Showing papers on "Gravitational field published in 2008"

Time delay and magnification centroid due to gravitational lensing by black holes and naked singularities

Abstract: We model the massive dark object at the center of the Galaxy as a Schwarzschild black hole as well as Janis-Newman-Winicour naked singularities, characterized by the mass and scalar charge parameters, and study gravitational lensing (particularly time delay, magnification centroid, and total magnification) by them. We find that the lensing features are qualitatively similar (though quantitatively different) for Schwarzschild black holes, weakly naked, and marginally strongly naked singularities. However, the lensing characteristics of strongly naked singularities are qualitatively very different from those due to Schwarzschild black holes. The images produced by Schwarzschild black hole lenses and weakly naked and marginally strongly naked singularity lenses always have positive time delays. On the other hand, strongly naked singularity lenses can give rise to images with positive, zero, or negative time delays. In particular, for a large angular source position the direct image (the outermost image on the same side as the source) due to strongly naked singularity lensing always has a negative time delay. We also found that the scalar field decreases the time delay and increases the total magnification of images; this result could have important implications for cosmology. As the Janis-Newman-Winicour metric also describes the exterior gravitational field of a scalar star, naked singularities as well as scalar star lenses, if these exist in nature, will serve as more efficient cosmic telescopes than regular gravitational lenses.

Probes and Tests of Strong-Field Gravity with Observations in the Electromagnetic Spectrum

Abstract: Neutron stars and black holes are the astrophysical systems with the strongest gravitational fields in the universe. In this article, I review the prospect of using observations of such compact objects to probe some of the most intriguing general relativistic predictions in the strong-field regime: the absence of stable circular orbits near a compact object and the presence of event horizons around black-hole singularities. I discuss the need for a theoretical framework, within which future experiments will provide detailed, quantitative tests of gravity theories. Finally, I summarize the constraints imposed by current observations of neutron stars on potential deviations from general relativity.

Numerical Hydrodynamics and Magnetohydrodynamics in General Relativity

Abstract: This article presents a comprehensive overview of numerical hydrodynamics and magneto-hydrodynamics (MHD) in general relativity. Some significant additions have been incorporated with respect to the previous two versions of this review (2000, 2003), most notably the coverage of general-relativistic MHD, a field in which remarkable activity and progress has occurred in the last few years. Correspondingly, the discussion of astrophysical simulations in general-relativistic hydrodynamics is enlarged to account for recent relevant advances, while those dealing with general-relativistic MHD are amply covered in this review for the first time. The basic outline of this article is nevertheless similar to its earlier versions, save for the addition of MHD-related issues throughout. Hence, different formulations of both the hydrodynamics and MHD equations are presented, with special mention of conservative and hyperbolic formulations well adapted to advanced numerical methods. A large sample of numerical approaches for solving such hyperbolic systems of equations is discussed, paying particular attention to solution procedures based on schemes exploiting the characteristic structure of the equations through linearized Riemann solvers. As previously stated, a comprehensive summary of astrophysical simulations in strong gravitational fields is also presented. These are detailed in three basic sections, namely gravitational collapse, black-hole accretion, and neutron-star evolutions; despite the boundaries, these sections may (and in fact do) overlap throughout the discussion. The material contained in these sections highlights the numerical challenges of various representative simulations. It also follows, to some extent, the chronological development of the field, concerning advances in the formulation of the gravitational field, hydrodynamics and MHD equations and the numerical methodology designed to solve them. To keep the length of this article reasonable, an effort has been made to focus on multidimensional studies, directing the interested reader to earlier versions of the review for discussions on one-dimensional works.

Nonminimal coupling of perfect fluids to curvature

Abstract: In this work, we consider different forms of relativistic perfect fluid Lagrangian densities that yield the same gravitational field equations in general relativity (GR). A particularly intriguing example is the case with couplings of the form [1+f{sub 2}(R)]L{sub m}, where R is the scalar curvature, which induces an extra force that depends on the form of the Lagrangian density. It has been found that, considering the Lagrangian density L{sub m}=p, where p is the pressure, the extra-force vanishes. We argue that this is not the unique choice for the matter Lagrangian density, and that more natural forms for L{sub m} do not imply the vanishing of the extra force. Particular attention is paid to the impact on the classical equivalence between different Lagrangian descriptions of a perfect fluid.

