints on the temporal variation of effective gravitational constant G. Among them there are two exact solutions in dimensions D = 22, 28 with constant G and also an infinite series of solutions in dimensions D \ge 2690 with the variation of G o…
A relatively simple method of overcoming the Standard Quantum Limit in the next-generation Advanced LIGO gravitational wave detector is considered. It is based on the quantum variational measurement with a single short (a few tens of meters) filter cavity. Estimates show that this method allows to reduce the radiation pressure noise at low frequencies ($<100 \mathrm{Hz}$) to the level comparable with or smaller than the low-frequency noises of non-quantum origin (mirrors suspension noise, mirrors internal thermal noise, and gravity gradients fluctuations).
We propose a method to constrain the variation of the gravitational constant $G$ with cosmic time using gravitational-wave (GW) observations of merging binary neutron stars. The method essentially relies on the fact that the maximum and minimum allowed masses of neutron stars at a particular cosmic epoch has a simple dependence on the value of $G$ at that epoch. GWs carry an imprint of the value of $G$ at the time of the merger. Thus, if the value of $G$ at merger is significantly different from its current value, the masses of the neutron stars inferred from the GW observations will be incons…
The possible variation of the electromagnetic fine structure constant $α_e$ on cosmological scales arouses great interests in recent years. The strongly lensed gravitational waves and the electromagnetic counterparts could be used to test this variation. Under the assumption that the speed of photon could be modified, while the speed of GW is the same as GR predicated, and they both propagate in a flat Friedman-Robertson-Walker universe, we investigate the difference of time delays of the images and derive the upper bound of the variation of $α_e$. For a typical lensing system in the standard …
Experimental projects using spherical antennas to detect gravitational waves are nowdays a concrete reality. The main purpose of this paper is to give a possible way of interpreting output data from such a system. Responses of the five fundamental quadrupole modes and of the six resonators in TIGA collocations are shown as a function of the incoming direction of the incident wave. Then, for a source lying in the galactic plane, sidereal time and galactic longitude dependence is given. Thus, once a candidate source of gravitational waves is considered, we can exactly predict the resonators' res…
We derive a set of equations describing the linear response of the convergence properties of a geodesic congruence to arbitrary geometry variations. It is a combination of equations describing the deviations from the standard Raychaudhuri-type equations due to the geodesic shifts and an equation describing the geodesic shifts due to the geometry variations. In this framework, the geometry variations, which can be chosen arbitrarily, serve as probes to investigate the gravitational contraction processes from various angles. We apply the obtained framework to the case of conformal geometry varia…
A scheme of an optical detector is proposed for checking Einsteins equivalence principle (EEP) in a null gravitational redshift experiment and for testing methods for calculating the length of a resonator in a weak variable gravitational field by recording the variations of the difference frequency of resonators caused by lunisolar variations of the geopotential in a double or a two-resonator laser system.
To clarify certain nonlinear properties of strong gravitational field, we investigate cylindrically symmetric gravitational waves that are localized as regular wave packets in the space of radial and time coordinates. The waves are constructed by applying a certain kind of harmonic mapping method to the seed solutions with linear polarization, which are generalizations of the solution representing a cylindrical gravitational pulse wave discussed by Weber-Wheeler and Bonnor. The solutions obtained here, though their form is rather simple, show occurrence of strong mutual conversion between a li…
Constructing a well-posed variational principle is a non-trivial issue in general relativity. For spacelike and timelike boundaries, one knows that the addition of the Gibbons-Hawking-York (GHY) counter-term will make the variational principle well-defined. This result, however, does not directly generalize to null boundaries on which the 3-metric becomes degenerate. In this work, we address the following question: What is the counter-term that may be added on a null boundary to make the variational principle well-defined? We propose the boundary integral of $2 \sqrt{-g} \left( Θ+κ\right)$ as …
The intracavity topologies of laser gravitational-wave detectors are the promising way to obtain sensitivity of these devices significantly better than the Standard Quantum Limit (SQL). The most challenging element of the intracavity topologies is the \emph{local meter} which has to monitor position of a small ($1\div10$ gram) local mirror and which precision defines the sensitivity of the detector. To overcome the SQL, the quantum variational measurement can be used in the local meter. In this method a frequency-dependent correlation between the meter back-action noise and measurement noise i…
I prove an old unsolved conjecture, the hard part of its obvious sufficiency, namely that all identically conserved symmetric two-tensors are necessarily metric variations of invariant actions, thus sparing the world more alternative gravity theories. The proof is reasonably simple, if perhaps a physicist's.
