Extension of loop quantum gravity to f(R) theories

The four-dimensional metric f(R) theories of gravity are cast into connection-dynamical formalism with real su(2) connections as configuration variables. Through this formalism, the classical metric f(R) theories are quantized by extending the loop quantization scheme of general relativity. Our results imply that the nonperturbative quantization procedure of loop quantum gravity is valid not only for general relativity but also for a rather general class of four-dimensional metric theories of gravity.     

Selfadjointness and positivity of a certain partial differential operator associated with the Kerr metric in general relativity

A second-order partial differential operator singular on the boundary, is shown to be positive selfadjoint without zero eigenvalue. The operator may serve as a kind of the Hamiltonian operator for the Klein-Gordon equation in the Kerr metric of general relativity.     

Letter: Space-Time Uncertainty from Higher-Dimensional Determinism

Heisenberg's uncertainty relation is commonly regarded as defining a level of unpredictability that is fundamentally incompatible with the deterministic laws embodied in classical field theories such as Einstein's general relativity. We here show that this is not necessarily the case. Using 5D as an example of dimensionally-extended relativity, we employ a novel metric to derive the standard quantum rule for the action and a form of Heisenberg's relation that applies to real and virtual particles. The philosophical implications of these technical results are somewhat profound.     

Stationary axisymmetric fields in a teleparallel theory of gravitation

The existence of a set of tetrads satisfying the Møller equations and leading to the Kerr metric is proved by using a particular procedure, which could be very useful to deal with other stationary axisymmetric cases of general relativity in the framework of Møller's theory of gravitation.     

Cosmological tests of gravity

Modifications of general relativity provide an alternative explanation to dark energy for the observed acceleration of the universe. We review recent developments in modified gravity theories, focusing on higher-dimensional approaches and chameleon/f(R) theories. We classify these models in terms of the screening mechanisms that enable such theories to approach general relativity on small scales (and thus satisfy solar system constraints). We describe general features of the modified Friedman equation in such theories.The second half of this review describes experimental tests of gravity in light of the new theoretical approaches. We summarize the high precision tests of gravity on laboratory and solar system scales. We describe in some detail tests on astrophysical scales ranging from ∼ kpc (galaxy scales) to ∼ Gpc (large-scale structure). These tests rely on the growth and inter-relationship of perturbations in the metric potentials, density and velocity fields which can be measured using gravitational lensing, galaxy cluster abundances, galaxy clustering and the integrated Sachs-Wolfe effect. A robust way to interpret observations is by constraining effective parameters, such as the ratio of the two metric potentials. Currently tests of gravity on astrophysical scales are in the early stages — we summarize these tests and discuss the interesting prospects for new tests in the coming decade.     

Slightly Bimetric Gravitation

The inclusion of a flat metric tensor in gravitation permits the formulation of a gravitational stress-energy tensor and the formal derivation of general relativity from a linear theory in flat spacetime. Building on the works of Kraichnan and Deser, we present such a derivation using universal coupling and gauge invariance.Next we slightly weaken the assumptions of universal coupling and gauge invariance, obtaining a larger "slightly bimetric" class of theories, in which the Euler-Lagrange equations depend only on a curved metric, matter fields, and the determinant of the flat metric. The theories are equivalent to generally covariant theories with an arbitrary cosmological constant and an arbitrarily coupled scalar field, which can serve as an inflaton or dark matter.The question of the consistency of the null cone structures of the two metrics is addressed.     

Center of mass and far field metric in relativistic magnetohydrodynamics

The uniform motion of the center of mass of a charged, conducting fluid, in the presence of an electromagnetic field, is derived in the first post-Newtonian approximation of general relativity. Also the source's far field metric tensor is determined, and it is expressed in terms of parameters known as three-dimensional volume integrals over its interior. These results for the above system permit the physical identification, to post-Newtonian accuracy, of the integration constants and the coordinate systems involved in the Schwarzschild and the Kerr metric tensors.     

北京光速各向异性实验的广义相对论(及度规理论)预言值

基于广义相对论及度规引力理论的基本原理,计算了北京“光速各向异性检验”实验的预期值。结论是该实验将不可能在广义相对论传统观点和文献[1]提出的观点之间作出判断。     

Does the planck mass run on the cosmological-horizon scale?