A Massive Core in Jupiter Predicted From First-Principles Simulations

Abstract: Hydrogen-helium mixtures at conditions of Jupiter’s interior are studied with first-principles computer simulations The resulting equation of state (EOS) implies that Jupiter possesses a central core of 14 – 18 Earth masses of heavier elements, a result that supports core accretion as standard model for the formation of hydrogen-rich giant planets Our nominal model has about 2 Earth masses of planetary ices in the H-He-rich mantle, a result that is, within modeling errors, consistent with abundances measured by the 1995 Galileo Entry Probe mission (equivalent to about 5 Earth masses of planetary ices when extrapolated to the mantle), suggesting that the composition found by the probe may be representative of the entire planet Interior models derived from this first-principles EOS do not give a match to Jupiter’s gravity moment J4 unless one invokes interior differential rotation, implying that jovian interior dynamics has an observable effect on the measured gravity field

The GeoForschungsZentrum Potsdam/Groupe de Recherche de Gèodésie Spatiale satellite-only and combined gravity field models: EIGEN-GL04S1 and EIGEN-GL04C

Abstract: The recent improvements in the Gravity Recovery And Climate Experiment (GRACE) tracking data processing at GeoForschungsZentrum Potsdam (GFZ) and Groupe de Recherche de Geodesie Spatiale (GRGS) Toulouse, the availability of newer surface gravity data sets in the Arctic, Antarctica and North-America, and the availability of a new mean sea surface height model from altimetry processing at GFZ gave rise to the generation of two new global gravity field models. The first, EIGEN-GL04S1, a satellite-only model complete to degree and order 150 in terms of spherical harmonics, was derived by combination of the latest GFZ Potsdam GRACE-only (EIGEN-GRACE04S) and GRGS Toulouse GRACE/LAGEOS (EIGEN-GL04S) mean field solutions. The second, EIGEN-GL04S1 was combined with surface gravity data from altimetry over the oceans and gravimetry over the continents to derive a new high-resolution global gravity field model called EIGEN-GL04C. This model is complete to degree and order 360 and thus resolves geoid and gravity anomalies at half- wavelengths of 55 km at the equator. A degree-dependent combination method has been applied in order to preserve the high accuracy from the GRACE satellite data in the lower frequency band of the geopotential and to form a smooth transition to the high-frequency information coming from the surface data. Compared to pre-CHAMP global high-resolution models, the accuracy was improved at a spatial resolution of 200 km (half-wavelength) by one order of magnitude to 3 cm in terms of geoid heights. The accuracy of this model (i.e. the commission error) at its full spatial resolution is estimated to be 15 cm. The model shows a reduced artificial meridional striping and an increased correlation of EIGEN-GL04C-derived geostrophic meridional currents with World Ocean Atlas 2001 (WOA01) data. These improvements have led to select EIGEN-GL04C for JASON-1 satellite altimeter data reprocessing.

Generalized Vaidya spacetime in Lovelock gravity and thermodynamics on the apparent horizon

Abstract: We present a kind of generalized Vaidya solutions in a generic Lovelock gravity. This solution generalizes the simple case in Gauss-Bonnet gravity reported recently by some authors. We study the thermodynamics of apparent horizon in this generalized Vaidya spacetime. Treating those terms except for the Einstein tensor as an effective energy-momentum tensor in the gravitational field equations, and using the unified first law in Einstein gravity theory, we obtain an entropy expression for the apparent horizon. We also obtain an energy expression of this spacetime, which coincides with the generalized Misner-Sharp energy proposed by Maeda and Nozawa in Lovelock gravity.

