Testing general metric theories of gravity with bursting neutron stars

We propose the almost-geodesic motion of self-gravitating test bodies as a possible selection rule among metric theories of gravity. Starting from a heuristic statement, the ``gravitational weak equivalence principle,'' we build a formal operative test able to probe the validity of the principle for any metric theory of gravity in an arbitrary number of spacetime dimensions. We show that, if the theory admits a well-posed variational formulation, this test singles out only the purely metric theories of gravity. This conclusion reproduces known results in the cases of general relativity (as well as with a cosmological constant term) and scalar-tensor theories, but extends also to debated or unknown scenarios, such as the $f(R)$ and Lanczos-Lovelock theories. We thus provide new tools going beyond the standard methods, where the latter turn out to be inconclusive or inapplicable.

In this paper, we present generalization of anisotropic analogue of charged Heintzmann’s solution of the general relativistic field equations in curvature coordinates. These exact solutions are stable and well behaved in all respect for a wide range of anisotropy parameter and charge parameter. We have found that these new solutions are suitable for the modeling of super dense stars like neutron stars and quark stars because they yield a wide range of masses and radii with simple mathematical expressions. By tuning different values of the few parameters, we can model various neutron stars and quark stars which are compatible with the experimentally observed values of masses and radii. Therefore, we have synchronized our solution with the observed values of some of the compact stars XTE J1739 − 217, EXO 0748 − 676, PSR J1614 − 2230, PSR J0348 + 0432 and PSR B0943 + 10.

The increasing importance of relativistic gravity in astrophysics has led to the need for a detailed analysis of theories of gravity and their viability. Accordingly, in this thesis, metric theories of gravity are compiled, and are classified into four groups: (i) general relativity (ii) scalar-tensor theories (iii) conformally flat theories and (iv) stratified theories. The post-Newtonian limit of each theory is constructed and its Parametrized Post-Newtonian (PPN) values are obtained. These results, when combined with experimental data and with recent work by Nordtvedt and Will, show that, of all theories thus far examined by our group, the only currently viable ones are (i) general relativity, (ii) the Bergmann-Wagoner scalar-tensor theory and its special cases (Nordtvedt; Brans-Dicke-Jordan, (iii) recent, (as yet unpublished ) vector-tensor theory by Nordtvedt, Hellings, and Will, and (iv) a new stratified theory by the author, which is presented for the first time in this thesis. The PPN formalism is used to analyze stellar stability in any metric theory of gravity. This analysis enables one to infer, for any given gravitation theory, the extent to which post-Newtonian effects induce instabilities in white dwarfs, in neutron stars, and in supermassive stars. It also reveals the extent to which our current empirical knowledge of post-Newtonian gravity (based on solar-system experiments) actually guarantees that relativistic instabilities exist. In particular, it shows that for conservative theories of gravity, current solar-system experiments gua­rantee that relativistic corrections do induce dynamical instabilities in stars with adiabatic indices slightly greater than 4/3, while for non-conservative theories, current experiments do not permit any firm conclusion.

LORENTZ‐covariant theories of gravitation which fulfil EINSTEIN's weak principle of equivalence and which contain a pure Newtonian theory as an approximation are tensortheories with the linear approximative form for the field equations. In the case of EINSTEIN's strong principle of equivalence the exact field equations must be the general relativistic EINSTEIN‐equations (or the bimetrical EINSTEIN‐ROSEN‐equations). This follows from the dynamical equations and the BIANCHI identity according to JÁNOSSY and TREDER.However, from NEWTON's axiom of reaction together with the weak principle of equivalence results that the strong principle of equivalence must be valid for the linear approximation of the field equations with sources. Therefore, the linear approximation of all physically meaningful Lorentz‐covariant theories of gravitation is given by the linearized EINSTEIN‐equations (with HILBERT‐conditions): , that is by the ansatz α = 2.The main point of our arguments is LAUE's postulate of the self‐consistency of perfect static systems of isolated gravitational masses. In the lowest order of approximation this self‐consistency is only possible if the gravitational matter‐tensor is identical with the special‐relativistic energy‐momentum‐tensor Tμv. LAUE's postulate is fulfilled exactly for the general relativistic field equations according to the theorems of BIRKHOFF, TOLMAN and EINSTEIN and PAULI.

Generalizations of Einstein's field equations in general relativity are derived by considering variational principles in which the components of an ennuple, or tetrad, are the quantities which undergo variation. The conservation law for the field equations is established and the weak field approximations discussed. The equations are solved by the method developed in a previous article (abstr. A32263 of 1970). Many solutions are obtained, all of which are inferior to the Schwarzschild solution.

