Showing papers on "Gravitational field published in 2009"

Relativistic images of Schwarzschild black hole lensing

Abstract: We model massive dark objects at centers of many galaxies as Schwarzschild black hole lenses and study gravitational lensing by them in detail We show that the ratio of mass of a Schwarzschild lens to the differential time delay between outermost two relativistic images (both of them either on the primary or on the secondary image side) is extremely insensitive to changes in the angular source position as well as the lens-source and lens-observer distances Therefore, this ratio can be used to obtain very accurate values for masses of black holes at centers of galaxies Similarly, angular separations between any two relativistic images are also extremely insensitive to changes in the angular source position and the lens-source distance Therefore, with the known value of mass of a black hole, angular separation between two relativistic images would give a very accurate result for the distance of the black hole Accuracies in determination of masses and distances of black holes would however depend on accuracies in measurements of differential time delays and angular separations between images Deflection angles of primary and secondary images as well as effective deflection angles of relativistic images on the secondary image side are always positive However, the effective deflection angles of relativistic images on the primary image side may be positive, zero, or negative depending on the value of angular source position and the ratio of mass of the lens to its distance We show that effective deflection angles of relativistic images play significant role in analyzing and understanding strong gravitational field lensing

Chiral Primordial Gravitational Waves from a Lifshitz Point

Abstract: We study primordial gravitational waves produced during inflation in quantum gravity at a Lifshitz point proposed by Horava. Assuming power-counting renormalizability, foliation-preserving diffeomorphism invariance, and the condition of detailed balance, we show that primordial gravitational waves are circularly polarized due to parity violation. The chirality of primordial gravitational waves is a quite robust prediction of quantum gravity at a Lifshitz point which can be tested through observations of cosmic microwave background radiation and stochastic gravitational waves.

Gravitational self force in extreme mass-ratio inspirals

Abstract: This review is concerned with the gravitational self-force acting on a mass particle in orbit around a large black hole. Renewed interest in this old problem is driven by the prospects of detecting gravitational waves from strongly gravitating binaries with extreme mass ratios. We begin here with a summary of recent advances in the theory of gravitational self-interaction in curved spacetime, and proceed to survey some of the ideas and computational strategies devised for implementing this theory in the case of a particle orbiting a Kerr black hole. We review in detail two of these methods: (i) the standard mode-sum method, in which the metric perturbation is regularized mode-by-mode in a multipole decomposition, and (ii) m-mode regularization, whereby individual azimuthal modes of the metric perturbation are regularized in 2+1 dimensions. We discuss several practical issues that arise, including the choice of gauge, the numerical representation of the particle singularity, and how high-frequency contributions near the particle are dealt with in frequency-domain calculations. As an example of a full end-to-end implementation of the mode-sum method, we discuss the computation of the gravitational self-force for eccentric geodesic orbits in Schwarzschild, using a direct integration of the Lorenz-gauge perturbation equations in the time domain. With the computational framework now in place, researchers have recently turned to explore the physical consequences of the gravitational self-force; we will describe some preliminary results in this area. An appendix to this review presents, for the first time, a detailed derivation of the 'regularization parameters' necessary for implementing the mode-sum method in Kerr spacetime.

Extreme- and intermediate-mass ratio inspirals in dynamical Chern-Simons modified gravity

