General Relativity and Quantum Cosmology (gr-qc)

Abstract: Very recently Harada proposed a gravitational theory which is of third order in the derivatives of the metric tensor with the property that any solution of Einstein's field equations (EFEs) possibly with a cosmological constant is necessarily a solution of the new theory. He then applied his theory to derive a second-order ODE for the evolution of the scale factor of the FLRW metric. Remarkably he showed that, even in a matter-dominated universe with zero cosmological constant, there is a late-time transition from decelerating to accelerating expansion. Harada also derived a generalisation of the Schwarzschild solution. However, as his starting point he assumed an unnecessarily restricted form for a static spherically symmetric metric. In this note the most general spherically symmetric static vacuum solution of the theory is derived. Mantica and Molinari have shown that Harada's theory may be recast into the form of the EFEs with an additional source term in the form of a second-order conformal Killing tensor(CKT). Accordingly they have dubbed the theory conformal Killing gravity. Then, using a result in a previous paper of theirs on CKTs in generalised Robertson-Walker spacetimes, they rederived Harada's generalised evolution equation for the scale factor of the FLRW metric. However, Mantica and Molinari appear to have overlooked the fact that all solutions of the new theory (except those satisfying the EFEs) admit a non-trivial second-order Killing tensor. Such Killing tensors are invaluable when considering the geodesics of a metric as they lead to a second quadratic invariant of the motion in addition to that derived from the metric.

Abstract: We find exact solutions of topologically massive gravity (TMG) and new massive gravity (NMG) in ${2+1}$ dimensions (3D) with an arbitrary cosmological constant, pure radiation, and gyratons, i.e., with possibly non-zero $T_{uu}$ and $T_{ux}$ in canonical coordinates. Since any `reasonable' geometry in 3D (i.e., admitting a null geodesic congruence) is either expanding Robinson-Trautman ($\Theta\neq 0$) or Kundt (${\Theta=0}$), we focus on these two classes. Assuming expansions ${\Theta=1/r}$ (`GR-like' Robinson-Trautman) or ${\Theta=0}$ (general Kundt), we systematically integrate the field equations of TMG and NMG and identify new classes of exact solutions. The case of NMG contains an additional assumption of $g_{ux}$ being quadratic in $r$, which is automatically enforced in TMG as well as in 3D GR. In each case, we reduce the field equations as much as possible and identify new classes of solutions. We also discuss various special subclasses and study some explicit solutions.

Abstract: Despite its elegance, the theory of General Relativity is subject to experimental, observational, and theoretical scrutiny to arrive at tighter constraints or an alternative, more preferred theory. In alternative gravity theories, the macroscopic properties of neutron stars, such as mass, radius, tidal deformability, etc. are modified. This creates a degeneracy between the uncertainties in the equation of state (EoS) and gravity since assuming a different EoS can be mimicked by changing to a different theory of gravity. We formulate a hierarchical Bayesian framework to simultaneously infer the EoS and gravity parameters by combining multiple astrophysical observations. We test this framework for a particular 4D Horndeski scalar-tensor theory originating from higher-dimensional Einstein-Gauss-Bonnet gravity and a set of 20 realistic EoS and place improved constraints on the coupling constant of the theory with current observations. Assuming a large number of observations with upgraded or third-generation detectors, we find that the $A+$ upgrade could place interesting bounds on the coupling constant of the theory, whereas with the LIGO Voyager upgrade or the third-generation detectors (Einstein Telescope and Cosmic Explorer), the degeneracy between EoS and gravity could be resolved with high confidence, even for small deviations from GR.