Increasing sophistication and precision of experimental tests of relativistic gravitation theories has led to the need for a detailed theoretical framework for analysing and interpreting these experiments. Such a framework is the Parametrized Post-Newtonian (PPN) formalism, which treats the post-Newtonian limit of arbitrary metric theories of gravity in terms of nine metric parameters, whose values vary from theory to theory. The theoretical and experimental foundations of the PPN formalism are laid out and discussed, and the detailed definitions and equations for the formalism are given. It is shown that some metric theories of gravity predict that a massive, self-gravitating body's passive gravitational mass should not be equal to its inertial mass, but should be an anisotropic tensor which depends on the body's self-gravitational energy (violation of the principle of equivalence). Two theorems are presented which probe the theoretical structure of the PPN formalism. They state that (i) a metric theory of gravity possesses post-Newtonian integral conservation laws if and only if its nine PP parameters have values which satisfy a set of seven constraint equations, and (ii) a metric theory of gravity is invariant under asymptotic Lorentz transformations if and only if its PPN parameters satisfy a set of three constraint equations. Some theories of gravity (including Whitehead's theory and theories which violate one of the Lorentz-invariance parameter constraints) are shown to predict an anisotropy in the Newtonian gravitational constant. Gravimeter data on the tides of the solid Earth are used to put an upper limit on the magnitude of the predicted anisotropy, and thence to rule out such theories.

Observations of compact objects in the electromagnetic spectrum and the detection of gravitational waves from them can lead to quantitative tests of the theory of general relativity in the strong-field regime following two very different approaches. In the first approach, the general relativistic field equations are modified at a fundamental level and the magnitudes of the potential deviations are constrained by comparison with observations. In the second approach, the exterior spacetimes of compact objects are parametrized in a phenomenological way, the various parameters are measured observationally, and the results are finally compared against the general relativistic predictions. In this article, I discuss the current status of both approaches, focusing on the lessons learned from a large number of recent investigations.

Apart from the familiar structure firmly-rooted in the general relativistic field equations where the energy–momentum tensor has a null divergence i.e., it conserves, there exists a considerable number of extended theories of gravity allowing departures from the usual conservative framework. Many of these theories became popular in the last few years, aiming to describe the phenomenology behind dark matter and dark energy. However, within these scenarios, it is common to see attempts to preserve the conservative property of the energy–momentum tensor. Most of the time, it is done by means of some additional constraint that ensures the validity of the standard conservation law, as long as this option is available in the theory. However, if no such extra constraint is available, the theory will inevitably carry a non-trivial conservation law as part of its structure. In this work, we review some of such proposals discussing the theoretical construction leading to the non-conservation of the energy–momentum tensor.

One of the central predictions of metric theories of gravity, such as general relativity, is that a clock in a gravitational potential U will run more slowly by a factor of 1 + U/c(2), where c is the velocity of light, as compared to a similar clock outside the potential. This effect, known as gravitational redshift, is important to the operation of the global positioning system, timekeeping and future experiments with ultra-precise, space-based clocks (such as searches for variations in fundamental constants). The gravitational redshift has been measured using clocks on a tower, an aircraft and a rocket, currently reaching an accuracy of 7 x 10(-5). Here we show that laboratory experiments based on quantum interference of atoms enable a much more precise measurement, yielding an accuracy of 7 x 10(-9). Our result supports the view that gravity is a manifestation of space-time curvature, an underlying principle of general relativity that has come under scrutiny in connection with the search for a theory of quantum gravity. Improving the redshift measurement is particularly important because this test has been the least accurate among the experiments that are required to support curved space-time theories.

The fact that gravity is a metric theory follows from the Einstein equivalence principle. This principle consists of (i) the universality of free fall, (ii) the universality of the gravitational redshift and (iii) the local validity of Lorentz invariance. Many experiments searching for deviations from standard general relativity test the various aspects of the Einstein equivalence principle. Here we report on experiments covering the whole Einstein equivalence principle. Until now all experiments have been in agreement with the Einstein equivalence principle. As a consequence, gravity has to be described by a metric theory. Any metric theory of gravity leads to effects such as perihelion shift, deflection of light, gravitational redshift, gravitational time delay, Lense–Thirring effect, Schiff effect, etc. A particular theory of that sort is Einstein's general relativity. For weak gravitational fields which are asymptotically flat any deviation from Einstein's general relativity can be parametrized by a few constants, the PPN parameters. Many astrophysical observations and space experiments are devoted to a better measurement of the effects and, thus, of the PPN parameters. It is clear that gravity is best tested for intermediate ranges, that is, for distances between 1 m and several astronomical units. It is highly interesting to push forward our domain of experience and to strengthen the experimental foundation of gravity also beyond these scales. This point is underlined by the fact that many quantum gravity and unification-inspired theories suggest deviation from the standard laws of gravity at very small or very large scales. In this session summary we briefly outline the status and report on the talks presented in session C1 about experimental gravitation.

