We review the experimental evidence for Einstein's special and general relativity. A variety of high precision null experiments verify the weak equivalence principle and local Lorentz invariance, while gravitational redshift and other clock experiments support local position invariance. Together these results confirm the Einstein Equivalence Principle which underlies the concept that gravitation must be described by a metric theory. Solar system experiments that test the weak-field, post-Newtonian limit of metric theories strongly favor general relativity. The Binary Pulsar provides tests of gravitational-wave damping and of strong-field general relativity. Recently discovered binary pulsar systems may provide additional tests. Ongoing and future experiments, such as the Gravity Probe B Gyroscope Experiment, satellite tests of the Equivalence principle, and tests of gravity at short distance to look for extra spatial dimensions could constrain extensions of general relativity. Laser interferometric gravitational-wave observatories on Earth and in space may provide new tests of gravitational theory via detailed measurements of the properties of gravitational waves.

The search for gravitational waves has reached a new era as currently a network of interferometric gravitational wave detectors is in operation around the globe at its initial target sensitivity, in parallel with existing acoustic bar-type detectors, and searches are underway aimed at the first direct detection of gravitational radiation from astrophysical sources. This paper briefly summarizes the status of operating gravitational wave facilities, plans for future detector upgrades and the status of the space-based gravitational wave detector LISA. It also describes some of the most promising sources of gravitational waves for ground-based detectors like LIGO and VIRGO and LISA.

Gamma-Ray Bursts (GRBS) are the brightest explosions observed. After a serendipitous discovery and forty years of search we begin to understand their origin (type Ic supernovae for long bursts and neutron star mergers for short ones) and how they operate. While the research on the nature of GRBs still goes on we turn to application of GRBs to study other phenomena. GRBs have an enormous potential to explore new regimes of ultra-relativistic flows and of very high magnetic fields. A lot have been said about the potential usage of GRBs to determine the conditions at the early universe. Here we discuss an application of GRBs that involve new physics – namely, using the arrival times of photons and neutrinos at different energies to set limits on Lorentz invariance violation that could arise from quantum gravity effects.

I summarize some of the observational phenomenology in compact X-ray sources (neutron stars, stellar-mass black holes and super-massive black holes) where X-ray observations reveal strong gravity in action. Although there is no attempt to claim that these observations constitute or might lead in the future to real tests of General Relativity, they allow us to witness a variety of its effects in the strong field limit.

Gravitational lenses yield a very high rate of return on observational investment. Given their scarcity, their impact on our knowledge of the universe is very significant. In the weak-field limit, lensing studies are based on well-established physics and thus offer a straightforward approach to pursue many currently pressing problems of astrophysics and cosmology. Examples of these are the significance of dark matter and the density, age and size of the universe. I present recent developments in cosmological applications of gravitational lenses, focusing on estimates of the Hubble constant using strong lensing of quasars. I describe our recent measurements of time delays for the images of SDSS J1004+4112, and discuss prospects for the future utilizing synoptic telescopes, planned and under construction.

The harmonic formulation of Einstein's field equations is considered, where the gauge conditions are introduced as dynamical constraints. The difference between the fully constrained approach (used in analytical approximations) and the free evolution one (used in most numerical approximations) is pointed out. As a generalization, quasi-stationary gauge conditions are also discussed, including numerical experiments with the gauge-waves testbed. The complementary 3+1 approach is also considered, where constraints are related instead with energy and momentum first integrals and the gauge must be provided separately. The relationship between the two formalisms is discussed in a more general framework (Z4 formalism). Different strategies in black hole simulations follow when introducing singularity avoidance as a requirement. More flexible quasi-stationary gauge conditions are proposed in this context, which can be seen as generalizations of the current “freezing shift” prescriptions.

Interacting quintessence models have been proposed to explain or, at least alleviate, the coincidence problem of late cosmic acceleration. We show that it is possible to construct models that give rise to three different epochs: radiation, matter and accelerated, lasting long enough to allow the emergence of large scale structure. We confront our model with data on Cosmic Microwave Background temperature anisotropies, matter power spectrum and Supernovae type Ia luminosity distances and find that the data are only capable of setting upper limits on the interaction. We show how the integrated Sachs-Wolfe effect could provide indirect evidence of the existence of the interaction but, at present, the prospects that the coincidence problem can be explained by the coupling of dark matter to dark energy are not statistically favored by the data.