Abstract: In this paper, Ricci-inverse gravity is investigated. It is an alternative theory of gravity that introduces into the Einstein-Hilbert action an anti-curvature scalar that is obtained from the anti-curvature tensor which is the inverse of the Ricci tensor. An axially symmetric spacetime with causality violation is studied. Two classes of the model are discussed. Different sources of matter are considered. Then a direct relation between the content of matter and causality violation is shown. Our results confirm that Ricci-inverse gravity allows the existence of Closed Time-like Curves (CTCs) that lead to the violation of causality. Furthermore, a comparison is made between the results of general relativity and Ricci-inverse gravity. Other spacetimes, such as G\"{o}del and G\"{o}del-type universes, which are exact solutions of general relativity and allow for causality violations, are also explored in Ricci-inverse gravity framework.

Abstract: The cosmological tensor perturbation equation with generalized holonomy corrections is derived in the framework of effective loop quantum gravity. This results in a generalized dispersion relation for gravitational waves, encompassing holonomy corrections. Furthermore, we conduct an examination of the constraint algebra concerning vector modes with generalized holonomy corrections. The requirement of anomaly cancellation for vector modes imposes constraints on the possible functional forms of the generalized holonomy corrections.

Abstract: Arm locking is one of the key technologies to suppress the laser phase noise in spaced-based gravitational waves observatories. Since arm locking was proposed, phase margin criterion was always used as the fundamental design strategy for the controller development. In this paper, we find that this empirical method from engineering actually cannot guarantee the arm locking stability. Therefore, most of the advanced arm locking controllers reported so far may have instable problems. After comprehensive analysis of the single arm locking's transient responses, strict analytical stability criterions are summarized for the first time. These criterions are then generalized to dual arm locking, modified-dual arm locking and common arm locking, and special considerations for the design of arm locking controllers in different architectures are also discussed. It is found that PI controllers can easily meet our stability criterions in most of the arm locking systems. Using a simple high gain PI controller, it is possible to suppress the laser phase noise by 5 orders of magnitude within the science band. Our stability criterions can also be used in other feedback systems, where several modules with different delays are connected in parallel.

Abstract: We use the formalism of Fermi coordinates to describe the interaction of a plane gravitational wave in the proper detector frame. In doing so, we emphasize that in this frame the action of the gravitational wave can be explained in terms of a gravitoelectromagnetic analogy. In particular, up to linear displacements from the reference world-line, the effects of the wave on test masses can be described in terms of a Lorentz-like force equation. In this framework we focus on the effects on time measurements provoked by the passage of the wave, and evaluate their order of magnitude. Eventually, we calculate the expression of the local spacetime metric in cylindrical coordinates adapted to the symmetries of the gravitational field and show its relevance in connection with the helicity-rotation coupling.

Abstract: For conformally K\"ahler Riemannian four-manifolds with a Killing field, we develop a framework to solve the field equations for generalised gravitational instantons corresponding to conformal self-duality and to cosmological Einstein-Maxwell. We obtain generic identities for the curvature of such manifolds without assuming field equations. After applying the framework to recover standard solutions, we find conformally self-dual generalisations of the Page-Pope, Plebanski-Demianski, and Chen-Teo solutions, which are neither hyper-K\"ahler nor quaternionic-K\"ahler, giving new self-dual gravitational instantons in conformal gravity.

Abstract: We provide accurate universal relations that allow to estimate the moment of inertia $I$ and the ratio of kinetic to gravitational binding energy $T/W$ of uniformly rotating neutron stars from the knowledge of mass, radius, and moment of inertia of an associated non-rotating neutron star. Based on these, several other fluid quantities can be estimated as well. Astrophysical neutron stars rotate to varying degrees and although rotational effects may be neglected in some cases, not modeling them will inevitably introduce bias when performing parameter estimation. This is especially important for future, high-precision measurements coming from electromagnetic and gravitational wave observations. The proposed universal relations facilitate computationally cheap EOS inference codes that permit the inclusion of observations of rotating neutron stars. To demonstrate this, we deploy them into a recent Bayesian framework for equation of state parameter estimation that is now valid for arbitrary, uniform rotation. Our inference results are robust up to around percent level precision for the generated neutron star observations, consisting of the mass, equatorial radius, rotation rate, as well as co- and counter-rotating $f$-mode frequencies, that enter the framework as data.