Showing papers on "Gravitational field published in 2019"

Black hole shadow in a general rotating spacetime obtained through Newman-Janis algorithm

Abstract: The Newman-Janis (NJ) algorithm has been extensively used in the literature to generate rotating black hole solutions from nonrotating seed spacetimes. In this work, we show, using various constants of motion, that the null geodesic equations in an arbitrary stationary and axially symmetric rotating spacetime obtained through the NJ algorithm can be separated completely, provided that the algorithm is applied successfully without any inconsistency. Using the separated null geodesic equations, we then obtain an analytic general formula for obtaining the contour of a shadow cast by a compact object whose gravitational field is given by the arbitrary rotating spacetime under consideration. As special cases, we apply our general analytic formula to some known black holes and reproduce the corresponding results for black hole shadow. Finally, we consider a new example and study shadow using our analytic general formula.

Action Principle for Newtonian Gravity

Abstract: We derive an action whose equations of motion contain the Poisson equation of Newtonian gravity. The construction requires a new notion of Newton-Cartan geometry based on an underlying symmetry algebra that differs from the usual Bargmann algebra. This geometry naturally arises in a covariant $1/c$ expansion of general relativity, with $c$ being the speed of light. By truncating this expansion at subleading order, we obtain the field content and transformation rules of the fields that appear in the action of Newtonian gravity. The equations of motion generalize Newtonian gravity by allowing for the effect of gravitational time dilation due to strong gravitational fields.

Probing gravity by holding atoms for 20 seconds

Abstract: Atom interferometers are powerful tools for both measurements in fundamental physics and inertial sensing applications. Their performance, however, has been limited by the available interrogation time of freely falling atoms in a gravitational field. By suspending the spatially separated atomic wave packets in a lattice formed by the mode of an optical cavity, we realize an interrogation time of 20 seconds. Our approach allows gravitational potentials to be measured by holding, rather than dropping, atoms. After seconds of hold time, gravitational potential energy differences from as little as micrometers of vertical separation generate megaradians of interferometer phase. This trapped geometry suppresses the phase variance due to vibrations by three to four orders of magnitude, overcoming the dominant noise source in atom-interferometric gravimeters.

A novel model of plane waves of two-temperature fiber-reinforced thermoelastic medium under the effect of gravity with three-phase-lag model

Abstract: In the present paper, the three-phase-lag (3PHL) model, Green-Naghdi theory without energy dissipation (G-N II) and Green-Naghdi theory with energy dissipation (G-N III) are used to study the influence of the gravity field on a two-temperature fiber-reinforced thermoelastic medium.,The analytical expressions for the displacement components, the force stresses, the thermodynamic temperature and the conductive temperature are obtained in the physical domain by using normal mode analysis.,The variations of the considered variables with the horizontal distance are illustrated graphically. Some comparisons of the thermo-physical quantities are shown in the figures to study the effect of the gravity, the two-temperature parameter and the reinforcement. Also, the effect of time on the physical fields is observed.,To the best of the author’s knowledge, this model is a novel model of plane waves of two-temperature fiber-reinforced thermoelastic medium, and gravity plays an important role in the wave propagation of the field quantities. It explains that there are significant differences in the field quantities under the G-N II theory, the G-N III theory and the 3PHL model because of the phase-lag of temperature gradient and the phase-lag of heat flux.

