Nondynamical Chern-Simons Research Articles

Chern-Simons modified gravity and closed timelike curves

We verify the consistency of the G\"odel-type solutions within the four-dimensional Chern-Simons modified gravity with the non-dynamical Chern-Simons coefficient, for different forms of matter including dust, fluid, scalar field and electromagnetic field, and the related causality issues. Unlike the general relativity, the vacuum solution turns out to be possible in our theory. Another essentially new result of our theory having no analogue in the general relativity consists in the existence of the hyperbolic causal solutions for the physically well-motivated matter.

Signature of biased range in the non-dynamical Chern–Simons modified gravity and its measurements with satellite-satellite tracking missions: theoretical studies

Having great accuracy in the range and range rate measurements,he GRACE mission and the planed GRACE Follow On mission can in principle be employed to place strong constraints on certain relativistic gravitational theories. In this paper, we work out the range observable of the non-dynamical Chern-Simons modified gravity for the Satellite-to-Satellite Tracking (SST) measurements. We find out that a characteristic time accumulating range signal appears in non-dynamical Chern-Simons gravity, which has no analogue found in the standard parity-preserving metric theories of gravity. The magnitude of this Chern-Simons range signal will reach a few times of $\chi cm$ for each free flight of these SST missions, here $\chi$ is the dimensionless post-Newtonian parameter of the non-dynamical Chern-Simons theory. Therefore, with the 12 years data of the GRACE mission, one expects that the mass scale $M_{CS}=\frac{4\hbar c}{\chi a}$ of the non-dynamical Chern-Simons gravity could be constrained to be larger than $1.9\times10^{-9}eV$. For the GRACE FO mission that scheduled to be launched in 2017, the much stronger bound that $M_{CS}\geq5\times10^{-7}eV$ is expected.

Testing Chern-Simons modified gravity with orbiting superconductive gravity gradiometers: the non-dynamical formulation

High precision Superconductivity Gravity Gradiometers (SGG) are powerful tools for relativistic experiments. In this paper, we work out the tidal signals in non-dynamical Chern-Simons modified gravity, which could be measured by orbiting SGGs around Earth. We find that, with proper orientations of multi-axes SGGs, the tidal signals from the Chern-Simons modification can be isolated in the combined data of different axes. Furthermore, for three-axes SGGs, such combined data is the trace of the total tidal matrix, which is invariant under the rotations of SGG axes and thus free from axis pointing errors. Following nearly circular orbits, the tests of the parity-violating Chern-Simons modification and the measurements of the gravitomagnetic sector in parity-conserving metric theories can be carried out independently in the same time. A first step analysis on noise sources is also included.

Massive gravitational waves in Chern-Simons modified gravity

We consider the nondynamical Chern-Simons (nCS) modified gravity, which is regarded as a parity-odd theory of massive gravity in four dimensions. We first find polarization modes of gravitational waves for θ=x/μ in nCS modified gravity by using the Newman-Penrose formalism where the null complex tetrad is necessary to specify gravitational waves. We show that in the Newman–Penrose formalism, the number of polarization modes is one in addition to an unspecified Ψ4, implying three degrees of freedom for θ=x/μ. This compares with two for a canonical embedding of θ=t/μ. Also, if one introduces the Ricci tensor formalism to describe a massive graviton arising from the nCS modified gravity, one finds one massive mode after making second-order wave equations, which is compared to five found from the parity-even Einstein–Weyl gravity.

Revisiting the double-binary-pulsar probe of nondynamical Chern-Simons gravity

One of the popular modifications to the theory of general relativity is nondynamical Chern-Simons (CS) gravity, in which the metric is coupled to an externally prescribed scalar field. Setting accurate constraints to the parameters of the theory is important owing to their implications for the scalar field and/or the underlying fundamental theory. The current best constraints rely on measurements of the periastron precession rate in the double-binary-pulsar system and place a very tight bound on the characteristic CS length scale ${k}_{\mathrm{cs}}^{\ensuremath{-}1}\ensuremath{\lesssim}3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}9}\text{ }\text{ }\mathrm{km}$. This paper considers several effects that were not accounted for when deriving this bound and lead to a substantial suppression of the predicted rate of periastron precession. It is shown, in particular, that the point-mass approximation for extended test bodies does not apply in this case. The constraint to the characteristic CS length scale is revised to ${k}_{\mathrm{cs}}^{\ensuremath{-}1}\ensuremath{\lesssim}0.4\text{ }\text{ }\mathrm{km}$, 8 orders of magnitude weaker than what was previously found.

Extended solution space for Chern-Simons gravity: The slowly rotating Kerr black hole

In the Einstein-Cartan formulation, an iterative procedure to find solutions in non-dynamical Chern-Simons (CS) gravity in vacuum is proposed. The iterations, in powers of a small parameter $\beta$ which codifies the CS coupling, start from an arbitrary torsionless solution of Einstein equations. With Schwarzschild as the zeroth-order choice, we derive a second-order differential equation for the $\mathcal{O}(\beta)$ corrections to the metric, for an arbitrary zeroth-order embedding parameter. In particular, the slowly rotating Kerr metric is an $\mathcal{O}(\beta)$ solution in either the canonical or the axial embeddings.

Double-binary-pulsar test of Chern-Simons modified gravity

Chern-Simons modified gravity is a string-theory and loop-quantum-gravity inspired effective theory that modifies General Relativity by adding a parity-violating Pontryagin density to the Einstein-Hilbert action multiplied by a coupling scalar. We strongly constrain non-dynamical Chern-Simons modified gravity with a timelike Chern-Simons scalar through observations of the double binary pulsar PSR J0737-3039A/B. We first calculate Chern-Simons corrections to the orbital evolution of binary systems. We find that the ratio of the correction to periastron precession to the general relativistic prediction scales quadratically with the semi-major axis and inversely with the square of the object's radius. Binary pulsar systems are thus ideal to test this theory, since periastron precession can be measured with sub-degree accuracies and the semi-major axis is millions of times larger than the stellar radius. Using data from PSR J0737-3039A/B we dramatically constrain the non-dynamical Chern-Simons coupling to $M_{\CS} := 1/|\dot{\vartheta}| > 33 {\textrm{meV}}$, approximately a hundred billion times better than current Solar System tests.