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The two-center problem in General Relativity is the problem of geodesic motion in the two black-hole spacetime defined by the Majumdar-Papapetrou solution of the Einstein-Maxwell equations.
We study the cosmological consequences of a recently proposed nonlocal modification of general relativity, obtained by adding a term m{sup 2}R □{sup −2}R to the Einstein-Hilbert action. The model has the same number of parameters as ΛCDM, with m replacing Ω{sub Λ}. At the background level, after fixing m so to reproduce the observed value of Ω{sub M}, we get a pure prediction for the equation of state of dark energy as a function of redshift, w{sub DE}(z), with w{sub DE}(0) in the range [−1.165,−1.135] as Ω{sub M} varies over the broad range Ω{sub M} element of [0.20,0.36]. We find that the cosmological perturbations are well-behaved, and the model fully fixes the dark energy perturbations as a function of redshift z and wavenumber k. The nonlocal model provides a good fit to supernova data and predicts deviations from General Relativity in structure formation and in weak lensing at the level of 3-4%, therefore consistent with existing data but readily detectable by future surveys. For the logarithmic growth factor we obtain γ ≅ 0.53, to be compared with γ ≅ 0.55 in ΛCDM. For the Newtonian potential on subhorizon scales our results are well fitted by Ψ(a;k) = [1+μ{sub s}a{sup s}]Ψ{sub GR}(a;k) with a scale-independent μ{sub s} ≅ 0.09 and s ≅ 2, while the anisotropic stress is negligibly small.
We explore the complementarity of weak lensing and galaxy peculiar velocity measurements to better constrain modifications to General Relativity. We find no evidence for deviations from General Relativity on cosmological scales from a combination of peculiar velocity measurements (for Luminous Red Galaxies in the Sloan Digital Sky Survey) with weak lensing measurements (from the Canadian France Hawaii Telescope Legacy Survey). We provide a Fisher error forecast for a Euclid-like space-based survey including both lensing and peculiar velocity measurements and show that the expected constraints on modified gravity will be at least an order of magnitude better than with present data, i.e. we will obtain {approx_equal}5% errors on the modified gravity parametrization described here. We also present a model-independent method for constraining modified gravity parameters using tomographic peculiar velocity information, and apply this methodology to the present data set.
Gravitational waves enable tests of general relativity in the highly dynamical and strong-field regime. Using events detected by LIGO-Virgo up to 1 October 2019, we evaluate the consistency of the data with predictions from the theory. We first establish that residuals from the best-fit waveform are consistent with detector noise, and that the low- and high-frequency parts of the signals are in agreement. We then consider parametrized modifications to the waveform by varying post-Newtonian and phenomenological coefficients, improving past constraints by factors of ∼2; we also find consistency with Kerr black holes when we specifically target signatures of the spin-induced quadrupole moment. Looking for gravitational-wave dispersion, we tighten constraints on Lorentz-violating coefficients by a factor of ∼2.6 and bound the mass of the graviton to m(g)≤1.76 x 10^(-23) eV/sq. c with 90% credibility. We also analyze the properties of the merger remnants by measuring ringdown frequencies and damping times, constraining fractional deviations away from the Kerr frequency to δ{\hat {f}}(220)=0.03(+0.38,-0.35) for the fundamental quadrupolar mode, and δ{\hat {f}}(221)=0.04(+0.27,-0.32) for the first overtone; additionally, we find no evidence for postmerger echoes. Finally, we determine that our data are consistent with tensorial polarizations through a template-independent method. When possible, we assess the validity of general relativity based on collections of events analyzed jointly. We find no evidence for new physics beyond general relativity, for black hole mimickers, or for any unaccounted systematics.
Two theories of matter in general relativity, the fluid theory and the kinetic theory, were studied. Results include: (1) a discussion of various methods of completing the fluid equations; (2) a method of constructing charged general relativistic solutions in kinetic theory; and (3) a proof and discussion of the incompatibility of perfect fluid solutions in anisotropic cosmologies. Interpretations of NASA gravitational experiments using the above mentioned results were started. Two papers were prepared for publications based on this work.
General relativity lectures concerning geometrodynamics and gravitational radiation, emphasizing geometrization and axisymmetric waves
Physical nature of cosmological equations, general relativity for idealized universe, and Newtonian cosmology
Planar scalar field configurations in general relativity differ considerably from those in flat space. It is shown that static domain walls of finite thickness in curved space-time do not possess a reflection symmetry. At infinity, the space-time tends to the Taub vacuum on one side of the wall and to the Minkowski vacuum (Rindler space-time) on the other. Massive test particles are always accelerated towards the Minkowski side, i.e., domain walls are attractive on the Taub side, but repulsive on the Minkowski side (Taub-vacuum cleaner). It is also proved that the pressure in all directions is always negative. Finally, a brief comment is made concerning the possibility of infinite, i.e., bigger than horizon size, domain walls in our universe. All of the results are independent of the form of the potential V(phi) greater than or equal to 0 of the scalar field phi.