Tests of gravitational symmetries with pulsar binary J1713+0747

Abstract: Symmetries play a fundamental role in modern theories of gravity. The strong equivalence principle (SEP) constitutes a collection of gravitational symmetries which are all implemented by general relativity. Alternative theories, however, are generally expected to violate some aspects of SEP. We test three aspects of SEP using observed change rates in the orbital period and eccentricity of binary pulsar J1713+0747: (1) the gravitational constant’s constancy as part of locational invariance of gravitation; (2) the universality of free fall (UFF) for strongly self-gravitating bodies; (3) the post-Newtonian parameter |$\hat{\alpha }_3$| in gravitational Lorentz invariance. Based on the pulsar timing result of the combined data set from the North American Nanohertz Gravitational Observatory and the European Pulsar Timing Array, we find |$\dot{G}/G = (-0.1 \pm 0.9) \times 10^{-12}\, {\rm yr}^{-1}$|⁠, which is weaker than Solar system limits, but applies for strongly self-gravitating objects. Furthermore, we obtain an improved test for a UFF violation by a strongly self-gravitating mass falling in the gravitational field of our Galaxy, with a limit of |Δ| < 0.002 (95 per cent C.L.). Finally, we derive an improved limit on the self-acceleration of a gravitationally bound rotating body, to a preferred reference frame in the Universe, with |$-3\times 10^{-20} \lt \hat{\alpha }_3 \lt 4\times 10^{-20}$| (95 per cent C.L.). These results are based on direct UFF and |$\hat{\alpha }_3$| tests using pulsar binaries, and they overcome various limitations of previous tests of this kind.

Parametrized black hole quasinormal ringdown. II. Coupled equations and quadratic corrections for nonrotating black holes

Abstract: Linear perturbations of spherically symmetric spacetimes in general relativity are described by radial wave equations, with potentials that depend on the spin of the perturbing field. In previous work we studied the quasinormal mode spectrum of spacetimes for which the radial potentials are slightly modified from their general relativistic form, writing generic small modifications as a power-series expansion in the radial coordinate. We assumed that the perturbations in the quasinormal frequencies are linear in some perturbative parameter, and that there is no coupling between the perturbation equations. In general, matter fields and modifications to the gravitational field equations lead to coupled wave equations. Here we extend our previous analysis in two important ways: we study second-order corrections in the perturbative parameter, and we address the more complex (and realistic) case of coupled wave equations. We highlight the special nature of coupling-induced corrections when two of the wave equations have degenerate spectra, and we provide a ready-to-use recipe to compute quasinormal modes. We illustrate the power of our parametrization by applying it to various examples, including dynamical Chern-Simons gravity, Horndeski gravity and an effective field theory-inspired model.

Testing the gravitational field generated by a quantum superposition

Abstract: What gravitational field is generated by a massive quantum system in a spatial superposition? Despite decades of intensive theoretical and experimental research, we still do not know the answer. On the experimental side, the difficulty lies in the fact that gravity is weak and requires large masses to be detectable. However, it becomes increasingly difficult to generate spatial quantum superpositions for increasingly large masses, in light of the stronger environmental effects on such systems. Clearly, a delicate balance between the need for strong gravitational effects and weak decoherence should be found. We show that such a trade off could be achieved in an optomechanics scenario that allows to determine whether the gravitational field generated by a quantum system in a spatial superposition is in a coherent superposition or not. We estimate the magnitude of the effect and show that it offers perspectives for observability.

The Dirac oscillator in a spinning cosmic string spacetime

Abstract: We examine the effects of gravitational fields produced by topological defects on a Dirac field and a Dirac oscillator in a spinning cosmic string spacetime. We obtain the eigenfunctions and the energy levels of the relativistic field in that background and consider the effect of various parameters, such as the frequency of the rotating frame, the oscillator’s frequency, the string density and other quantum numbers.

Concept study and preliminary design of a cold atom interferometer for space gravity gradiometry

Abstract: We study a space-based gravity gradiometer based on cold atom interferometry and its potential for the Earth's gravitational field mapping. The instrument architecture has been proposed in [Carraz et al., Microgravity Science and Technology 26, 139 (2014)] and enables high-sensitivity measurements of gravity gradients by using atom interferometers in a differential accelerometer configuration. We present the design of the instrument including its subsystems and analyze the mission scenario, for which we derive the expected instrument performances, the requirements on the sensor and its key subsystems, and the expected impact on the recovery of the Earth gravity field.

A surface gravity traverse on Mars indicates low bedrock density at Gale crater

Abstract: Gravimetry, the precise measurement of gravitational fields, can be used to probe the internal structure of Earth and other planets. The Curiosity rover on Mars carries accelerometers normally used for navigation and attitude determination. We have recalibrated them to isolate the signature of the changing gravitational acceleration as the rover climbs through Gale crater. The subsurface rock density is inferred from the measured decrease in gravitational field strength with elevation. The density of the sedimentary rocks in Gale crater is 1680 ± 180 kilograms per cubic meter. This value is lower than expected, indicating a high porosity and constraining maximum burial depths of the rocks over their history.