Hydrological Signals Observed by the GRACE Satellites

Abstract: The main objective of the US-German twin-satellite mission GRACE (Gravity Recovery and Climate Experiment), launched in March 2002, is a precise survey of the Earth’s time-variable gravity field at unprecedented temporal and spatial scales Temporal changes in the gravity field are related to continuous mass redistributions near the Earth’s surface which are caused by various geophysical and climatologically driven processes Vice versa, transferring the GRACE-based gravity variations into time series of the spatial variability of surface mass anomalies, the mission allows for the first time for a quantification of the ongoing mass transport Such data is of unique importance for a comprehensive modeling, understanding and interplay of these processes In this contribution we give an overview of the basic features of the GRACE satellite mission, the gravity recovery process and the derived gravity products at GeoForschungsZentrum Potsdam (GFZ), as well as the interpretation of the GRACE gravity data with the focus on the detection of hydrological signals This includes a description of the evolution and present status of the quality of GFZ’s GRACE-based global gravity models on the actual fourth model generation (called GFZ-RL04), and an overview of recent findings using GRACE data in hydrological applications

Transition rate of the Unruh-DeWitt detector in curved spacetime

Abstract: We examine the Unruh-DeWitt particle detector coupled to a scalar field in an arbitrary Hadamard state in four-dimensional curved spacetime. Using smooth switching functions to turn on and off the interaction, we obtain a regulator-free integral formula for the total excitation probability, and we show that an instantaneous transition rate can be recovered in a suitable limit. Previous results in Minkowski space are recovered as a special case. As applications, we consider an inertial detector in the Rindler vacuum and a detector at rest in a static Newtonian gravitational field. Gravitational corrections to decay rates in atomic physics laboratory experiments on the surface of the Earth are estimated to be suppressed by 42 orders of magnitude.

Comparison of approximate gravitational lens equations and a proposal for an improved new one

Abstract: Keeping the exact general relativistic treatment of light bending as a reference, we compare the accuracy of commonly used approximate lens equations. We conclude that the best approximate lens equation is the Ohanian lens equation, for which we present a new expression in terms of distances between observer, lens, and source planes. We also examine a realistic gravitational lensing case, showing that the precision of the Ohanian lens equation might be required for a reliable treatment of gravitational lensing and a correct extraction of the full information about gravitational physics.

Thin accretion disks in f(R) modified gravity models

Abstract: We consider the basic physical properties of matter forming a thin accretion disc in the static and spherically symmetric space-time metric of the vacuum f(R) modified gravity models. The Lagrangian of the generalized gravity theory is also obtained in a parametric form, and the conditions of the viability of the model are also discussed. The exact Schwarzschild-type solution of the gravitational field equations in the f(R) gravity contains a linearly increasing term, as well as a logarithmic correction, as compared to the standard Schwarzschild solution of general relativity, and it depends on four arbitrary integration constants. The energy flux and the emission spectrum from the accretion disk around the f(R) gravity black holes are obtained, and they are compared to the general relativistic case. Particular signatures can appear in the electromagnetic spectrum, thus leading to the possibility of directly testing modified gravity models by using astrophysical observations of the emission spectra from accretion disks.

Performance and scientific objectives of the SELENE (KAGUYA) Multiband Imager

Abstract: The Multiband Imager (MI) is one of the 14 instruments for the Japanese SELENE (KAGUYA) mission. Goal of the SELENE (KAGUYA) mission is to understand origin and evolution of the Moon by obtaining global element and mineral compositions, topological structure, gravity field of the whole Moon, and electromagnetic and particle environment of the Moon. MI is designed to be a high-resolution multiband imaging camera with a spatial resolution in visible bands of 20 m and a spatial resolution in near-infrared bands of 62 m from the 100 km SELENE (KAGUYA) orbit altitude. The MI flight model has been manufactured and integrated. MTF, viewing vector, over-all sensibility, sensor linearity and electrical noise level (S/N estimation test) were measured, and the results indicate that the MI will provide sufficient MTF and low-noise data, just as estimated in the MI design phase. Operation and data analyses plans have been established, and related tools and algorithms have been developed and checked. One of MI scientific objectives is to investigate small but scientifically very important areas such as crater central peaks and crater walls and to investigate magnesian anorthosites.

f ( R ) gravity equation of state

Abstract: The $\mathbf{f}(R)$ gravity field equations are derived as an equation of state of local space-time thermodynamics. Jacobson's arguments are nontrivially extended, by means of a more general definition of local entropy, for which Wald's definition of dynamic black hole entropy is used, as well as the concept of an effective Newton constant for graviton exchange, which recently appeared in the literature.