Abstract: Chern-Simons modified gravity is a four-dimensional, effective theory that descends both from string theory and loop quantum gravity, and that corrects the Einstein-Hilbert action by adding the product of a scalar field and the parity-violating, Pontryagin density. The Chern-Simons modification deforms the gravitational field of spinning black holes, which is now described by a modified Kerr geometry whose multipole moments deviate from the Kerr ones only at the fourth multipole $\ensuremath{\ell}=4$. This paper investigates possible signatures of this theory in the gravitational-wave emission produced in the inspiral of stellar compact objects into massive black holes, both for intermediate- and extreme-mass ratios. We use the semirelativistic approximation, where the trajectory of the small compact object is modeled via geodesics of the massive black hole geometry, while the gravitational waveforms are obtained from a multipolar decomposition of the radiative field. The main Chern-Simons corrections to the waveforms arise from modifications to the geodesic trajectories, which in turn are due to changes to the massive black hole geometry, and manifest themselves as an accumulating dephasing relative to the general relativistic case. We also explore the propagation and the stress-energy tensor of gravitational waves in this theory, using the short-wavelength approximation. We find that, although this tensor has the same form as in general relativity, the energy and angular momentum balance laws are indeed modified through the stress-energy tensor of the Chern-Simons scalar field. These balance laws could be used to describe the inspiral through adiabatic changes in the orbital parameters, which in turn would enhance the dephasing effect. Gravitational-wave observations of intermediate- or extreme-mass-ratio inspirals with advanced ground detectors or with the Laser Interferometer Space Antenna could use such dephasing to test the dynamical theory to unprecedented levels, thus beginning the era of gravitational-wave tests of effective quantum gravity theories.

Deriving daily snapshots of the Earth's gravity field from GRACE L1B data using Kalman filtering

Abstract: [1] Different GRACE data analysis centers provide temporal variations of the Earth's gravity field as monthly, 10-daily or weekly mean fields. These solutions are derived independently for each time span, i.e., no correlation between the analyzed batches is considered. Following this procedure, an increase in temporal resolution is accompanied by a loss in accuracy. To avoid this problem, a new approach is followed, which takes into account the temporal correlations of the gravity field variations thus enabling the enhancement of the temporal resolution up to daily snapshots. The GRACE Level-1B (L1B) instrument data processing is performed within the framework of a Kalman filter estimation procedure, where the information about the temporal correlation patterns can be derived from geophysical models. The WaterGAP hydrological model was analyzed to derive the required information in terms of an empirical auto-covariance function. First results are presented and compared to GFZ-RL04 monthly and weekly gravity field solutions.

Unitarity and Holography in Gravitational Physics

Abstract: Because the gravitational Hamiltonian is a pure boundary term on shell, asymptotic gravitational fields store information in a manner not possible in local field theories. This fact has consequences for both perturbative and nonperturbative quantum gravity. In perturbation theory about an asymptotically flat collapsing black hole, the algebra generated by asymptotic fields on future null infinity within any neighborhood of spacelike infinity contains a complete set of observables. Assuming that the same algebra remains complete at the nonperturbative quantum level, we argue that either (1) the $S$ matrix is unitary or (2) the dynamics in the region near timelike, null, and spacelike infinity is not described by perturbative quantum gravity about flat space. We also consider perturbation theory about a collapsing asymptotically anti-de Sitter (AdS) black hole, where we show that the algebra of boundary observables within any neighborhood of any boundary Cauchy surface is similarly complete. Whether or not this algebra continues to be complete nonperturbatively, the assumption that the Hamiltonian remains a boundary term implies that information available at the AdS boundary at any one time ${t}_{1}$ remains present at this boundary at any other time ${t}_{2}$.

Einstein Gravity Explorer-a medium-class fundamental physics mission

Abstract: The Einstein Gravity Explorer mission (EGE) is devoted to a precise measurement of the properties of space-time using atomic clocks. It tests one of the most fundamental predictions of Einstein’s Theory of General Relativity, the gravitational redshift, and thereby searches for hints of quantum effects in gravity, exploring one of the most important and challenging frontiers in fundamental physics. The primary mission goal is the measurement of the gravitational redshift with an accuracy up to a factor 104 higher than the best current result. The mission is based on a satellite carrying cold atom-based clocks. The payload includes a cesium microwave clock (PHARAO), an optical clock, a femtosecond frequency comb, as well as precise microwave time transfer systems between space and ground. The tick rates of the clocks are continuously compared with each other, and nearly continuously with clocks on earth, during the course of the 3-year mission. The highly elliptic orbit of the satellite is optimized for the scientific goals, providing a large variation in the gravitational potential between perigee and apogee. Besides the fundamental physics results, as secondary goals EGE will establish a global reference frame for the Earth’s gravitational potential and will allow a new approach to mapping Earth’s gravity field with very high spatial resolution. The mission was proposed as a class-M mission to ESA’s Cosmic Vision Program 2015–2025.