Tests of general relativity (GR) are still in their infancy on cosmological scales, but forthcoming experiments promise to greatly improve their precision over a wide range of distance scales and redshifts. One such experiment, the Square Kilometre Array (SKA), will carry out several wide and deep surveys of resolved and unresolved neutral hydrogen (H i) 21 cm line-emitting galaxies, mapping a significant fraction of the sky from 0⩽z≲6. I present forecasts for the ability of a suite of possible SKA H i surveys to detect deviations from GR by reconstructing the cosmic expansion and growth history. SKA Phase 1 intensity mapping surveys can achieve sub-1% measurements of fσ{sub 8} out to z≈1, with an SKA1-MID Band 2 survey out to z ≲ 0.6 able to surpass contemporary spectroscopic galaxy surveys such as DESI and Euclid in terms of constraints on modified gravity parameters if challenges such as foreground contamination can be tackled effectively. A more futuristic Phase 2 H i survey of ∼10{sup 9} spectroscopic galaxy redshifts would be capable of detecting a ∼2% modification of the Poisson equation out to z ≈ 2.
The detection of gravitational waves by Advanced LIGO and Advanced Virgo provides an opportunity to test general relativity in a regime that is inaccessible to traditional astronomical observations and laboratory tests. We present four tests of the consistency of the data with binary black hole gravitational waveforms predicted by general relativity. One test subtracts the best-fit waveform from the data and checks the consistency of the residual with detector noise. The second test checks the consistency of the low- and high-frequency parts of the observed signals. The third test checks that phenomenological deviations introduced in the waveform model (including in the post-Newtonian coefficients) are consistent with 0. The fourth test constrains modifications to the propagation of gravitational waves due to a modified dispersion relation, including that from a massive graviton. We present results both for individual events and also results obtained by combining together particularly strong events from the first and second observing runs of Advanced LIGO and Advanced Virgo, as collected in the catalog GWTC-1. We do not find any inconsistency of the data with the predictions of general relativity and improve our previously presented combined constraints by factors of 1.1 to 2.5. In particular, we bound the mass of the graviton to be 𝑚𝑔≤4.7×10 −23 eV/𝑐 2 (90% credible level), an improvement of a factor of 1.6 over our previously presented results. Additionally, we check that the four gravitational-wave events published for the first time in GWTC-1 do not lead to stronger constraints on alternative polarizations than those published previously.
Von Neumann’s procedure is applied to quantizing general relativity. Initial data for dynamical variables in the Planck epoch, where the Hubble parameter value coincided with the Planck mass are quantized. These initial data are defined in terms of the Fock orthogonal simplex in the tangent Minkowski spacetime and the Dirac conformal interval. The Einstein cosmological principle is used to average the logarithm of the determinant of the spatial metric over the spatial volume of the visible Universe. The splitting of general coordinate transformations into diffeomorphisms and transformations of the initial data is introduced. In accordance with von Neumann’s procedure, the vacuum state is treated is a quantum ensemble that is degenerate in quantum numbers of nonvacuum states. The distribution of the vacuum state leads to the Casimir effect in gravidynamics in just the same way as in electrodynamics. The generating functional for perturbation theory in gravidynamics is found by solving the quantum energy constraint. The applicability range of gravidynamics is discussed along with the possibility of employing this theory to interpret modern observational data.
Highlights: • We present model for anisotropic compact star under general relativity. • Here a 4-dimensional spacetime is embedded into the 5-dimensional flat metric. • The spherically symmetric metric has class 1 under which solution set is obtained. • Interesting and physically viable results are found out. • Investigations on the physical features of the model are performed. - Abstract: We present model for anisotropic compact star under the general theory of relativity of Einstein. In the study a 4-dimensional spacetime has been considered which is embedded into the 5-dimensional flat metric so that the spherically symmetric metric has class 1. A set of solutions for the field equations are found depending on the index n involved in the physical parameters. The interior solutions have been matched smoothly at the boundary of the spherical distribution to the exterior Schwarzschild solution which necessarily provides values of the unknown constants. We have chosen the values of n as n=2 and n=10 to 20000 for which interesting and physically viable results can be found out. The investigations on the physical features of the model include several astrophysical issues, like (i) regularity behaviour of stars at the centre, (ii) well behaved condition for velocity of sound, (iii) energy conditions, (iv) stability of the system via the following three techniques — adiabatic index, Herrera cracking concept and TOV equation, (v) total mass, effective mass and compactification factor and (vi) surface redshift. Specific numerical values of the compact star candidates LMC X-4 and SMC X-1 are calculated for central and surface densities as well as central pressure to compare the model value with actual observational data.