Gravitational-wave probe of effective quantum gravity

Abstract: All modern routes leading to a quantum theory of gravity - i.e., perturbative quantum gravitational one-loop exact correction to the global chiral current in the standard model, string theory, and loop quantum gravity - require modification of the classical Einstein-Hilbert action for the spacetime metric by the addition of a parity-violating Chern-Simons term. The introduction of such a term leads to spacetimes that manifest an amplitude birefringence in the propagation of gravitational waves. While the degree of birefringence may be intrinsically small, its effects on a gravitational wave accumulate as the wave propagates. Observation of gravitational waves that have propagated over cosmological distances may allow the measurement of even a small birefringence, providing evidence of quantum gravitational effects. The proposed Laser Interferometer Space Antenna (LISA) will be sensitive enough to observe the gravitational waves from sources at cosmological distances great enough that interesting bounds on the Chern-Simons coupling may be found. Here we evaluate the effect of a Chern-Simons induced spacetime birefringence to the propagation of gravitational waves from such systems. Focusing attention on the gravitational waves from coalescing binary black holes systems, which LISA will be capable of observing at redshifts approaching 30, we find that the signature ofmore » Chern-Simons gravity is a time-dependent change in the apparent orientation of the binary's orbital angular momentum with respect to the observer line-of-sight, with the magnitude of change reflecting the integrated history of the Chern-Simons coupling over the worldline of the radiation wave front. While spin-orbit coupling in the binary system will also lead to an evolution of the system's orbital angular momentum, the time dependence and other details of this real effect are different than the apparent effect produced by Chern-Simons birefringence, allowing the two effects to be separately identified. In this way gravitational-wave observations with LISA may thus provide our first and only opportunity to probe the quantum structure of spacetime over cosmological distances.« less

Waveless Approximation Theories of Gravity

Abstract: The analysis of a general multibody physical system governed by Einstein's equations is quite difficult, even if numerical methods (on a computer) are used. Some of the difficulties — many coupled degrees of freedom, dynamic instability — are associated with the presence of gravitational waves. We have developed a number of "waveless approximation theories" (WAT's) which repress the gravitational radiation and thereby simplify the analysis. The matter, according to these theories, evolves dynamically. The gravitational field, however, is determined at each time step by a set of elliptic equations with matter sources. There is reason to believe that for many physical systems, the WAT-generated system evolution is a very accurate approximation to that generated by the full Einstein theory.

A comparison of different mass elements for use in gravity gradiometry

Abstract: Topographic and isostatic mass anomalies affect the external gravity field of the Earth. Therefore, these effects also exist in the gravity gradients observed, e.g., by the satellite gravity gradiometry mission GOCE (Gravity and Steady-State Ocean Circulation Experiment). The downward continuation of the gravitational signals is rather difficult because of the high-frequency behaviour of the combined topographic and isostatic effects. Thus, it is preferable to smooth the gravity field by some topographic-isostatic reduction. In this paper the focus is on the modelling of masses in the space domain, which can be subdivided into different mass elements and evaluated with analytical, semi-analytical and numerical methods. Five alternative mass elements are reviewed and discussed: the tesseroid, the point mass, the prism, the mass layer and the mass line. The formulae for the potential, the attraction components and the Marussi tensor of second-order potential derivatives are provided. The formulae for different mass elements and computation methods are checked by assuming a synthetic topography of constant height over a spherical cap and the position of the computation point on the polar axis. For this special situation an exact analytical solution for the tesseroid exists and a comparison between the analytical solution of a spherical cap and the modelling of different mass elements is possible. A comparison of the computation times shows that modelling by tesseroids with different methods produces the most accurate results in an acceptable computation time. As a numerical example, the Marussi tensor of the topographic effect is computed globally using tesseroids calculated by Gauss–Legendre cubature (3D) on the basis of a digital height model. The order of magnitude in the radial-radial component is about ± 8 E.U.