Finsler gravity action from variational completion

Abstract: In the attempts to apply Finsler geometry to construct an extension of general relativity, the question about a suitable generalization of the Einstein equations is still under debate. Since Finsler geometry is based on a scalar function on the tangent bundle, the field equation which determines this function should also be a scalar equation. In the literature two such equations have been suggested: the one by Rutz and the one by one of the authors. Here we employ the method of canonical variational completion to show that Rutz equation can not be obtained from a variation of an action and that its variational completion yields the latter field equations. Moreover, to improve the mathematical rigor in the derivation of the Finsler gravity field equation, we formulate the Finsler gravity action on the positive projective tangent bundle. This has the advantage of allowing us to apply the classical variational principle, by choosing the domains of integration to be compact and independent of the dynamical variable. In particular in the pseudo-Riemannian case, the vacuum field equation becomes equivalent to the vanishing of the Ricci tensor.

Waveform of gravitational waves in the ghost-free parity-violating gravities

Abstract: Gravitational waves (GWs) provide an excellent opportunity to test the gravity in the strong gravitational fields. In this article, we calculate the waveform of GWs, produced by the coalescence of compact binaries, in an extension of the Chern-Simons gravity by including higher derivatives of the coupling scalar field. By comparing the two circular polarization modes, we find the effects of amplitude birefringence and velocity birefringence of GWs in their propagation caused by the parity violation in gravity, which are explicitly presented in the GW waveforms by the amplitude and phase modifications, respectively. Combining the two modes, we obtain the GW waveforms in the Fourier domain and find that the deviations from those in general relativity are dominated by effects of velocity birefringence of GWs. In addition, we also map the effects of the parity violation on the waveform onto the parametrized post-Einsteinian (PPE) framework and identify explicitly the PPE parameters.

The Dirac oscillator in a spinning cosmic string spacetime

Abstract: We examine the effects of gravitational fields produced by topological defects on a Dirac field and a Dirac oscillator in a spinning cosmic string spacetime. We obtain the eigenfunctions and the energy levels of the relativistic field in that background and consider the effect of various parameters, such as the frequency of the rotating frame, the oscillator's frequency, the string density and other quantum numbers.

Exact Kerr-like solution and its shadow in a gravity model with spontaneous Lorentz symmetry breaking

Abstract: We obtain an exact Kerr-like black hole solution by solving the corresponding gravitational field equations in Einstein-bumblebee gravity model where Lorentz symmetry is spontaneously broken once a vector field acquires a vacuum expectation value. Results are presented for the purely radial Lorentz symmetry breaking. In order to study the effects of this breaking, we consider the black hole shadow and find that the radial of the unstable spherical orbit on the equatorial plane $r_c$ decreases with the Lorentz breaking constant $\ell>0$, and increases with $\ell<0$. These shifts are similar to those of Einstein-aether black hole. The effect of the LV parameter on the black hole shadow is that it accelerates the appearance of shadow distortion, and could be detected by the new generation of gravitational antennas.

Finite distance corrections to the light deflection in a gravitational field with a plasma medium

Abstract: The aim of the present work is twofold: first, we present general remarks about the application of recent procedures to compute the deflection angle in spherically symmetric and asymptotically flat spacetimes, taking into account finite distance corrections based on the Gauss-Bonnet theorem. Second, and as the main part of our work, we apply this powerful technique to compute corrections to the deflection angle produced by astrophysical configurations in the weak gravitational regime when a plasma medium is taken into account. For applications, we use these methods to introduce new general formulas for the bending angle of light rays in plasma environments in different astrophysical scenarios, generalizing previously known results. We also present new and useful formulas for the separation angle between the images of two sources when they are lensed by an astrophysical object surrounded by plasma. In particular, for the case of a homogeneous plasma we study these corrections for the case of light rays propagating near astrophysical objects described in the weak gravitational regime by a parametrized-post-Newtonian metric which takes into account the mass of the objects and a possible quadrupole moment. Even when our work concentrates on finite distance corrections to the deflection angle, we also obtain as particular cases of our expressions new formulas which are valid for the more common assumption of infinite distance between receiver, lens and source. We also consider the presence of an inhomogeneous plasma media introducing as particular cases of our general results explicit expressions for particular charge number density profiles.