Einstein's theory of general relativity contains a universal value of the Planck mass. However, one may envisage that in alternative theories of gravity the effective value of the Planck mass (or Newton's constant), which quantifies the coupling of matter to metric perturbations, can run on the cosmological-horizon scale. In this Letter, we study the consequences of a glitch in the Planck mass from subhorizon to superhorizon scales. We show that current cosmological observations severely constrain this glitch to less than 1.2%.     

What is modified gravity and how to differentiate it from particle dark matter?

An obvious criterion to classify theories of modified gravity is to identify their gravitational degrees of freedom and their coupling to the metric and the matter sector. Using this simple idea, we show that any theory which depends on the curvature invariants is equivalent to general relativity in the presence of new fields that are gravitationally coupled to the energy-momentum tensor. We show that they can be shifted into a new energy-momentum tensor. There is no a priori reason to identify these new fields as gravitational degrees of freedom or matter fields. This leads to an equivalence between dark matter particles gravitationally coupled to the standard model fields and modified gravity theories designed to account for the dark matter phenomenon. Due to this ambiguity, it is impossible to differentiate experimentally between these theories and any attempt of doing so should be classified as a mere interpretation of the same phenomenon.     

The dynamics of metric-affine gravity

Metric-affine theories of gravity provide an interesting alternative to general relativity: in such an approach, the metric and the affine (not necessarily symmetric) connection are independent quantities. Furthermore, the action should include covariant derivatives of the matter fields, with the covariant derivative naturally defined using the independent connection. As a result, in metric-affine theories a direct coupling involving matter and connection is also present. The role and the dynamics of the connection in such theories is explored. We employ power counting in order to construct the action and search for the minimal requirements it should satisfy for the connection to be dynamical. We find that for the most general action containing lower order invariants of the curvature and the torsion the independent connection does not carry any dynamics. It actually reduces to the role of an auxiliary field and can be completely eliminated algebraically in favour of the metric and the matter field, introducing extra interactions with respect to general relativity. However, we also show that including higher order terms in the action radically changes this picture and excites new degrees of freedom in the connection, making it (or parts of it) dynamical. Constructing actions that constitute exceptions to this rule requires significant fine tuned and/or extra a priori constraints on the connection. We also consider f(R) actions as a particular example in order to show that they constitute a distinct class of metric-affine theories with special properties, and as such they cannot be used as representative toy theories to study the properties of metric-affine gravity.     

McGuire-Ruffini solution in new general relativity

We obtain a solution of new general relativity from a solution of Einstein's general relativity which includes many known solutions, such as Kerr-Newman-Kasuya, Kerr-Newman, Kerr, and NUT, as special cases.     

Area invariance of apparent horizons under arbitrary Lorentz boosts

It is a well known analytic result in general relativity that the 2-dimensional area of the apparent horizon of a black hole remains invariant regardless of the motion of the observer, and in fact is independent of the t = constant slice, which can be quite arbitrary in general relativity. Nonetheless the explicit computation of horizon area is often substantially more difficult in some frames (complicated by the coordinate form of the metric), than in other frames. Here we give an explicit demonstration for very restricted metric forms of (Schwarzschild and Kerr) vacuum black holes. In the Kerr–Schild coordinate expression for these spacetimes they have an explicit Lorentz-invariant form. We consider boosted versions with the black hole moving through the coordinate system. Since these are stationary black hole spacetimes, the apparent horizons are two dimensional cross sections of their event horizons, so we compute the areas of apparent horizons in the boosted space with (boosted) t = constant, and obtain the same result as in the unboosted case. Note that while the invariance of area is generic, we deal only with black holes in the Kerr–Schild form, and consider only one particularly simple change of slicing which amounts to a boost. Even with these restrictions we find that the results illuminate the physics of the horizon as a null surface and provide a useful pedagogical tool. As far as we can determine, this is the first explicit calculation of this type demonstrating the area invariance of horizons. Further, these calculations are directly relevant to transformations that arise in computational representation of moving black holes. We present an application of this result to initial data for boosted black holes.     

The confrontation between general relativity and experiment: An update

The status of experimental tests of general relativity to the end of 1983 is reviewed. The experimental support for the Einstein equivalence principle is summarized. If this principle is valid, gravitation must be described by a curved space-time, “metric” theory of gravity. General properties of metric theories are described and the parametrized post-Newtonian (PPN) formalism for treating the weak-field, slow-motion limit of such theories is set up. A zoo of selected metric theories of gravity is presented. Experimental tests of metric theories are then described, including the “classical” tests, tests of the strong equivalence principle, and others. The possibility of using gravitational-wave observations to test metric theories is discussed. A review is presented of the binary pulsar, in which the first evidence for gravitational radiation has been found. Finally cosmological tests of alternative theories are briefly described.     