Relativistic closed-form Hamiltonian for many-body gravitating systems in the post-Minkowskian approximation.

Abstract: The Hamiltonian for a system of relativistic bodies interacting by their gravitational field is found in the post-Minkowskian approximation, including all terms linear in the gravitational constant. It is given in a surprisingly simple closed form as a function of canonical variables describing the bodies only. The field is eliminated by solving inhomogeneous wave equations, applying transverse-traceless projections, and using the Routh functional. By including all special relativistic effects our Hamiltonian extends the results described in classical textbooks of theoretical physics. As an application, the scattering of relativistic objects is considered.

Anomalous cosmic-microwave-background polarization and gravitational chirality.

Abstract: We consider the possibility that gravity breaks parity, with left and right-handed gravitons coupling to matter with a different Newton's constant and show that this would affect their zero-point vacuum fluctuations during inflation. Should there be a cosmic background of gravity waves, the effect would translate into anomalous cosmic microwave background polarization. Nonvanishing temperature-magnetic (TB) mode [and electric-magnetic mode] components emerge, revealing interesting experimental targets. Indeed, if reasonable chirality is present a TB measurement would provide the easiest way to detect a gravitational wave background. We speculate on the theoretical implications of such an observation.

Inflationary perturbations: The Cosmological Schwinger effect

Abstract: This pedagogical review aims at presenting the fundamental aspects of the theory of inflationary cosmological perturbations of quantum-mechanical origin. The analogy with the well-known Schwinger effect is discussed in detail and a systematic comparison of the two physical phenomena is carried out. In particular, it is demonstrated that the two underlying formalisms differ only up to an irrelevant canonical transformation. Hence, the basic physical mechanisms at play are similar in both cases and can be reduced to the quantization of a parametric oscillator leading to particle creation due to the interaction with a classical source: pair production in vacuum is therefore equivalent to the appearance of a growing mode for the cosmological fluctuations. The only difference lies in the nature of the source: an electric field in the case of the Schwinger effect and the gravitational field in the case of inflationary perturbations. Although, in the laboratory, it is notoriously diffcult to produce an electric field such that pairs extracted from the vacuum can be detected, the gravitational field in the early universe can be strong enough to lead to observable effects that ultimately reveal themselves as temperature fluctuations in the cosmic microwave background. Finally, the question of how quantum cosmological perturbations can be considered as classical is discussed at the end of this chapter.

Measurement Analysis and Quantum Gravity

Abstract: We consider the question of whether consistency arguments based on measurement theory show that the gravitational field must be quantized. Motivated by the argument of Eppley and Hannah, we apply a DeWitt-type measurement analysis to a coupled system that consists of a gravitational wave interacting with a mass cube. We also review the arguments of Eppley and Hannah and of DeWitt, and investigate a second model in which a gravitational wave interacts with a quantized scalar field. We argue that one cannot conclude from the existing gedanken experiments that gravity has to be quantized. Despite the many physical arguments which speak in favor of a quantum theory of gravity, it appears that the justification for such a theory must be based on empirical tests and does not follow from logical arguments alone.

A data-driven approach to local gravity field modelling using spherical radial basis functions