Definition of Functionals of the Geopotential and Their Calculation from Spherical Harmonic Models

Abstract: (TYPE=)The intention of this article is to present the definitions of different functionals of the Earth's gravity field and possibilities for their approximative calculation from a mathematical representation of the outer potential. In history this topic has usually been treated in connection with the boundary value problems of geodesy, i.e. starting from measurements at the Earth's surface and their use to derive a mathematical representation of the geopotential. Nowadays global gravity field models, mainly derived from satellite measurements, become more and more detailed and accurate and, additionally, the global topography can be determined by modern satellite methods independently from the gravity field. On the one hand the accuracy of these gravity field models has to be evaluated and on the other hand they should be combined with classical (e.g. gravity anomalies) or recent (e.g. GPS-levelling-derived or altimetry-derived geoid heights) data. Furthermore, an important task of geodesy is to make the gravity field functionals available to other geosciences. For all these purposes it is necessary to calculate the corresponding functionals as accurately as possible or, at least, with a well-defined accuracy from a given global gravity field model and, if required, with simultaneous consideration of the topography model. We will start from the potential, formulate the definition of some functionals and derive the formulas for the calculation. In doing so we assume that the Earth's gravity potential is known outside the masses, the normal potential outside the ellipsoid and that mathematical representations are available for both. Here we neglect time variations and deal with the stationary part of the potential only. Approximate calculation formulas with different accuracies are formulated and specified for the case that the mathematical representation of the potential is in terms of spherical harmonics. The accuracies of the formulas are demonstrated by practical calculations using the gravity field model EIGEN-GL04C. More or less, what is compiled here is well-known in physical geodesy but distributed over a lot of articles and books which are not cited here. In the first instance this text is targeted at non-geodesists and it should be `stand-alone readable'.

Global maps of the CRUST 2.0 crustal components stripped gravity disturbances

Abstract: We use the CRUST 2.0 crustal model and the EGM08 geopotential model to compile global maps of the gravity disturbances corrected for the gravitational effects (attractions) of the topography and of the density contrasts of the oceans, sediments, ice, and the remaining crust down to the Moho discontinuity. Techniques for a spherical harmonic analysis of the gravity field are used to compute both the gravity disturbances and the topographic and bathymetric corrections with a spectral resolution complete to degree 180 of the spherical harmonics. The ice stripping correction is computed with a spectral resolution complete to degree 90. The sediment and consolidated crust stripping corrections are computed in spatial form by forward modeling their respective attractions. All data are evaluated on a 1 × 1 arc degree grid at the Earth's surface and provided in Data Sets S1–S5 in the auxiliary material for the scientific community for use in global geophysical studies. The complete crust-stripped gravity disturbances (globally having a range of 1050 mGal) contain the gravitational signal coming dominantly from the global mantle lithosphere (upper mantle) morphology and density composition and partially from the sublithospheric density heterogeneities. Large errors are expected because of uncertainties of the CRUST 2.0 model (i.e., deviations of the CRUST 2.0 model density from the real Earth's crustal density heterogeneities and the Moho relief uncertainties).

Can higher curvature corrections cure the singularity problem in f(R) gravity

Abstract: Although f(R) modified gravity models can be made to satisfy solar system and cosmological constraints, it has been shown that they have the serious drawback of the nonexistence of stars with strong gravitational fields. In this paper, we discuss whether or not higher curvature corrections can remedy the nonexistence consistently. The following problems are shown to arise as the costs one must pay for the f(R) models that allow for neutrons stars: (i) the leading correction must be fine-tuned to have the typical energy scale {mu} < or approx. 10{sup -19} GeV, which essentially comes from the free fall time of a relativistic star; (ii) the leading correction must be further fine-tuned so that it is not given by the quadratic curvature term. The second problem is caused because there appears an intermediate curvature scale, and laboratory experiments of gravity will be under the influence of higher curvature corrections. Our analysis thus implies that it is a challenge to construct viable f(R) models without very careful and unnatural fine-tuning.