Probing the existence of ultralight bosons with a single gravitational-wave measurement

Abstract: Light bosons, proposed as a possible solution to various problems in fundamental physics and cosmology1–3, include a broad class of candidates for physics beyond the standard model, such as dilatons and moduli4, wave dark matter5 and axion-like particles6. If light bosons exist in nature, they will spontaneously form ‘clouds’ by extracting rotational energy from rotating massive black holes through superradiance, a classical wave amplification process that has been studied for decades7,8. The superradiant growth of the cloud sets the geometry of the final black hole, and the black hole geometry determines the shape of the cloud9–11. Hence, both the black hole geometry and the cloud encode information about the light boson. For this reason, measurements of the gravitational field of the black hole/cloud system (as encoded in gravitational waves) are over-determined. We show that a single gravitational-wave measurement can be used to verify the existence of light bosons by model selection, rule out alternative explanations for the signal, and measure the boson mass. Such measurements can be done generically for bosons in the mass range [10−16.5, 10−14] eV using observations of extreme mass-ratio inspirals (EMRIs) by the forthcoming Laser Interferometer Space Antenna (LISA). A single gravitational-wave measurement, for example of extreme-mass ratio inspirals by LISA, can be used to verify the existence of light bosons by model selection, rule out alternative explanations for the signal and measure the boson mass.

Gravitational dressing, soft charges, and perturbative gravitational splitting

Abstract: In gauge theories and gravity, field variables are generally not gauge-invariant observables, but such observables may be constructed by “dressing” these or more general operators. Dressed operators create particles, together with their gauge or gravitational fields which typically extend to infinity. This raises an important question of how well quantum information can be localized; one version of this is the question of whether soft charges fully characterize a given localized charge or matter distribution. This paper finds expressions for the nontrivial soft charges of such dressed operators. However, a large amount of flexibility in the dressing indicates that the soft charges, and other asymptotic observables, are not inherently correlated with details of the charge or matter distribution. Instead, these asymptotic observables can be changed by adding a general radiative (source-free) field configuration to the original one. A dressing can be chosen, perturbatively, so that the asymptotic observables are independent of details of the distribution, besides its total electric or Poincare charges. This provides an approach to describing localization of information in gauge theories or gravity, and thus subsystems, that avoids problems associated with nonlocality of operator subalgebras. Specifically, this construction suggests the notions of electromagnetic or gravitational splittings, which involve networks of Hilbert space embeddings in which the charges play an important role.

Quantum-first gravity

Abstract: This paper elaborates on an intrinsically quantum approach to gravity, which begins with a general framework for quantum mechanics and then seeks to identify additional mathematical structure on Hilbert space that is responsible for gravity and other phenomena. A key principle in this approach is that of correspondence: this structure should reproduce spacetime, general relativity, and quantum field theory in a limit of weak gravitational fields. A central question is that of “Einstein separability,” and asks how to define mutually independent subsystems, e.g. through localization. Familiar definitions involving tensor products or operator subalgebras do not clearly accomplish this in gravity, as is seen in the correspondence limit. Instead, gravitational behavior, particularly gauge invariance, suggests a network of Hilbert subspaces related via inclusion maps, contrasting with other approaches based on tensor-factorized Hilbert spaces. Any such localization structure is also expected to place strong constraints on evolution, which are also supplemented by the constraint of unitarity.

Post-Newtonian Hamiltonian description of an atom in a weak gravitational field

Abstract: We extend the systematic calculation of an approximately relativistic Hamiltonian for center of mass and internal dynamics of an electromagnetically bound two-particle system by Sonnleitner and Barnett [Phys. Rev. A 98, 042106 (2018)] to the case including a weak post-Newtonian gravitational background field, described by the Eddington-Robertson parametrized post-Newtonian metric. Starting from a proper relativistic description of the situation, this approach allows us to systematically derive the coupling of the model system to gravity, instead of ``guessing'' it by means of classical notions of relativistic effects. We embed this technical result into a critical discussion concerning the problem of implementing and interpreting general couplings to the gravitational field and the connected problem of how to properly address the question concerning the validity of the Equivalence Principle in Quantum Mechanics.