Core-collapse supernovae have been supposed to be one of the most plausible sources of gravitational waves. Based on a series of our magnetohydrodynamic core-collapse simulations, we find that the gravitational amplitudes at core bounce can be within the detection limits for the currently running laser-interferometers for a galactic supernova if the central core rotates sufficiently rapidly. This is regardless of the difference of the realistic equations of state and the possible occurrence of the QCD phase transition near core bounce. Even if the core rotates slowly, we point out that the gravitational waves generated from anisotropic neutrino radiation in the postbounce phase due to the standing accretion shock instability (SASI) could be within the detection limits of the detectors in the next generation such as LCGT and the advanced LIGO for the galactic source. Since the waveforms significantly depend on the exploding scenarios, our results suggest that we can obtain the information about the long-veiled explosion mechanism from the gravitational wave signals. Furthermore we discuss the gravitational wave background (GWB) from the explosions of Pop III stars and show that the GWB from Pop III, depending on their formation rates, can be large enough to be within the detection limits of future planned interferometers such as DECIGO and BBO in the frequency interval of ~0.1-1 Hz. This means that the detections of GW background from Pop III stars can be an important tool to supply the information about the star formation history in the early universe.

A new type of singularity theorem, based on spatial averages of physical quantities, is presented and discussed. Alternatively, the results inform us of when a spacetime can be singularity-free. This theorem provides a decisive observational difference between singular and non-singular, globally hyperbolic, open cosmological models.

Following an earlier work (Tod 2007a), we consider static and stationary solutions of the Einstein-Maxwell equations in which the Maxwell field is not constant along the Killing vector defining time-independence, so that the symmetry of the space-time is not inherited by the electromagnetic field. In particular, we look for noninheriting black hole solutions and find severe constraints on the possibilities.

We study the behaviour of an initially spherical bunch of particles emitted along trajectories parallel to the symmetry axis of a Kerr black hole. We show that, under suitable conditions, curvature and inertial strains compete to generate jet-like structures.

The theory of location systems involves the geometric and physical description of the protocols allowing the realization of coordinate systems. In this communication, the incidence of the space-time causal structure (Newtonian or relativistic) on the construction of location systems is remarked. Specifically, we focus our attention: (i) on the construction of Newtonian emission coordinates that are contrasted with those associated with relativistic positioning systems, and (ii) on the role played by non-absolute synchronizations (like the one provided by the local Solar time) in the comprehension of Newtonian and relativistic location systems.

The trajectory of a charged-massive point-particle in presence of an external magnetic field, at the classical level, is here obtained by using spinorial equations of motion. Within this representation the solution is given by means of two 2-component Weyl-spinors which contain global phase-factors coinciding with the quantum representation of a 1/2 spin particle in its rest-frame. Each individual spinor may be then associated to the up- and -down state respectively. The formalism then appears to reveal classical properties of the spin as well as quantum ones.

FLRW models filled with just dark energy are shown to have a finite past, since causal geodesics cannot be extended beyond a certain proper time. It is shown that curvature measured along causal geodesics becomes infinity on travelling to the past, though curvature scalars tend to zero. Furthermore the time measured by free-falling observers from coincidence time to Big Rip is shown to be as short as wished by increasing their linear momentum.

We summarize our studies on properties of double neutron stars observable in gravitational waves and in the radio. Binary population synthesis is used to calculate expected masses of neutron stars in binary systems taking into account the selection efects specific to each method of detection. We discuss recent relativistic results on final phase of inspiral of neutron star binaries showing how we can impose constraints on the equation of state of dense nuclear matter with gravitational wave observations.

We present the Covariant and Gauge Invariant theory of scalar perturbations of a Friedmann-Lemaître-Robertson-Walker universe for Fourth Order Gravity, where the matter is described by a perfect fluid with a barotropic equation of state. The general perturbation equations are applied to a simple background solution of Rn gravity and we obtain exact solutions of the perturbation equations for scales much bigger than the Hubble radius. These solutions have a number of interesting features. In particular we find that for all values of n there is always a growing mode for the density contrast, even if the universe is in a state of accelerated expansion. Such a behavior does not occur in standard General Relativity, where as soon as Dark Energy dominates, the density contrast experiences an unrelenting decay. Consequently, this peculiarity in the framework of higher order gravity model is sufficently novel to warrant further investigation.

It was Zel'dovich who first clearly realized the importance of quantum vacuum fluctuations in connection with cosmology. Since then, this issue has been more a problem than a solution, even if the acceleration of the universe expansion could, in principle, be easily explained by resorting to it. We have calculated those contributions in a number of different models. Under some specific conditions, the results look promising, although a general acceptable solution looks still far from reach.

We constrain a set of general relativistic dark energy models, together with some other models motivated by extra dimensions, using a combination of three background geometry tests: H(z) data, CMB shift and SNIa data. Resting mostly on Bayesian statistics, we conclude that LCDM is at least substantially favored, and that models with extra dimensional motivation are less favored than general relativistic ones.

We find that deviation from the virial equilibrium of the Abell Cluster A586 yields evidence of the interaction between dark matter and dark energy. We argue that this interaction might imply a violation of the Equivalence Principle. These evidences are found in the context of two different models of dark energy-dark matter interaction.