Spin dynamics in gravitational fields of rotating bodies and the equivalence principle

Abstract: We discuss the quantum and classical dynamics of a particle with spin in the gravitational field of a rotating source. A relativistic equation describing the motion of classical spin in curved spacetimes is obtained. We demonstrate that the precession of the classical spin is in a perfect agreement with the motion of the quantum spin derived from the Foldy-Wouthuysen approach for the Dirac particle in a curved spacetime. We show that the precession effect depends crucially on the choice of a tetrad. The results obtained are compared to the earlier computations for different tetrad gauges.

Relativistic stars in f(R) gravity

Abstract: We study the strong gravity regime in viable models of so-called $f(R)$ gravity that account for the observed cosmic acceleration. In contrast with recent works suggesting that very relativistic stars might not exist in these models, we find numerical solutions corresponding to static star configurations with a strong gravitational field. The choice of the equation of state for the star is crucial for the existence of solutions. Indeed, if the pressure exceeds 3 times the energy density in a large part of the star, static configurations do not exist. In our analysis, we use a polytropic equation of state, which is not plagued with this problem and, moreover, provides a better approximation for a realistic neutron star.

Perturbations of Schwarzschild black holes in dynamical Chern-Simons modified gravity

Abstract: Dynamical Chern-Simons modified gravity is an attractive, yet relatively unexplored, candidate to an alternative theory of gravity. The dynamical Chern-Simons correction couples a dynamical scalar field to the gravitational field. In this framework, we analyze the perturbation formalism and stability properties of spherically symmetric black holes. Assuming that no background scalar field is present, gravitational perturbations with polar and axial parities decouple. We find no effect of the Chern-Simons coupling on the polar sector, while axial perturbations couple to the Chern-Simons scalar field. The axial sector can develop strong instabilities if the coupling parameter $\ensuremath{\beta}$, associated to the dynamical coupling of the scalar field, is small enough; this yields a constraint on $\ensuremath{\beta}$ which is much stronger than the constraints previously known in the literature.

Unambiguous determination of gravitational waveforms from binary black hole mergers.

Abstract: Gravitational radiation is properly defined only at future null infinity (J^+), but in practice it is estimated from data calculated at a finite radius. We have used characteristic extraction to calculate gravitational radiation at J^+ for the inspiral and merger of two equal-mass nonspinning black holes. Thus we have determined the first unambiguous merger waveforms for this problem. The implementation is general purpose and can be applied to calculate the gravitational radiation, at J^+, given data at a finite radius calculated in another computation.

Testing Horava-Lifshitz gravity using thin accretion disk properties

Abstract: Recently, a renormalizable gravity theory with higher spatial derivatives in four dimensions was proposed by Horava. The theory reduces to Einstein gravity with a nonvanishing cosmological constant in IR, but it has improved UV behaviors. The spherically symmetric black hole solutions for an arbitrary cosmological constant, which represent the generalization of the standard Schwarzschild-(anti) de Sitter solution, have also been obtained for the Horava-Lifshitz theory. The exact asymptotically flat Schwarzschild-type solution of the gravitational field equations in Horava gravity contains a quadratic increasing term, as well as the square root of a fourth order polynomial in the radial coordinate, and it depends on one arbitrary integration constant. The IR-modified Horava gravity seems to be consistent with the current observational data, but in order to test its viability more observational constraints are necessary. In the present paper we consider the possibility of observationally testing Horava gravity by using the accretion disk properties around black holes. The energy flux, the temperature distribution, the emission spectrum, as well as the energy conversion efficiency are obtained, and compared to the standard general relativistic case. Particular signatures can appear in the electromagnetic spectrum, thus leading to the possibility of directly testing Horava gravity models bymore » using astrophysical observations of the emission spectra from accretion disks.« less