It appears possible to deduce black holes, general relativity and the standard model of elementary particles from one-dimensional strands that fluctuate at the Planck scale. This appears possible as long as only switches of skew strand crossings are observable, but not the strands themselves. Woven fluctuating strands behave like horizons and imply black hole entropy, the field equations of general relativity and cosmological observations. Tangled fluctuating strands in flat space imply Dirac’s equation. The possible families of unknotted rational tangles produce the spectrum of elementary particles. Fluctuating rational tangles also yield the gauge groups U(1), broken SU(2), and SU(3), produce all Feynman diagrams of the standard model, and exclude any unknown elementary particle, gauge group, and Feynman diagram. The conjecture agrees with all known experimental data. Predictions for experiments arise, and the fundamental constants of the standard model can be calculated. Objections are discussed. Predictions and calculations allow testing the conjecture. As an example, an ab initio estimate of the fine structure constant is outlined.
The system of the spherical-symmetric vacuum equations of the General Relativity Theory is considered. The general solution to a problem representing two classes of line elements with arbitrary functions g{sub 00} and g{sub 22} is obtained. The properties of the found solutions are analyzed.
We show that physical scattering observables for compact spinning objects in general relativity can depend on additional degrees of freedom in the spin tensor beyond those described by the spin vector alone. The impulse, spin kick, and leading-order waveforms exhibit such a nontrivial dependence. A signal of this additional structure is the change in the magnitude of the spin vector under conservative Hamiltonian evolution, similar to our previous studies in electrodynamics. These additional degrees of freedom describe dynamical mass multipoles of compact objects and decouple for black holes. We also show that the conservative impulse, spin kick, and change of the additional degrees of freedom are encoded in the eikonal phase.
We assume a GL(4,R) space-time symmetry which is spontaneously broken to SO(3,1). We carry out the coset construction of the effective theory for the nonlinearly realized broken symmetry in terms of the Goldstone fields and matter fields transforming linearly under the unbroken Lorentz subgroup. We then identify functions of the Goldstone and matter fields that transform linearly also under the broken symmetry. Expressed in terms of these quantities the effective theory reproduces the vierbein formalism of general relativity with general coordinate invariance being automatically realized nonlinearly over GL(4,R). The coset construction makes no assumptions about any underlying theory that might be responsible for the assumed symmetry breaking. We give a brief discussion of the possibility of field theories with GL(4,R) rather than Lorentz space-time symmetry providing the underlying dynamics.
The change of frequency of an interplanetary radar signal sent from the earth to another planet or to a space probe is worked out according to general relativity. The Schwarzschild spacetime is employed and its null geodesics control the motion of the signals. Exact Doppler frequency formulas are derived for one-way and two-way radar in terms of an arbitrary Schwarzschild radial coordinate. A reduction to the special relativity case is used to interpret the formulas in terms of the relative radial velocity of emitter and target. The general relativity corrections are worked out approximately for each of three possible Schwarzschild radial coordinates, and a numerical example is given. The amount of the correction is different according as one or the other of the Schwarzschild coordinates is identified with the radius vector deduced from classical celestial mechanics. The identification problem is discussed.
We have carried out general relativistic particle simulations of stars tidally disrupted by massive black holes. When a star is disrupted in a bound orbit with moderate eccentricity instead of a parabolic orbit, the temporal behavior of the resulting stellar debris changes qualitatively. The debris is initially all bound, returning to pericenter in a short time about the original stellar orbital timescale. The resulting fallback rate can thus be much higher than the Eddington rate. Furthermore, if the star is disrupted close to the hole, in a regime where general relativity is important, the stellar and debris orbits display general relativistic precession. Apsidal precession can make the debris stream cross itself after several orbits, likely leading to fast debris energy dissipation. If the star is disrupted in an inclined orbit around a spinning hole, nodal precession reduces the probability of self-intersection, and circularization may take many dynamical timescales, delaying the onset of flare activity. An examination of the particle dynamics suggests that quasi-periodic flares with short durations, produced when the center of the tidal stream passes pericenter, may occur in the early-time light curve. The late-time light curve may still show power-law behavior which is generic to disk accretion processes. The detection triggers for future surveys should be extended to capture such 'non-standard' short-term flaring activity before the event enters the asymptotic decay phase, as this activity is likely to be more sensitive to physical parameters such as the black hole spin.