A new variational approach for general relativity and modified theories of gravity is presented. In addition to the metric tensor, two independent affine connections enter the action as dynamical variables. In the matter action the dependence upon one of the connections is left completely unspecified. When the variation is applied to the Einstein-Hilbert action the Einstein field equations are recovered. However when applied to $f(R)$ and Scalar-Tensor theories, it yields gravitational field equations which differ from their equivalents obtained with a metric or Palatini variation and reduce t…
We present an alternative nonconservative gravitational theory based on the Herglotz variational principle in a fully covariant form. The present model may be seen as an improvement of the theory proposed in Ref. [Lazo et al, Phys. Rev. D 95, 101501 (2017)], whose resulting theory is meaningful just in particular coordinate systems. In the present work, we report a new theory that is free from such a restriction. It is also obtained using the Herglotz variational principle and by taking advantage of the restricted equivalence between Lagrangian functions in the scope of such action principle. …
We examine the variational and conformal structures of higher order theories of gravity which are derived from a metric-connection Lagrangian that is an arbitrary function of the curvature invariants. We show that the constrained first order formalism when applied to these theories may lead consistently to a new method of reduction of order of the associated field equations. We show that the similarity of the field equations which are derived from appropriate actions via this formalism to those produced by Hilbert varying purely metric Lagrangians is not merely formal but is implied by the dif…
We apply a regularized Rudin-Osher-Fatemi total variation (TV) method to denoise the transient gravitational wave signal GW150914. We have previously applied TV techniques to denoise numerically generated grav- itational waves embedded in additive Gaussian noise, obtaining satisfactory results irrespective of the signal morphology or astrophysical origin. We find that the non-Gaussian, non-stationary noise from the gravitational wave event GW150914 can also be successfully removed with TV-denoising methods. The quality of the de- noised waveform is comparable to that obtained with the Bayesian…
We use big bang nucleosynthesis bounds on the variation of the gravitational coupling to derive constraints on the strength of the deviation from the gravitational inverse-square law due to tensor and vector unparticle exchange.
We investigate the variation of the gravitational constant $G$ over the history of the Universe by modeling the effects on the evolution and asteroseismology of the low-mass star KIC 7970740, which is one of the oldest (~11 Gyr) and best-observed solar-like oscillators in the Galaxy. From these data we find $\dot{G}/G = (1.2 \pm 2.6) \times 10^{-12}~\text{yr}^{-1}$, that is, no evidence for any variation in $G$. We also find a Bayesian asteroseismic estimate of the age of the Universe as well as astrophysical S-factors for five nuclear reactions obtained through a 12-dimensional stellar evolut…
Considering the fact that the present universe might have been formed out of a system of ficticious self-gravitating particles, fermionic in nature, each of mass $m$, we are able to obtain a compact expression for the radius $R_0$ of the universe by using a model density distribution $ρ(r)$ for the particles which is singular at the origin. This singularity in $ρ(r)$ can be considered to be consistent with the socalled Big Bang theory of the universe. By assuming that Mach's principle holds good in the evolution of the universe, we determine the number of particles, $N$, of the universe and it…
Recently, several deep learning methods are proposed for the gravitational wave data analysis. One is conditional variational auto encoder (CVAE), proposed by Gabbard et al. [1]. We study the accuracy of a CVAE in the context of the estimation of the QNM frequency of the ringdown. We show that the accuracy of the estimation by the CVAE is better than the matched filtering. The areas of confidence regions are also compared and it is shown that the CVAE can return smaller confidence regions. Also, we assess the reliability of the confidence regions estimated by the CVAE. Our work confirms that t…
We describe new methods for denoising and detection of gravitational waves embedded in additive Gaussian noise. The methods are based on Total Variation denoising algorithms. These algorithms, which do not need any a priori information about the signals, have been originally developed and fully tested in the context of image processing. To illustrate the capabilities of our methods we apply them to two different types of numerically-simulated gravitational wave signals, namely bursts produced from the core collapse of rotating stars and waveforms from binary black hole mergers. We explore the …
A model is proposed, according to which the metric tensor field in the standard gravitational Lagrangian is decomposed into a projection (generally - with a non-zero covariant derivative) tensor field, orthogonal to an arbitrary 4-vector field and a tensor part along the same vector field. A theorem has been used, according to which the variation and the partial derivative, when applied to a tensor field, commute with each other if and only if the tensor field and its variation have zero covariant derivatives, provided also the connection variation is zero. Since the projection field obviously…