Alternative mission architectures for a gravity recovery satellite mission

Abstract: Since its launch in 2002, the Gravity Recovery and Climate Experiment (GRACE) mission has been providing measurements of the time-varying Earth gravity field. The GRACE mission architecture includes two satellites in near-circular, near-polar orbits separated in the along-track direction by approximately 220 km (e.g. collinear). A microwave ranging instrument measures changes in the distance between the spacecraft, while accelerometers on each spacecraft are used to measure changes in distance due to non-gravitational forces. The fact that the satellites are in near-polar orbits coupled with the fact that the inter-satellite range measurements are directed in the along-track direction, contributes to longitudinal striping in the estimated gravity fields. This paper examines four candidate mission architectures for a future gravity recovery satellite mission to assess their potential in measuring the gravity field more accurately than GRACE. All satellites were assumed to have an improved measurement system, with an inter-satellite laser ranging instrument and a drag-free system for removal of non-gravitational accelerations. Four formations were studied: a two-satellite collinear pair similar to GRACE; a four-satellite architecture with two collinear pairs; a two-satellite cartwheel formation; and a four-satellite cartwheel formation. A cartwheel formation consists of satellites performing in-plane, relative elliptical motion about their geometric center, so that inter-satellite measurements are, at times, directed radially (e.g. parallel to the direction towards the center of the Earth) rather than along-track. Radial measurements, unlike along-track measurements, have equal sensitivity to mass distribution in all directions along the Earth’s surface and can lead to higher spatial resolution in the derived gravity field. The ability of each architecture to recover the gravity field was evaluated using numerical simulations performed with JPL’s GIPSY-OASIS software package. Thirty days of data were used to estimate gravity fields complete to degree and order 60. Evaluations were done for 250 and 400 km nominal orbit altitudes. The sensitivity of the recovered gravity field to under-sampled effects was assessed using simulated errors in atmospheric/ocean dealiasing (AOD) models. Results showed the gravity field errors associated with the four-satellite cartwheel formation were approximately one order of magnitude lower than the collinear satellite pair when only measurement system errors were included. When short-period AOD model errors were introduced, the gravity field errors for each formation were approximately the same. The cartwheel formations eliminated most of the longitudinal striping seen in the gravity field errors. A covariance analysis showed the error spectrum of the cartwheel formations to be lower and more isotropic than that of the collinear formations.

Secular Evolution of a Satellite by Tidal Effect: Application to Triton

Abstract: Some of the satellites in the solar system, including the Moon, appear to have been captured from heliocentric orbits at some point in their past, and then have evolved to the present configurations. The exact process of how this trapping occurred is unknown, but the dissociation of a planetesimal binary in the gravitational field of the planet, gas drag, or a massive collision seem to be the best candidates. However, all these mechanisms leave the satellites in elliptical orbits that need to be damped to the present almost circular ones. Here, we give a complete description of the secular tidal evolution of a satellite just after entering a bounding state with the planet. In particular, we take into account the spin evolution of the satellite, which has often been assumed synchronous in previous studies. We apply our model to Triton and successfully explain some geophysical properties of this satellite, as well as the main dynamical features observed for the Neptunian system.

Tidal dynamics of extended bodies in planetary systems and multiple stars

Abstract: Context. With the discovery during the past decade of a large number of extrasolar planets orbiting their parent stars at distances lower than 0.1 astronomical unit (and the launch and the preparation of dedicated space missions such as CoRoT and KEPLER), with the position of inner natural satellites around giant planets in our Solar System and with the existence of very close but separated binary stars, tidal interaction has to be studied carefully.Aims. This interaction is usually studied with a punctual approximation for the tidal perturber. The purpose of this paper is to examine the step beyond this traditional approach by considering the tidal perturber as an extended body. To achieve this, we studied the gravitational interaction between two extended bodies and, more precisely, the interaction between mass multipole moments of their gravitational fields and the associated tidal phenomena.Methods. We use cartesian symmetric trace free tensors, their relation with spherical harmonics and Kaula's transform enables us to analytically derive the tidal and mutual interaction potentials, as well as the associated disturbing functions in extended body systems.Results. The tidal and mutual interaction potentials of two extended bodies are derived. In addition, the external gravitational potential of such a tidally disturbed extended body is obtained, using the Love number theory, as well as the associated disturbing function. Finally, the dynamical evolution equations for such a system are given in their more general form without any linearization. We also compare, under a simplified assumption, this formalism to the punctual case. We show that the non-punctual terms have to be taken into account for strongly deformed perturbers (J 2 ≥ 10-2 ) in very close systems (a B /R B ≤ 5).Conclusions. We show how to derive the dynamical equations for the gravitational and tidal interactions between extended bodies and associated dynamics. The conditions for applying this formalism are given.