Comment on ‘singularity theorems and the [general relativity + additional matter fields] formulation of metric theories of gravitation’

Many metric theories of gravitation can be transformed into general relativity with matter fields. We consider the circumstances under which such a transformation may be used to study the singularity structure (where in this context, singularities are characterised by incomplete causal geodesics).     

The collisional Penrose process

Shortly after the discovery of the Kerr metric in 1963, it was realized that a region existed outside of the black hole’s event horizon where no time-like observer could remain stationary. In 1969, Roger Penrose showed that particles within this ergosphere region could possess negative energy, as measured by an observer at infinity. When captured by the horizon, these negative energy particles essentially extract mass and angular momentum from the black hole. While the decay of a single particle within the ergosphere is not a particularly efficient means of energy extraction, the collision of multiple particles can reach arbitrarily high center-of-mass energy in the limit of extremal black hole spin. The resulting particles can escape with high efficiency, potentially serving as a probe of high-energy particle physics as well as general relativity. In this paper, we briefly review the history of the field and highlight a specific astrophysical application of the collisional Penrose process: the potential to enhance annihilation of dark matter particles in the vicinity of a supermassive black hole.     

Axisymmetric vacuum fields in general projective relativity

A method has been derived which enables one to obtain solutions to the stationary, axially symmetric vacuum fields in general projective relativity developed by Arcidiacono from known solutions of the vacuum field in Einstein's theory. The analogue of the Kerr solution in general projective relativity has been obtained as an example. Finally, a relation between the stationary and static axially symmetric vacuum fields in general projective relativity has been derived.     

Gyro precession and mach's principle

The precession of a gyroscope is calculated in a nonrelativistic theory due to Harbour which satisfies Mach's principle. It is shown that the theory predicts both the geodetic and motional precession of general relativity to within factors of order 1. The significance of the gyro experiment is discussed from the point of view of metric theories of gravity and this is contrasted with its significance from the point of view of Mach's principle.     

Scalar torsion and a new symmetry of general relativity

We reformulate the general theory of relativity in the language of Riemann–Cartan geometry. We start from the assumption that the space-time can be described as a non-Riemannian manifold, which, in addition to the metric field, is endowed with torsion. In this new framework, the gravitational field is represented not only by the metric, but also by the torsion, which is completely determined by a geometric scalar field. We show that in this formulation general relativity has a new kind of invariance, whose invariance group consists of a set of conformal and gauge transformations, called Cartan transformations. These involve both the metric tensor and the torsion vector field, and are similar to the well known Weyl gauge transformations. By making use of the concept of Cartan gauges, we show that, under Cartan transformations, the new formalism leads to different pictures of the same gravitational phenomena. We illustrate this fact by looking at the one of the classical tests of general relativity theory, namely the gravitational spectral shift. Finally, we extend the concept of space-time symmetry to Riemann–Cartan space-times with scalar torsion and obtain the conservation laws for auto-parallel motions in a static spherically symmetric vacuum space-time in a Cartan gauge, whose orbits are identical to Schwarzschild orbits in general relativity.     

Hamiltonian approach to frame dragging

A Hamiltonian approach makes the phenomenon of frame dragging apparent “up front” from the appearance of the drag velocity in the Hamiltonian of a test particle in an arbitrary metric. Hamiltonian (1) uses the inhomogeneous force equation (4), which applies to non-geodesic motion as well as to geodesics. The Hamiltonian is not in manifestly covariant form, but is covariant because it is derived from Hamilton’s manifestly covariant scalar action principle. A distinction is made between manifest frame dragging such as that in the Kerr metric, and hidden frame dragging that can be made manifest by a coordinate transformation such as that applied to the Robertson–Walker metric in Sect. 2. In Sect. 3 a zone of repulsive gravity is found in the extreme Kerr metric. Section 4 treats frame dragging in special relativity as a manifestation of the equivalence principle in accelerated frames. It answers a question posed by Bell about how the Lorentz contraction can break a thread connecting two uniformly accelerated rocket ships. In Sect. 5 the form of the Hamiltonian facilitates the definition of gravitomagnetic and gravitoelectric potentials.