In extensions of general relativity and in theories aiming at unifying gravity with the forces of the Standard Model, the value of the "fundamental constants" is often determined by the vacuum expectation value of new fields, which may thus change in different backgrounds. Variations of fundamental constants with respect to the values measured today in laboratories on Earth are expected to be more evident on cosmological timescales and/or in strong gravitational fields. In this paper, I show that the analysis of the K$α$ iron line observed in the X-ray spectrum of black holes can potentially b…
We perform a detailed analysis on a primordial gravitational-wave background amplified during a Kasner-like pre-inflationary phase allowing for general triaxial anisotropies. It is found that the predicted angular distribution map of gravitational-wave intensity on large scales exhibits topologically distinctive patterns according to the degree of the pre-inflationary anisotropy, thereby serving as a potential probe for the pre-inflationary early universe with future all-sky observations of gravitational waves. We also derive an observational limit on the amplitude of such anisotropic gravitat…
The recent discovery of a $γ$-ray counterpart to a gravitational wave event has put extremely stringent constraints on the speed of gravitational waves at the present epoch. In turn, these constraints place strong theoretical pressure on potential modifications of gravity, essentially allowing only a conformally-coupled scalar to be active in the present Universe. In this paper, we show that direct detection of gravitational waves from optically identified sources can also measure or constrain the strength of the conformal coupling in scalar--tensor models through the time variation of the Pla…
I argue that an angular momentum scale is necessary to explain energy-momentum propagation along a single null geodesic, the scale being known as Planck's constant $(h)$. If $h$ and $c$ (the velocity of light in vacuum), are considered to be given fundamental (constant) scales in local measurements, then the rest mass scale varies exactly inversely as the time scale varies in two different locally flat regions of a curved spacetime. As the time scale variation gives rise to gravitational redshift, the rest mass scale variation leads to a change in the Compton length scale associated with an el…
We present cosmological constraints on the scalar-tensor theory of gravity by analyzing the angular power spectrum data of the cosmic microwave background obtained from the Planck 2015 results together with the baryon acoustic oscillations (BAO) data. We find that the inclusion of the BAO data improves the constraints on the time variation of the effective gravitational constant by more than $10\%$, that is, the time variation of the effective gravitational constant between the recombination and the present epochs is constrained as $G_{\rm rec}/G_0-1 <1.9\times 10^{-3}\ (95.45\%\ {\rm C.L.})$ …
A variation of the gravitational constant over cosmological ages modifies the main sequence lifetimes and white dwarf cooling ages. Using an state-of-the-art stellar evolutionary code we compute the effects of a secularly varying G on the main sequence ages and, employing white dwarf cooling ages computed taking into account the effects of a running G, we place constraints on the rate of variation of Newton's constant. This is done using the white dwarf luminosity function and the distance of the well studied open Galactic cluster NGC 6791. We derive an upper bound G'/G ~ -1.8 10^{-12} 1/yr. T…
We consider the action of exact plane gravitational waves, or pp-waves, on free particles. The analysis is carried out by investigating the variations of the geodesic trajectories of the particles, before and after the passage of the wave. The initial velocities of the particles are non-vanishing. We evaluate numerically the Kinetic energy per unit mass of the free particles, and obtain interesting, quasi-periodic behaviour of the variations of the Kinetic energy with respect to the width $λ$ of the gaussian that represents the wave. The variation of the energy of the free particle is expected…
This work is the first step in a two-part investigation of real-time replica wormholes. Here we study the associated real-time gravitational path integral and construct the variational principle that will define its saddle-points. We also describe the general structure of the resulting real-time replica wormhole saddles, setting the stage for construction of explicit examples. These saddles necessarily involve complex metrics, and thus are accessed by deforming the original real contour of integration. However, the construction of these saddles need not rely on analytic continuation, and our f…
This paper compares three different methods about computing joint terms in on-shell action of gravity, which are identifying the joint term by the variational principle in Dirichlet boundary condition, treating the joint term as the limit contribution of smooth boundary and finding the joint term by local SO(1,$d-1$) transformation. In general metric gravitational theory, we show that the differences between these joint terms are some variational invariants under fixed boundary condition. We also give an explicit condition to judge the existence of joint term determined by variational principl…