Gravitational wave background from superinflation in loop quantum cosmology

Abstract: We investigate the behavior of tensor fluctuations in Loop Quantum Cosmology, focusing on a class of scaling solutions which admit a near scale-invariant scalar field power spectrum. We obtain the spectral index of the gravitational field perturbations, and find a strong blue tilt in the power spectrum with n{sub t}{approx_equal}2. The amplitude of tensor modes are, therefore, suppressed by many orders of magnitude on large scales compared to those predicted by the standard inflationary scenario where n{sub t}{approx_equal}0.

Odyssey: a Solar System Mission

Abstract: The Solar System Odyssey mission uses modern-day high-precision experimental techniques to test the laws of fundamental physics which determine dynamics in the solar system. It could lead to major discoveries by using demonstrated technologies and could be flown within the Cosmic Vision time frame. The mission proposes to perform a set of precision gravitation experiments from the vicinity of Earth to the outer Solar System. Its scientific objectives can be summarized as follows: (1) test of the gravity force law in the Solar System up to and beyond the orbit of Saturn; (2) precise investigation of navigation anomalies at the fly-bys; (3) measurement of Eddington’s parameter at occultations; (4) mapping of gravity field in the outer solar system and study of the Kuiper belt. To this aim, the Odyssey mission is built up on a main spacecraft, designed to fly up to 13 AU, with the following components: (a) a high-precision accelerometer, with bias-rejection system, measuring the deviation of the trajectory from the geodesics, that is also giving gravitational forces; (b) Ka-band transponders, as for Cassini, for a precise range and Doppler measurement up to 13 AU, with additional VLBI equipment; (c) optional laser equipment, which would allow one to improve the range and Doppler measurement, resulting in particular in an improved measurement (with respect to Cassini) of the Eddington’s parameter. In this baseline concept, the main spacecraft is designed to operate beyond the Saturn orbit, up to 13 AU. It experiences multiple planetary fly-bys at Earth, Mars or Venus, and Jupiter. The cruise and fly-by phases allow the mission to achieve its baseline scientific objectives [(1) to (3) in the above list]. In addition to this baseline concept, the Odyssey mission proposes the release of the Enigma radio-beacon at Saturn, allowing one to extend the deep space gravity test up to at least 50 AU, while achieving the scientific objective of a mapping of gravity field in the outer Solar System [(4) in the above list].

Unitarity and Holography in Gravitational Physics

Abstract: Because the gravitational Hamiltonian is a pure boundary term on shell, asymptotic gravitational fields store information in a manner not possible in local field theories. This fact has consequences for both perturbative and nonperturbative quantum gravity. In perturbation theory about an asymptotically flat collapsing black hole, the algebra generated by asymptotic fields on future null infinity within any neighborhood of spacelike infinity contains a complete set of observables. Assuming that the same algebra remains complete at the nonperturbative quantum level, we argue that either (1) the $S$ matrix is unitary or (2) the dynamics in the region near timelike, null, and spacelike infinity is not described by perturbative quantum gravity about flat space. We also consider perturbation theory about a collapsing asymptotically anti-de Sitter (AdS) black hole, where we show that the algebra of boundary observables within any neighborhood of any boundary Cauchy surface is similarly complete. Whether or not this algebra continues to be complete nonperturbatively, the assumption that the Hamiltonian remains a boundary term implies that information available at the AdS boundary at any one time ${t}_{1}$ remains present at this boundary at any other time ${t}_{2}$.

