General Relativity and Quantum Cosmology (gr-qc)

Abstract: Numerical relativity waveforms are a critical resource in the quest to deepen our understanding of the dynamics of, and gravitational waves emitted from, merging binary systems. We present 181 new numerical relativity simulations as the second MAYA catalog of binary black hole waveforms (a sequel to the Georgia Tech waveform catalog). Most importantly, these include 55 high mass ratio (q >= 4), 48 precessing, and 92 eccentric (e > 0.01) simulations, including 7 simulations which are both eccentric and precessing. With these significant additions, this new catalog fills in considerable gaps in existing public numerical relativity waveform catalogs. The waveforms presented in this catalog are shown to be convergent and are consistent with current gravitational wave models. They are available to the public at https://cgp.ph.utexas.edu/waveform.

Abstract: The quantum spin effects inside matter can be modeled via the Weyssenhoff fluid, which permits to unearth a formal analogy between general relativity and Einstein-Cartan theory at the first post-Newtonian order. In this framework, we provide some analytical formulas pertaining to the dynamics of binary systems having the spins aligned perpendicular to the orbital plane. We derive the expressions of the relative orbit and the coordinate time, which in turn allow to determine the gravitational waveform, and the energy and angular momentum fluxes. The potentialities of our results are presented in two astrophysical applications, where we compute: ($i$) the quantum spin contributions to the energy flux and gravitational waveform during the inspiral phase; ($ii$) the macroscopic angular momentum of one of the bodies starting from the time-averaged energy flux and the knowledge of few timing parameters.

Abstract: We consider the quantized bi-scalar gravity, which may serve as a locally Lorentz invariant cosmological model with varying speed of light and varying gravitational constant. The equation governing the quantum regime for the case of homogeneous and isotropic cosmological setup is a Dirac-like equation which replaces the standard Wheeler-DeWitt equation. We show that particular cosmogenesis may occur as a result of the action of the symmetry transformation which due to Wigner's theorem can either be unitary or antiunitary. We demonstrate that the transition from the pre-big-bang contraction to the post-big-bang expansion - a scenario that also occurs in string quantum cosmologies - can be attributed to the action of charge conjugation, which belongs to the class of antiunitary transformations. We also demonstrate that the emergence of the two classical expanding post-big-bang universe-antiuniverse pairs, each with opposite spin projections, can be understood as being triggered by the action of a unitary transformation resembling the Hadamard gate.

Abstract: Doppler anisotropies, induced by our relative motion with respect to the source rest frame, are a guaranteed property of stochastic gravitational wave backgrounds of cosmological origin. If detected by future pulsar timing array measurements, they will provide interesting information on the physics sourcing gravitational waves, which is hard or even impossible to extract from measurements of the isotropic part of the background only. We analytically determine the pulsar response function to kinematic anisotropies, including possible effects due to parity violation, to features in the frequency dependence of the isotropic part of the spectrum, as well as to the presence of extra scalar and vector polarizations. For the first time, we show how the sensitivity to different effects crucially depends on the pulsar configuration with respect to the relative motion among frames. Correspondingly, we propose examples of strategies of detection, each aimed at exploiting future measurements of kinematic anisotropies for characterizing distinct features of the cosmological gravitational wave background.

Abstract: We rigorously derive the quadrupole formula within the context of the Einstein-Vlasov system. The main contribution of this work is an estimate of the remainder terms, derived from well-defined assumptions, with explicitly stated error terms that depend on the solution's boundedness and decay properties, and the distance to the source. The assumptions are linked to established properties of global solutions of the Einstein-Vlasov system as in \cite{LT}. Prior derivations of the quadrupole formula have relied on post-Newtonian analysis and lacked comparisons with global solution properties. The importance of the no-incoming-radiation condition is emphasized underscoring the need for solutions satisfying this condition. This work thus addresses the limitations of existing results and provides motivation for further research on global solution properties of the Einstein-Vlasov system.

Abstract: We investigate non-radial oscillations of anisotropic neutron stars within the framework of general relativity. Our study involves nonrotating, spherically symmetric anisotropic neutron stars as the unperturbed equilibrium configuration. We employ the BSk21 equation of state to describe neutron star matter and introduce a phenomenological ansatz to account for local anisotropy. Through considering small and adiabatic polar perturbations (even parity), we derive oscillation equations from the linearized Einstein equations. Notably, these oscillation equations explicitly incorporate the influence of pressure anisotropy. We calculate the frequencies and damping times of the fundamental (f) mode for various choices of anisotropic pressure strength. Interestingly, we observe that the f-mode frequencies continue to scale linearly with the average density of neutron stars, even in the presence of anisotropy. We conduct a comprehensive analysis of how anisotropy affects both the f-mode frequency and its associated damping time.

Abstract: The necessary and sufficient conditions are obtained for a unit time-like vector field $u$ to be the unit velocity of a divergence-free perfect fluid energy tensor. This plainly kinematic description of a conservative perfect fluid requires considering eighteen classes defined by differential concomitants of $u$. For each of these classes, we get the additional constraints that label the flow of a conservative energy tensor, and we obtain the pairs of functions $\{\rho,p\}$, energy density and pressure, which complete a solution to the conservation equations.

Abstract: In this short note we investigate canonical formalism for General Relativity which is formulated with the metric f^{ab}=(-g)^\alpha g^{ab}. We find corresponding Hamiltonian and we show that constraint structure is the same as in the standard formulation.

Abstract: Within the paradigm of non-perturbative Einstein gravity we study continuous manifolds which possess de Sitter interiors and Kerr exteriors. These manifolds could represent the spacetime of rotating gravastars or other similar black hole mimickers. The scheme presented here allows for a $C^{n}$ transition from the exactly de Sitter interior to the exactly Kerr exterior, with $n$ arbitrarily large. Generic properties that such models must possess are discussed, such as the changing of the topology of the ergosphere from $S^{2}$ to $S^{1}\times S^{1}$. It is shown how in the outer layers of the transition region (the "atmosphere" as it is often called in astrophysics) the dominant/weak and strong energy conditions can be respected. However, much like in the case of its static spherically symmetric gravastar counterpart, there must be some assumptions imposed in the atmosphere for the energy conditions to hold. These assumptions turn out to not be severe. The class of manifolds presented here are expected to possess all the salient features of the fully generic case. Strictly speaking, a number of the results are also applicable to the locally anti-de Sitter core scenario, although we focus on the case of a positive cosmological constant.