We assess total-variation methods to denoise gravitational-wave signals in real noise conditions, by injecting numerical-relativity waveforms from core-collapse supernovae and binary black hole mergers in data from the first observing run of Advanced LIGO. This work is an extension of our previous investigation where only Gaussian noise was used. Since the quality of the results depends on the regularization parameter of the model, we perform an heuristic search for the value that produces the best results. We discuss various approaches for the selection of this parameter, either based on the …
Analysis of transit times in exoplanetary systems accurately provides an instantaneous orbital period, $P(t)$, of their member planets. A long-term monitoring of those transiting planetary systems puts limits on the variability of $P(t)$, which are translated into the constraints on the time variation of the gravitational constant $G$. We apply this analysis to $10$ transiting systems observed by the Kepler spacecraft, and find that $ΔG/G\lesssim 5\times10^{-6}$ for 2009-2013, or $\dot{G}/G \lesssim 10^{-6}\,\mathrm{yr}^{-1}$ if $\dot{G}$ is constant. While the derived limit is weaker than tho…
Here we apply the Generalized Second Law of Thermodynamics (GSL) to black holes accreting and emitting in the present Universe and derive upper limits on the variation in the gravitational constant G. The limits depend on how the gravitational mass M varies with G. Parameterizing M goes as G^n, if n > -1/2 (including n = 0), the GSL applied to the full range of black holes theoretically allowed in the present Universe does not constrain an increase in G but any decrease must be less than about |(1/G) dG/dt| = 10^-52 per second. If n < -1/2, the GSL does not constrain a decrease in G but any in…
We study evolution of a hierarchical four-body (2+2) system composed by a pair of mass-transferring white dwarf binaries. Applying a simplified model around the synchronous state of two inner orbital periods, we newly find that the four body system could settle down to a limit cycle with a small period gap. The period gap generates an amplitude variation of emitted gravitational waves, as a beat effect. Depending on model parameters, the beat period could be 1-10 yr and a large amplitude variation might be observed by space gravitational-wave detectors.
A unique challenge for data analysis with the Laser Interferometer Space Antenna (LISA) is that the noise backgrounds from instrumental noise and astrophysical sources will change significantly over both the year and the entire mission. Variations in the noise levels will be on time scales comparable to, or shorter than, the time most signals spend in the detector's sensitive band. The variation in the amplitude of the galactic stochastic GW background from galactic binaries as the antenna pattern rotates relative to the galactic center is a particularly significant component of the noise vari…
A general $f(\mathcal{R})$ gravitational theory is considered within the Palatini formalism. By applying the variational principle and the usual conditions on the boundary, we show explicitly that a surface term remains such that as in their metric-compatible counterparts, an additional surface term has to be added in the gravitational action, which plays a fundamental role when calculating the entropy of the black hole.
In a recent work, Dai (arXiv:2103.11157) searched for a variability in Newton's constant $G$ using the IGETS based gravitational acceleration measurements. However, this analysis, obtained from $χ^2$ minimization, did not incorporate the errors in the gravitational acceleration measurements. We carry out a similar search with one major improvement, wherein we incorporate these aforementioned errors. To model any possible variation in the gravitational acceleration, we fit the data to four models: a constant value, two sinusoidal models, and finally, a linear model for the variation of gravitat…
In this paper we directly constrain possible spatial variations of the Newtonian gravitational constant G over ranges 0.01-5 AU in various extrasolar multi-planet systems. By means of the third Kepler's law we determine the quantity Γ_ XY=G_X/G_Y for each couple of planets X and Y located at different distances from their parent star: deviations of the measured values of Γfrom unity would signal variations of G. The obtained results for η=1-Γare found to be well compatible with zero within the experimental errors (η/δη= 0.2-0.3). A comparison with an analogous test previously performed in our …
In this paper, we analyze the variation of the gravitational action on a bounded region of spacetime whose boundary contains segments with various characters, including null. We develop a systematic approach to decompose the derivative of metric variations into orthogonal and tangential components with respect to the boundary and express them in terms of variations of geometric objects associated with the boundary hypersurface. We suggest that a double-foliation of spacetime provides a natural and useful set-up for treating the general problem and clarifies the assumptions and results in speci…
We study the effect of short term variations of the evolution of AM CVn systems on their gravitational wave emissions and in particular LISA observations. We model the systems according to their equilibrium mass-transfer evolution as driven by gravitational wave emission and tidal interaction, and determine their reaction to a sudden perturbation of the system. This is inspired by the suggestion to explain the orbital period evolution of the ultra-compact binary systems V407 Vul and RX-J0806+1527 by non-equilibrium mass transfer. The characteristics of the emitted gravitational wave signal are…