Gravitational corrections to the Euler-Heisenberg Lagrangian

Abstract: We use the worldline formalism for calculating the one-loop effective action for the Einstein-Maxwell background induced by charged scalars or spinors, in the limit of low energy and weak gravitational field but treating the electromagnetic field nonperturbatively. The effective action is obtained in a form which generalizes the standard proper-time representation of the Euler-Heisenberg Lagrangian. We compare with previous work and discuss possible applications.

Schrodinger formalism, black hole horizons, and singularity behavior

Abstract: The Gauss-Codazzi method is used to discuss the gravitational collapse of a charged Reisner-Nordstr\"om domain wall We solve the classical equations of motion of a thin charged shell moving under the influence of its own gravitational field and show that a form of cosmic censorship applies If the charge of the collapsing shell is greater than its mass, then the collapse does not form a black hole Instead, after reaching some minimal radius, the shell bounces back The Schr\"odinger canonical formalism is used to quantize the motion of the charged shell The limits near the horizon and near the singularity are explored Near the horizon, the Schr\"odinger equation describing evolution of the collapsing shell takes the form of the massive wave equation with a position dependent mass The outgoing and incoming modes of the solution are related by the Bogolubov transformation which precisely gives the Hawking temperature Near the classical singularity, the Schr\"odinger equation becomes nonlocal, but the wave function describing the system is nonsingular This indicates that while quantum effects may be able to remove the classical singularity, it may also introduce some new effects

Solar system tests of Ho\v{r}ava-Lifshitz gravity

Abstract: Recently, a renormalizable gravity theory with higher spatial derivatives in four dimensions was proposed by Ho\v{r}ava. The theory reduces to Einstein gravity with a non-vanishing cosmological constant in IR, but it has improved UV behaviors. The spherically symmetric black hole solutions for an arbitrary cosmological constant, which represent the generalization of the standard Schwarzschild-(A)dS solution, has also been obtained for the Ho\v{r}ava-Lifshitz theory. The exact asymptotically flat Schwarzschild type solution of the gravitational field equations in Ho\v{r}ava gravity contains a quadratic increasing term, as well as the square root of a fourth order polynomial in the radial coordinate, and it depends on one arbitrary integration constant. The IR modified Ho\v{r}ava gravity seems to be consistent with the current observational data, but in order to test its viability more observational constraints are necessary. In the present paper we consider the possibility of observationally testing Ho\v{r}ava gravity at the scale of the Solar System, by considering the classical tests of general relativity (perihelion precession of the planet Mercury, deflection of light by the Sun and the radar echo delay) for the spherically symmetric black hole solution of Ho\v{r}ava-Lifshitz gravity. All these gravitational effects can be fully explained in the framework of the vacuum solution of the gravity. Moreover, the study of the classical general relativistic tests also constrain the free parameter of the solution.

Gravitational waves from self-ordering scalar fields

Abstract: Gravitational waves were copiously produced in the early Universe whenever the processes taking place were sufficiently violent. The spectra of several of these gravitational wave backgrounds on subhorizon scales have been extensively studied in the literature. In this paper we analyze the shape and amplitude of the gravitational wave spectrum on scales which are superhorizon at the time of production. Such gravitational waves are expected from the self ordering of randomly oriented scalar fields which can be present during a thermal phase transition or during preheating after hybrid inflation. We find that, if the gravitational wave source acts only during a small fraction of the Hubble time, the gravitational wave spectrum at frequencies lower than the expansion rate at the time of production behaves as $\Omega_{\rm GW}(f) \propto f^3$ with an amplitude much too small to be observable by gravitational wave observatories like LIGO, LISA or BBO. On the other hand, if the source is active for a much longer time, until a given mode which is initially superhorizon ($k\eta_* \ll 1$), enters the horizon, for $k\eta \gtrsim 1$, we find that the gravitational wave energy density is frequency independent, i.e. scale invariant. Moreover, its amplitude for a GUT scale scenario turns out to be within the range and sensitivity of BBO and marginally detectable by LIGO and LISA. This new gravitational wave background can compete with the one generated during inflation, and distinguishing both may require extra information.