Phase shift in atom interferometers: Corrections for nonquadratic potentials and finite-duration laser pulses

Abstract: We derive an expression for the phase shift of an atom interferometer in a gravitational field taking into account both the finite duration of the light pulses and the effect of a small perturbing potential added to a stronger uniform gravitational field, extending the well-known results for rectangular pulses and at most quadratic potentials. These refinements are necessary for a correct analysis of present-day high-resolution interferometers.

Exact solutions in Chiral cosmology

Abstract: In multi-scalar field cosmologies new dynamical degrees of freedom are introduced which can explain the observational phenomena. Unlike the usual scalar field theory where a single scalar field is considered, the multi-scalar field cosmologies allow more than one scalar field and exhibits interetsing consequences, such as quintom, hybrid inflation etc. The current work study the existence of exact solutions and integrable dynamical systems in multi-scalar field cosmology and more specifically in the so-called Chiral cosmology where nonlinear terms exists in the kinetic term of the scalar fields. We present the exact analytic solutions for a system of N-scalar fields. In particular, we consider a multi scalar field cosmological scenario comprised of N-scalar fields that are minimally coupled to the Einstein gravity. The geometry of the universe is described by the spatially flat homogeneous and isotropic line element and the scalar fields may interact in their kinetic or/and potential terms. Within this set up, we show that for a specific geometry in the kinetic part of the scalar fields and specific potential form, the gravitational field equations for the class of N-scalar field models can be exactly solved. More specifically, we show that the Einstein field equations in N-scalar field cosmology can be reduced to that of a $$\left( N+1\right) $$ -linear system.

Constrained transport and adaptive mesh refinement in the Black Hole Accretion Code

Abstract: Worldwide very long baseline radio interferometry arrays are expected to obtain horizon-scale images of supermassive black hole candidates as well as of relativistic jets in several nearby active galactic nuclei. This motivates the development of models for magnetohydrodynamic flows in strong gravitational fields. The Black Hole Accretion Code (BHAC) intends to aid with the modelling of such sources by means of general relativistic magnetohydrodynamical (GRMHD) simulations in arbitrary stationary spacetimes. New additions were required to guarantee an accurate evolution of the magnetic field when small and large scales are captured simultaneously. We discuss the adaptive mesh refinement (AMR) techniques employed in BHAC, essential to keep several problems computationally tractable, as well as staggered-mesh-based constrained transport (CT) algorithms to preserve the divergence-free constraint of the magnetic field, including a general class of prolongation operators for face-allocated variables compatible with them. Through several standard tests, we show that the choice of divergence-control method can produce qualitative differences in simulations of scientifically relevant accretion problems. We demonstrate the ability of AMR to reduce the computational costs of accretion simulations while sufficiently resolving turbulence from the magnetorotational instability. In particular, we describe a simulation of an accreting Kerr black hole in Cartesian coordinates using AMR to follow the propagation of a relativistic jet while self-consistently including the jet engine, a problem set up-for which the new AMR implementation is particularly advantageous. The CT methods and AMR strategies discussed here are being employed in the simulations performed with BHAC used in the generation of theoretical models for the Event Horizon Telescope Collaboration.

The Spectrum of Teleparallel Gravity

Abstract: The observer’s frame is the more elementary description of the gravitational field than the metric. The most general covariant, even-parity quadratic form for the frame field in arbitrary dimension generalises the New General Relativity by nine functions of the d’Alembertian operator. The degrees of freedom are clarified by a covariant derivation of the propagator. The consistent and viable models can incorporate an ultra-violet completion of the gravity theory, an additional polarisation of the gravitational wave, and the dynamics of a magnetic scalar potential.