If the Pioneer anomaly has a gravitational origin, it would, according to the equivalence principle, distort the motions of the planets in the Solar System. Since no anomalous motion of the planets has been detected, it is generally believed that the Pioneer anomaly can not originate from a gravitational source in the Solar System. However, this conclusion becomes less obvious when considering models that either imply modifications to gravity over long distances or gravitational sources localized to the outer Solar System, given the uncertainty in the orbital parameters of the outer planets. Following the general assumption that the Pioneer spacecraft move geodesically in a spherically symmetric space-time metric, we derive the metric disturbance that is needed in order to account for the Pioneer anomaly. We then analyze the residual effects on the astronomical observables of the three outer planets that would arise from this metric disturbance, given an arbitrary metric theory of gravity. Providing a method for comparing the computed residuals with actual residuals, our results imply that the presence of a perturbation to the gravitational field necessary to induce the Pioneer anomaly is in conflict with available data for the planets Uranus and Pluto, but not for Neptune. Wemore » therefore conclude that the motion of the Pioneer spacecraft must be nongeodesic. Since our results are model-independent within the class of metric theories of gravity, they can be applied to rule out any model of the Pioneer anomaly that implies that the Pioneer spacecraft move geodesically in a perturbed space-time metric, regardless of the origin of this metric disturbance.« less

We search NANOGrav’s 12.5 yr data set for evidence of a gravitational-wave background (GWB) with all the spatial correlations allowed by general metric theories of gravity. We find no substantial evidence in favor of the existence of such correlations in our data. We find that scalar-transverse (ST) correlations yield signal-to-noise ratios and Bayes factors that are higher than quadrupolar (tensor-transverse, TT) correlations. Specifically, we find ST correlations with a signal-to-noise ratio of 2.8 that are preferred over TT correlations (Hellings and Downs correlations) with Bayesian odds of about 20:1. However, the significance of ST correlations is reduced dramatically when we include modeling of the solar system ephemeris systematics and/or remove pulsar J0030+0451 entirely from consideration. Even taking the nominal signal-to-noise ratios at face value, analyses of simulated data sets show that such values are not extremely unlikely to be observed in cases where only the usual TT modes are present in the GWB. In the absence of a detection of any polarization mode of gravity, we place upper limits on their amplitudes for a spectral index of γ = 5 and a reference frequency of f yr = 1 yr−1. Among the upper limits for eight general families of metric theories of gravity, we find the values of A TT 95 % = ( 9.7 ± 0.4 ) × 10 − 16 and A ST 95 % = ( 1.4 ± 0.03 ) × 10 − 15 for the family of metric spacetime theories that contain both TT and ST modes.

Einstein’s General theory of relativity (GR) successfully describes gravity. Although GR has been accurately tested in weak gravitational fields, it remains largely untested in the general strong field cases. One of the most fundamental predictions of GR is the existence of black holes (BHs). After the recent direct detection of gravitational waves by LIGO, there is now near conclusive evidence for the existence of stellar-mass BHs. In spite of this exciting discovery, there is not yet direct evidence of the existence of BHs using astronomical observations in the electromagnetic spectrum. Are BHs observable astrophysical objects? Does GR hold in its most extreme limit or are alternatives needed? The prime target to address these fundamental questions is in the center of our own Milky Way, which hosts the closest and best-constrained supermassive BH candidate in the universe, Sagittarius A* (Sgr A*). Three different types of experiments hold the promise to test GR in a strong-field regime using observations of Sgr A* with new-generation instruments. The first experiment consists of making a standard astronomical image of the synchrotron emission from the relativistic plasma accreting onto Sgr A*. This emission forms a “shadow” around the event horizon cast against the background, whose predicted size ([Formula: see text]as) can now be resolved by upcoming very long baseline radio interferometry experiments at mm-waves such as the event horizon telescope (EHT). The second experiment aims to monitor stars orbiting Sgr A* with the next-generation near-infrared (NIR) interferometer GRAVITY at the very large telescope (VLT). The third experiment aims to detect and study a radio pulsar in tight orbit about Sgr A* using radio telescopes (including the Atacama large millimeter array or ALMA). The BlackHoleCam project exploits the synergy between these three different techniques and contributes directly to them at different levels. These efforts will eventually enable us to measure fundamental BH parameters (mass, spin, and quadrupole moment) with sufficiently high precision to provide fundamental tests of GR (e.g. testing the no-hair theorem) and probe the spacetime around a BH in any metric theory of gravity. Here, we review our current knowledge of the physical properties of Sgr A* as well as the current status of such experimental efforts towards imaging the event horizon, measuring stellar orbits, and timing pulsars around Sgr A*. We conclude that the Galactic center provides a unique fundamental-physics laboratory for experimental tests of BH accretion and theories of gravity in their most extreme limits.

Test of the equivalence principle for nuclear-polarized bodies at low temperature

Test of the equivalence principle for nuclear-polarized bodies at low temperature