Abstract: We propose a methodology for local gravity field modelling from gravity data using spherical radial basis functions. The methodology comprises two steps: in step 1, gravity data (gravity anomalies and/or gravity disturbances) are used to estimate the disturbing potential using least-squares techniques. The latter is represented as a linear combination of spherical radial basis functions (SRBFs). A data-adaptive strategy is used to select the optimal number, location, and depths of the SRBFs using generalized cross validation. Variance component estimation is used to determine the optimal regularization parameter and to properly weight the different data sets. In the second step, the gravimetric height anomalies are combined with observed differences between global positioning system (GPS) ellipsoidal heights and normal heights. The data combination is written as the solution of a Cauchy boundary-value problem for the Laplace equation. This allows removal of the non-uniqueness of the problem of local gravity field modelling from terrestrial gravity data. At the same time, existing systematic distortions in the gravimetric and geometric height anomalies are also absorbed into the combination. The approach is used to compute a height reference surface for the Netherlands. The solution is compared with NLGEO2004, the official Dutch height reference surface, which has been computed using the same data but a Stokes-based approach with kernel modification and a geometric six-parameter “corrector surface” to fit the gravimetric solution to the GPS-levelling points. A direct comparison of both height reference surfaces shows an RMS difference of 0.6 cm; the maximum difference is 2.1 cm. A test at independent GPS-levelling control points, confirms that our solution is in no way inferior to NLGEO2004.

Off-equatorial orbits in strong gravitational fields near compact objects

Abstract: Near a black hole or an ultracompact star, motion of particles is governed by strong gravitational field. Electrically charged particles feel also electromagnetic force arising due to currents inside the star or plasma circling around. We study a possibility that the interplay between gravitational and electromagnetic action may allow for stable, energetically bound off-equatorial motion of charged particles. This would represent well-known generalized Stormer's 'halo' orbits, which have been discussed in connection with the motion of dust grains in planetary magnetospheres. We demonstrate that such orbits exist and can be astrophysically relevant when a compact star or a black hole is endowed with a dipole-type magnetic field. In the case of Kerr-Newman solution, numerical analysis shows that the mutually connected gravitational and electromagnetic fields do not allow existence of stable halo orbits above the outer horizon of black holes. Such orbits are either hidden under the inner black-hole horizon, or they require the presence of a naked singularity.

Astrod and astrod i — overview and progress

Abstract: In this paper, we present an overview of ASTROD (Astrodynamical Space Test of Relativity using Optical Devices) and ASTROD I mission concepts and studies. The missions employ deep-space laser ranging using drag-free spacecraft to map the gravitational field in the solar-system. The solar-system gravitational field is determined by three factors: the dynamic distribution of matter in the solar system; the dynamic distribution of matter outside the solar system (galactic, cosmological, etc.) and gravitational waves propagating through the solar system. Different relativistic theories of gravity make different predictions of the solar-system gravitational. eld. Hence, precise measurements of the solar-system gravitational. eld test these relativistic theories, in addition to gravitational wave observations, determination of the matter distribution in the solar-system and determination of the observable (testable) influence of our galaxy and cosmos. The tests and observations include: (i) a precise determination of the relativistic parameters beta and gamma with 3-5 orders of magnitude improvement over previous measurements; (ii) a 1 -2 order of magnitude improvement in the measurement of G; (iii) a precise determination of any anomalous, constant acceleration A(a) directed towards the Sun; (iv) a measurement of solar angular momentum via the Lense-Thirring effect; (v) the detection of solar g-mode oscillations via their changing gravity. eld, thus, providing a new eye to see inside the Sun; (vi) precise determination of the planetary orbit elements and masses; (vii) better determination of the orbits and masses of major asteroids; (viii) detection and observation of gravitational waves from massive black holes and galactic binary stars in the frequency range 50 mu Hz to 5 mHz; and (ix) exploring background gravitational waves. The baseline scheme of ASTROD is to have two spacecraft in separate solar orbits and one spacecraft near the Earth -Sun L1/L2 point carrying a payload of a proof mass, two telescopes, two 1 -2 W lasers with spares, a clock and a drag-free system ranging coherently among one another using lasers. ASTROD I is a first step towards ASTROD. Its scheme is to have one spacecraft in a Venus-gravity-assisted solar orbit, ranging optically with ground stations with less ambitious, but still significant scientific goals.

