General Relativity And Quantum Cosmology

An extreme mass ratio inspiral takes place when a compact stellar object is inspiraling into a supermassive black hole due to gravitational radiation reaction. Gravitational waves (GWs) from this system can be calculated using the Teukolsky equation (TE). In our case, we compute the asymptotic GW fluxes of a spinning body orbiting a Kerr black hole by solving numerically the TE both in time and frequency domain. Our ultimate goal is to produce GW templates for space-based detectors such as LISA.

Weak field gravitational wave solutions are investigated in Brans-Dicke (BD) theory in the presence of a cosmological constant. In this setting the background geometry is not flat but asymptotically de-Sitter. We investigate the linearised field equations, and their gravitational wave solutions in a certain gauge choice. We will show that this theory leads to massless scalar waves as in original BD theory and in contrast to massive BD theory. The effects of these waves on free particles and their polarization properties are studied extensively and effects of the cosmological constant is analyzed in these phenomena in detail. The energy flux of these waves are also discussed in this background. By analyzing this flux, we obtain a critical distance where the waves cannot propagate further, which extends Cosmic no Hair Conjecture (CNC) to BD theory with a cosmological constant.

The detection of gravitational waves is possible thanks to a multidisciplinary approach, involving different disciplines such as astrophysics, physics, engineering and quantum optics. Consequently, it is important today for teachers to introduce the basic features of gravitational waves science in the undergraduate curriculum. The usual approach to gravitational wave physics is based on the use of traceless and transverse coordinates, which do not have a direct physical meaning and, in a teaching perspective, may cause misconceptions. In this paper, using Fermi coordinates, which are simply related to observable quantities, we show that it is possible to introduce a gravitoelectromagnetic analogy that describes the action of gravitational waves on test masses in terms of electric-like and magnetic-like forces. We suggest that this approach could be more suitable when introducing the basic principles of gravitational waves physics to students.

We study the polarizations of gravitational waves (GWs) in two classes of extended gravity theories. First, we formulate the polarizations in linear massive gravity (MG) with generic mass terms of non-Fierz-Pauli type by identifying all the independent variables that obey Klein-Gordon-type equations. The dynamical degrees of freedom (dofs) in the generic MG consist of spin-2 and spin-0 modes, the former breaking down into two tensor (helicity-2), two vector (helicity-1) and one scalar (helicity-0) components, while the latter just corresponding to a scalar. We find convenient ways of decomposing the two scalar modes of each spin into distinct linear combinations of the transverse and longitudinal polarizations with coefficients directly expressed by the mass parameters, thereby serving as a useful tool in measuring the masses of GWs. Then we analyze the linear perturbations of generic higher-curvature gravity (HCG) whose Lagrangian is an arbitrary polynomial of the Riemann tensor. On a flat background, the linear dynamical dofs in this theory are identified as massless spin-2, massive spin-2, and massive spin-0 modes. As its massive part encompasses the identical structure to the generic MG, GWs in the generic HCG provide six massive polarizations on top of the ordinary two massless modes. In parallel to MG, we find convenient representations for the scalar-polarization modes directly connected to the parameters of HCG. In this analysis, we employ two distinct methods; One takes full advantage of the partial equivalence between the generic HCG and MG at the linear level, whereas the other relies upon a gauge-invariant formalism. We confirm that the two results agree. We also discuss methods to determine the theory parameters by GW-polarization measurements. Our method does not require measuring the propagation speeds or the details of the waveforms of the GWs. [Abridged]

The gravitational dynamics of a collapsing matter configuration which is simultaneously radiating heat flux is studied in f(R) gravity. Three particular functional forms in f(R) gravity are considered to show that it is possible to envisage boundary conditions such that the end state of the collapse has a weak singularity and that the matter configuration radiates away all of its mass before collapsing to reach the central singularity.

This paper aims at investigating the influence of space-time curvature on the uncertainty relation. In particular, relying on previous findings, we assume the quantum wave function to be confined to a geodesic ball on a given space-like hypersurface whose radius is a measure of the position uncertainty. On the other hand, we concurrently work out a viable physical definition of the momentum operator and its standard deviation in the non-relativistic limit of the 3+1 formalism. Finally, we evaluate the uncertainty relation which to second order depends on the Ricci scalar of the effective 3-metric and the corresponding covariant derivative of the shift vector. For the sake of illustration, we apply our general result to a number of examples arising in the context of both general relativity and extended theories of gravity.

A heuristic description of the spin-rotation-gravity coupling is presented and the implications of the corresponding gravitomagnetic Stern--Gerlach force are briefly mentioned. It is shown, within the framework of linearized general relativity, that the gravitomagnetic Stern--Gerlach force reduces in the appropriate correspondence limit to the classical Mathisson spin-curvature force.

In this Chapter we illustrate the close connection between the violation of the weak equivalence principle typical of gravitational interactions at finite temperature, and similar violations induced by a breaking of the local Lorentz symmetry. We also discuss the physical implications of the effective repulsive forces possibly arising in such a generalized gravitational context, by considering, for an illustrative purpose, a quasi-Riemannian model of gravity with rotational symmetry as the local gauge group in tangent space.

In this work, we investigate the quasinormal frequencies of a class of regular black hole solutions which generalize Bardeen and Hayward spacetimes. In particular, we analyze scalar, vector and gravitational perturbations of the black hole both with the semianalytic WKB method and their time-domain profiles. We analyze in detail the behavior of the spectrum depending on the parameter p/q of the black hole, the quantum number of angular momentum and the s number. In addition, we compare our results with the classical solution valid for p=q=1 .

We study the growth of linear matter density perturbations in a modified gravity approach of scalar field couplings with metric and torsion. In the equivalent scalar-tensor formulation, the matter fields in the Einstein frame interact as usual with an effective dark energy component, whose dynamics is presumably governed by a scalar field that sources a torsion mode. As a consequence, the matter density ceases to be self-conserved, thereby making an impact not only on the background cosmological evolution but also on the perturbative spectrum of the local inhomogeneities. In order to estimate the effect on the growth of the linear matter perturbations, with the least possible alteration of the standard parametric form of the growth factor, we resort to a suitable Taylor expansion of the corresponding exponent, known as the growth index, about the value of the cosmic scale factor at the present epoch. In particular, we obtain an appropriate fitting formula for the growth index in terms of the coupling function and the matter density parameter. While the overall parametric formulation of the growth factor is found to fit well with the latest redshift-space-distortion (RSD) and the observational Hubble (OH) data at low redshifts, the fitting formula enables us to constrain the growth index to well within the concordant cosmological limits, thus ensuring the viability of the formalism.