Further examples of ''Machian'' effects of rotating bodies in general relativity.
Field equations for metric of stationary rotating bodies in general relativity
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Field equations for metric of stationary rotating bodies in general relativity
The arrival times of the pulses from each pulsar are measured by a cesium clock. The observations are all made at a frequency of 2388 MHz (12.5 cm wavelength) on a 26 m dish antenna. The effect of interstellar charged particles is a random one that increases the noise level on the arrival time measurements. The variation in clock rate is shown consisting of two effects: the time dilation effect of special relativity and the red shift effect of general relativity.
It is shown that if the Hamiltonian constraint of general relativity is imposed as a restriction on the Hamilton principal functional in the classical theory, or on the state functional in the quantum theory, then the momentum constraints are automatically satisfied. This result holds both for closed and open spaces and it means that the full content of the theory is summarized by a single functional equation of the Tomonaga-Schwinger type.
A new model to describe the dynamics of particles undergoing diffusion in general relativity is proposed. The evolution of the particle system is described by a Fokker-Planck equation without friction on the tangent bundle of spacetime. It is shown that the energy-momentum tensor for this matter model is not divergence-free, which makes it inconsistent to couple the Fokker-Planck equation to the Einstein equations. This problem can be solved by postulating the existence of additional matter fields in spacetime or by modifying the Einstein equations. The case of a cosmological scalar field term added to the left hand side of the Einstein equations is studied in some details. For the simplest cosmological model, namely the flat Robertson-Walker spacetime, it is shown that, depending on the initial value of the cosmological scalar field, which can be identified with the present observed value of the cosmological constant, either unlimited expansion or the formation of a singularity in finite time will occur in the future. Future collapse into a singularity also takes place for a suitable small but positive present value of the cosmological constant, in contrast to the standard diffusion-free scenario.
We compare Einstein-Boltzmann solvers that include modifications to general relativity and find that, for a wide range of models and parameters, they agree to a high level of precision. We look at three general purpose codes that primarily model general scalar-tensor theories, three codes that model Jordan-Brans-Dicke (JBD) gravity, a code that models f(R) gravity, a code that models covariant Galileons, a code that models Horava-Lifschitz gravity, and two codes that model nonlocal models of gravity. Comparing predictions of the angular power spectrum of the cosmic microwave background and the power spectrum of dark matter for a suite of different models, we find agreement at the subpercent level. Furthermore this means that this suite of Einstein-Boltzmann solvers is now sufficiently accurate for precision constraints on cosmological and gravitational parameters.
We consider the observation of stellar-mass black holes binaries with the Laser Interferometer Space Antenna(LISA). Preliminary results based on Fisher information matrix analyses have suggested that gravitational waves from those sources could be very sensitive to possible deviations from the theory of general relativity (GR) andfrom the strong equivalence principle during the low-frequency binary inspiral. We perform a full Markov Chain Monte Carlo Bayesian analysis to quantify the sensitivity of these signals to two phenomenological modifications of GR, namely a putative gravitational dipole emission and a non-zero mass for the graviton, properly accounting for the detector’s response. Moreover, we consider a scenario where those sources could be observed also with Earth-based detectors, which should measure the coalescence time with precision better than 1 ms. This constraint on the coalescence time further improves the bounds that we can set on those phenomenological deviations from GR. We show that tests of dipole radiation and the graviton’s mass should improve respectively by seven and half an order(s) of magnitude over current bounds. Finally, we discuss under which conditions one may claim the detection of a modification to General Relativity.
Schiff gyroscope experiment as test of Brans- Dicke scalar tensor general relativity theory, deriving expression for gyroscope momentum precession
We simulate head-on collisions from rest at large separation of binary white dwarf-neutron stars (WDNSs) in full general relativity. Our study serves as a prelude to our analysis of the circular binary WDNS problem. We focus on compact binaries whose total mass exceeds the maximum mass that a cold-degenerate star can support, and our goal is to determine the fate of such systems. A fully general relativistic hydrodynamic computation of a realistic WDNS head-on collision is prohibitive due to the large range of dynamical time scales and length scales involved. For this reason, we construct an equation of state (EOS) which captures the main physical features of neutron stars (NSs) while, at the same time, scales down the size of white dwarfs (WDs). We call these scaled-down WD models 'pseudo-WDs (pWDs)'. Using pWDs, we can study these systems via a sequence of simulations where the size of the pWD gradually increases toward the realistic case. We perform two sets of simulations; One set studies the effects of the NS mass on the final outcome, when the pWD is kept fixed. The other set studies the effect of the pWD compaction on the final outcome, when the pWD mass and the NS are kept fixed. All simulations show that after the collision, 14%-18% of the initial total rest mass escapes to infinity. All remnant masses still exceed the maximum rest mass that our cold EOS can support (1.92M{sub {center_dot}}), but no case leads to prompt collapse to a black hole. This outcome arises because the final configurations are hot. All cases settle into spherical, quasiequilibrium configurations consisting of a cold NS core surrounded by a hot mantle, resembling Thorne-Zytkow objects. Extrapolating our results to realistic WD compactions, we predict that the likely outcome of a head-on collision of a realistic, massive WDNS system will be the formation of a quasiequilibrium Thorne-Zytkow-like object.