Pseudo-newtonian gravitational potential for schwarzschild–de sitter space–times

Abstract: Pseudo-Newtonian gravitational potential describing the gravitational field of static and spherically symmetric black holes in the universe with a repulsive cosmological constant is introduced. In order to demonstrate the accuracy of the pseudo-Newtonian approach, the related effective potential for test particle motion is constructed and compared with its general-relativistic counterpart given by the Schwarzschild–de Sitter geometry. The results indicate that such an approach could be useful in applications of developed Newtonian theories of accretion disks in astrophysically interesting situations in large galactic structures for the Schwarzschild–de Sitter space–times with the cosmological parameter y = Λ M2/3 ≤ 10-6.

Vestibular nuclei and cerebellum put visual gravitational motion in context.

Abstract: Animal survival in the forest, and human success on the sports field, often depend on the ability to seize a target on the fly. All bodies fall at the same rate in the gravitational field, but the corresponding retinal motion varies with apparent viewing distance. How then does the brain predict time-to-collision under gravity? A perspective context from natural or pictorial settings might afford accurate predictions of gravity's effects via the recovery of an environmental reference from the scene structure. We report that embedding motion in a pictorial scene facilitates interception of gravitational acceleration over unnatural acceleration, whereas a blank scene eliminates such bias. Functional magnetic resonance imaging (fMRI) revealed blood-oxygen-level-dependent correlates of these visual context effects on gravitational motion processing in the vestibular nuclei and posterior cerebellar vermis. Our results suggest an early stage of integration of high-level visual analysis with gravity-related motion information, which may represent the substrate for perceptual constancy of ubiquitous gravitational motion.

A new general relativistic magnetohydrodynamics code for dynamical spacetimes

Abstract: We present a new numerical code that solves the general relativistic magneto-hydrodynamical (GRMHD) equations coupled to the Einstein equations for the evolution of a dynamical spacetime within a conformally-flat approximation. This code has been developed with the main objective of studying astrophysical scenarios in which both, high magnetic fields and strong gravitational fields appear, such as the magneto-rotational collapse of stellar cores, the collapsar model of GRBs, and the evolution of neutron stars. The code is based on an existing and thoroughly tested purely hydrodynamical code and on its extension to accommodate weakly magnetized fluids (passive magnetic-field approximation). These codes have been applied in the past to simulate the aforementioned scenarios with increasing levels of sophistication in the input physics. The numerical code we present here is based on high-resolution shockcapturing schemes to solve the GRMHD equations, which are cast in first-order, flux-conservative hyperbolic form, together with the flux constraint transport method to ensure the solenoidal condition of the magnetic field. Since the astrophysical applications envisaged do not deviate significantly from spherical symmetry, the conformal flatness condition approximation is used for the formulation of the Einstein equations; this has repeatedly shown to yield very good agreement with full general relativistic simulations of corecollapse supernovae and the evolution of isolated neutron stars. In addition, the code can handle several equations of state, from simple analytical expressions to microphysical tabulated ones. In this paper we present stringent tests of our new GRMHD numerical code, which show its ability to handle all aspects appearing in the astrophysical scenarios for which the code is intended, namely relativistic shocks, highly magnetized fluids, and equilibrium configurations of magnetized neutron stars. As an application, magnetorotational core-collapse simulations of a realistic progenitor are presented and the results compared with our previous findings in the passive magnetic-field approximation.

Evolution of cosmological gravitational waves in f(R) gravity

Abstract: We give a rigorous and mathematically clear presentation of the covariant and gauge-invariant theory of gravitational waves in a perturbed Friedmann-Lemaitre-Robertson-Walker universe for fourth order gravity, where the matter is described by a perfect fluid with a barotropic equation of state. As an example of a consistent analysis of tensor perturbations in fourth order gravity, we apply the formalism to a simple background solution of R{sup n} gravity. We obtain the exact solutions of the perturbation equations for scales much bigger than and smaller than the Hubble radius. It is shown that the evolution of tensor modes is highly sensitive to the choice of n and an interesting new feature arises. During the radiation dominated era, their exists a growing tensor perturbation for nearly all choices of n. This occurs even when the background model is undergoing accelerated expansion as opposed to the case of general relativity. Consequently, cosmological gravitational wave modes can in principle provide a strong constraint on the theory of gravity independent of other cosmological data sets.