The Dirac equation in a class of topologically trivial flat Gödel-type space-time backgrounds

Abstract: In this work, we investigate the behaviour of Dirac particles in a class of Godel-type space-time backgrounds in the presence of non-minimal coupling of the gravitational field with background curvature. We obtain the allowed energies for this relativistic system by solving analytically the Dirac equation in flat and curved space in a topologically trivial flat Godel-type metric, and analyze the effects on the energy eiegnvalues.

General Relativity Measurements in the Field of Earth with Laser-Ranged Satellites: State of the Art and Perspectives

Abstract: Recent results of the LARASE research program in terms of model improvements and relativistic measurements are presented. In particular, the results regarding the development of new models for the non-gravitational perturbations that affect the orbit of the LAGEOS and LARES satellites are described and discussed. These are subtle and complex effects that need a deep knowledge of the structure and the physical characteristics of the satellites in order to be correctly accounted for. In the field of gravitational measurements, we present a new measurement of the relativistic Lense-Thirring precession with a 0.5 % precision. In this measurement, together with the relativistic effect we also estimated two even zonal harmonics coefficients. The uncertainties of the even zonal harmonics of the gravitational field of the Earth have been responsible, until now, of the larger systematic uncertainty in the error budget of this kind of measurements. For this reason, the role of the errors related to the model used for the gravitational field of the Earth in these measurements is discussed. In particular, emphasis is given to GRACE temporal models, that strongly help to reduce this kind of systematic errors.

Models of Saturn's Interior Constructed with Accelerated Concentric Maclaurin Spheroid Method

Abstract: The Cassini spacecraft's Grand Finale orbits provided a unique opportunity to probe Saturn's gravity field and interior structure. Doppler measurements yielded unexpectedly large values for the gravity harmonics J_6, J_8, and J_10 that cannot be matched with planetary interior models that assume uniform rotation. Instead we present a suite of models that assume the planet's interior rotates on cylinders, which allows us to match all the observed even gravity harmonics. For every interior model, the gravity field is calculated self-consistently with high precision using the Concentric Maclaurin Spheroid (CMS) method. We present an acceleration technique for this method, which drastically reduces the computational cost, allows us to efficiently optimize model parameters, map out allowed parameter regions with Monte Carlo sampling, and increases the precision of the calculated J_2n gravity harmonics to match the error bars of the observations, which would be difficult without acceleration. Based on our models, Saturn is predicted to have a dense central core of 15-18 Earth masses and an additional 1.5-5 Earth masses of heavy elements in the envelope. Finally, we vary the rotation period in the planet's deep interior and determine the resulting oblateness, which we compare with the value from radio occultation measurements by the Voyager spacecraft. We predict a rotation period of 10:33:34 h +- 55s, which is in agreement with recent estimates derived from ring seismology.

Decoding signatures of extra dimensions and estimating spin of quasars from the continuum spectrum

Abstract: The continuum spectrum emitted by the accretion disk around quasars holds a wealth of information regarding the strong gravitational field produced by the massive central object. Such a strong gravity regime is often expected to be the ideal place to look for deviations from general relativistic predictions. One possible avenue, which may lead to deviations from general relativity, corresponds to the presence of extra dimensions. Since extra dimensions are well motivated from the perspective of high energy physics, it is instructive to investigate the effect of more than four spacetime dimensions on the black hole continuum spectrum, an effective astrophysical probe to the strong gravity regime. To explore such a scenario, we compute the optical luminosity emitted by a thin accretion disk around a rotating supermassive black hole albeit in the presence of extra dimensions. The background metric resembles the Kerr-Newman spacetime of general relativity where the tidal charge parameter, inherited from extra dimensions, can also assume negative values. The theoretical luminosity computed in such a background is contrasted with optical observations of eighty quasars. The difference between the theoretical and observed luminosity for these quasars is used to infer the most favored choice of the rotation parameter for each quasar and the tidal charge parameter. This has been achieved by minimizing/maximizing several error estimators, e.g., ${\ensuremath{\chi}}^{2}$, Nash-Sutcliffe efficiency, index of agreement etc. Intriguingly, all of them favor a negative value for the tidal charge parameter, a characteristic signature of extra dimensions.