The metric outside an isolated object made up of ordinary matter is bound to be the classical Schwarzschild vacuum solution of General Relativity. Nevertheless, some solutions are known (e.g. Morris-Thorne wormholes) that do not match Schwarzschild asymptotically. On a phenomenological point of view, gravitational lensing in metrics falling as 1/r{sup q} has recently attracted great interest. In this work, we explore the conditions on the source matter for constructing static spherically symmetric metrics exhibiting an arbitrary power-law as Newtonian limit. For such space-times we also derive the expressions of gravitational redshift and force on probe masses, which, together with light deflection, can be used in astrophysical searches of non-Schwarzschild objects made up of exotic matter. Interestingly, we prove that even a minimally coupled scalar field with a power-law potential can support non-Schwarzschild metrics with arbitrary asymptotic behaviour.
According to general relativity, the calculated rate of motion of lunar perigee should include a contribution of 19.2 msec/yr from geodetic precession. It is shown that existing analyses of lunar-laser-ranging data confirm the general-relativistic rate for geodetic precession with respect to the planetary dynamical frame. In addition, the comparison of earth-rotation results from lunar laser ranging and from VLBI shows that the relative drift of the planetary dynamical frame and the extragalactic VLBI reference frame is small. The estimated accuracy is about 10 percent.
Perturbation analysis of the general theory of relativity and development of variations in the two-body keplerian orbital elements
Perturbation analysis of the general theory of relativity and development of variations in the two-body keplarian orbital elements /see accession no. a63-15324, issue no. 11/
For several years numerical simulations have been revealing the details of general relativity's predictions for the dynamical interactions of merging black holes. I will review what has been learned of the rich phenomenology of these mergers and the resulting gravitational wave signatures. These wave forms provide a potentially observable record of the powerful astronomical events, a central target of gravitational wave astronomy. Asymmetric radiation can produce a thrust on the system which may accelerate the single black hole resulting from the merger to high relative velocity.
Although general relativity (GR) has been tested extensively in the weak-gravity regime, similar tests in the strong-gravity regime are still missing. In this paper, we explore the possibility to use X-ray spectropolarimetric observations of black holes in X-ray binaries to distinguish between the Kerr metric and the phenomenological metrics introduced by Johannsen and Psaltis (which are not vacuum solutions of Einstein's equation) and thus to test the no-hair theorem of GR. To this end, we have developed a numerical code that calculates the radial brightness profiles of accretion disks and parallel transports the wave vector and polarization vector of photons through the Kerr and non-GR spacetimes. We used the code to predict the observational appearance of GR and non-GR accreting black hole systems. We find that the predicted energy spectra and energy-dependent polarization degree and polarization direction do depend strongly on the underlying spacetime. However, for large regions of the parameter space, the GR and non-GR metrics lead to very similar observational signatures, making it difficult to observationally distinguish between the two types of models.
Using the generally covariant magnetofluid formalism for a hot plasma, a spacetime curvature driven mechanism for generating seed vorticity/magnetic field is presented. The 'battery' owes its origin to the interaction between the gravity modified Lorentz factor of the fluid element and the inhomogeneous plasma thermodynamics. The general relativistic drive is evaluated for two simple cases: seed formation in a simplified model of a hot plasma accreting in stable orbits around a Schwarzschild black hole and for particles in free fall near the horizon. Some astrophysical applications are suggested.
Abstract We study gauge preheating following pseudoscalar-driven inflation in full general relativity. We implement the Baumgarte-Shapiro-Shibata-Nakamura (BSSN) scheme to solve the full nonlinear evolution of the metric alongside the dynamics of the pseudoscalar and gauge fields. The dynamics of the background and emission of gravitational waves are broadly consistent with simulations in a Friedmann-Lemaître-Robertson-Walker (FLRW) spacetime. We find large, localized overdensities in the BSSN simulations of orderδ=δρ/ρ∼ 30, and the dimensionless power spectrum ofδpeaks above unity. These overdense regions are seeded on length scales only slightly smaller than the horizon, and have a compactnessC∼ 0.1. The scale of peak compactness is shorter than the Jeans length, which implies that pressure of the matter fields plays an important role in the evolution of these objects.
Gravitation wave radiation rate from binary stars, using Brans-Dicke general relativity theory
Interesting new tests of general relativity could be performed in earth orbit using a sensitive superconducting gravity gradiometer under development. Two such experiments are discussed here: a null test of the tracelessness of the Riemann tensor and detection of the Lense-Thirring term in the earth's gravity field. The gravity gradient signals in various spacecraft orientations are derived, and dominant error sources in each experimental setting are discussed. The instrument, spacecraft, and orbit requirements imposed by the experiments are derived.