General Relativity and Quantum Cosmology (gr-qc)

Abstract: It is well-known that parity symmetry is broken in the weak interaction but conserved for Einstein's general relativity and Maxwell's electromagnetic theory. Nevertheless, parity symmetry could also be violated in the gravitational/electromagnetic sectors if a fundamental scalar field couples to the parity-violating gravitational/electromagnetic curvature terms. Such parity-violating terms, which flip signs under reversed spatial directions, can inevitably lead to a negative effective mass squared for the scalar field perturbations near nonspherical black holes and thus are expected to trigger tachyonic instability. As illustrative examples, we show that the scalar field coupled to gravitational/electromagnetic Chern-Simons terms near a Kerr-Newmann spacetime can develop tachyonic instabilities, leading to equilibrium scalar field configurations in certain parameter region of black holes. This instability, which is an indication of the black hole scalarization process, can occur in a broad class of nonspherical black holes and parity-violating theories.

Abstract: We discuss the potential alleviation of both the Hubble and the growth of galactic structure data tensions observed in the current epoch of Cosmology in the context of the so-called Stringy Running Vacuum Model (RVM) of Cosmology. This is a gravitational field theory coupled to matter, which, at early eras, contains gravitational (Chern-Simons (CS) type) anomalies and torsion, arising from the fundamental degrees of freedom of the massless gravitational multiplet of an underlying microscopic string theory. The model leads to RVM type inflation without external inflatons, arising from the quartic powers of the Hubble parameter that characterise the vacuum energy density due to primordial-gravitational-wave-induced anomaly CS condensates, and dominate the inflationary era. In modern eras, of relevance to this work, the gravitational anomalies are cancelled by chiral matter, generated at the end of the RVM inflationary era, but cosmic radiation and other matter fields are still responsible for a RVM energy density with terms exhibiting a quadratic-power-of-Hubble-parameter dependence, but also products of the latter with logarithmic $H$-dependencies, arising from potential quantum-gravity and quantum-matter loop effects. In this work, such terms are examined phenomenologically from the point of view of the potential alleviation of the aforementioned current tensions in Cosmology. Using standard information criteria, we find that these tensions can be substantially alleviated in a way consistent not only with the data, but also with the underlying microscopic theory predictions, associated with the primordial dynamical breaking of supergravity that characterise a pre-RVM-inflationary phase of the model.

Abstract: The gravitational and electromagnetic multipole moments of the charged rotating disc of dust, which is an axisymmetric, stationary solution of the Einstein-Maxwell equations in terms of a post-Newtonian expansion, are calculated and discussed. It turns out that the individual mass, angular momentum, electric and magnetic moments are ordered in the sense that higher moments have a lower absolute value. There is an interesting conjecture stating that the absolute values of all higher multipole moments of a uniformly rotating perfect fluid body are always greater than those of the corresponding Kerr spacetime, which we generalize to include charged bodies. We find that for the charged rotating disc of dust the conjecture holds (within the limits of accuracy of the post-Newtonian expansion).

Abstract: We consider the Einstein-Boltzmann system for massless particles in the Bianchi I space-time with scattering cross-sections in a certain range of soft potentials. We assume that the space-time has an initial conformal gauge singularity and show that the initial value problem is well posed with data given at the singularity. This is understood by considering conformally rescaled equations. The Einstein equations become a system of singular ordinary differential equations, for which we establish an existence theorem which requires several differentiability and eigenvalue conditions on the coefficient functions together with the Fuchsian conditions. The Boltzmann equation is regularized by a suitable choice of time coordinate, but still has singularities in momentum variables. This is resolved by considering singular weights, and the existence is obtained by exploiting singular moment estimates.

Abstract: We study the topological defects in the thermodynamics of regular black strings (from a four-dimensional perspective) that is symmetric under the double Wick rotation and constructed in the high-dimensional spacetime with an extra dimension compactified on a circle. We observe that the thermodynamic phases of regular black strings can be topologically classified by the positive and negative winding numbers (at the defects) which correspond to the thermodynamically stable and unstable branches. This topological classification implies a phase transition due to the decay of a thermodynamically unstable regular black string to another which is thermodynamically stable. We confirm these topological properties of the thermodynamics of regular black strings by investigating their free energy, heat capacity, and Ruppeiner scalar curvature of the state space. The Ruppeiner scalar curvature of regular black strings is found to be always negative, implying that the interactions among the microstructures of regular black strings are only attractive.

Abstract: We consider, from a dynamical systems point of view, a frozen, planar trivalent spin network model in Loop Quantum Gravity (LQG) presenting self-organized criticality (SOC). We obtain a partition function for the domains of stability connecting gauge non-invariant avalanches, leading to an entropy formula for the asymptotic SOC state. We use this formalism to obtain the entropy of a $(2+1)$-dimensional (BTZ) black hole, and conjecture that this entropy reduces to the Bekenstein-Hawking entropy law by an appropriate adjustment of a potential function.

Abstract: This is a companion article to `Using massless fields for observing black hole features in the collapsed phase of Euclidean dynamical triangulations' [1]. It clarifies a singular co\"{o}rdinate transformation of an $SO(4)$ invariant metric to the usual spherical co\"{o}rdinates in which, at an instant of time called zero, the metric takes the form of a black hole with an interior. Regular transformations are also studied and found to lead in the zero time limit to the same spatial components of the metric as with the singular one, whereas the time component ends up differently. Components of the Einstein tensor also end up the same. A regular black hole metric is inversely transformed and compared with simulation results in [1].

Abstract: According to a number of arguments in quantum gravity, both model-dependent and model-independent, Heisenberg's uncertainty principle is modified when approaching the Planck scale. This deformation is attributed to the existence of a minimal length. The ensuing models have found entry into the literature under the term Generalized Uncertainty Principle (GUP). In this work, we discuss several conceptual shortcomings of the underlying framework and critically review recent developments in the field. In particular, we touch upon the issues of relativistic and field theoretical generalizations, the classical limit and the application to composite systems. Furthermore, we comment on subtleties involving the use of heuristic arguments instead of explicit calculations. Finally, we present an extensive list of constraints on the model parameter $\beta$, classifying them on the basis of the degree of rigour in their derivation and reconsidering the ones subject to problems associated with composites.

Abstract: We consider a reduced phase space quantisation of a model with $T^3$ Gowdy symmetry in which gravity has been coupled to Gaussian dust. We complete the quantisation programme in reduced loop quantum gravity (LQG) as well as algebraic quantum gravity (AQG) and derive a Schr\"odinger-like equation with a physical Hamiltonian operator encoding the dynamics. Due to the classical symmetries of the physical Hamiltonian, the operators are quantised in a graph-preserving way in both cases -- a difference to former models available in the literature. As a first step towards applications of the model in AQG, we consider an ansatz that we use to first construct zero volume states as specific solutions of the Schr\"odiger-like equation. We then also find states with a vanishing action of the Euclidean part of the physical Hamiltonian and investigate the degeneracies these states experience via the action of the Lorentzian part of the physical Hamiltonian. The results presented here can be taken as a starting point for deriving effective models as well as analysing the dynamics numerically in future work.

Abstract: We revisit the cosmic evolution of the energy density of a quantized free scalar field and assess under what conditions the particle production and classical field approximations reproduce its correct value. Because the unrenormalized energy-momentum tensor diverges in the ultraviolet, it is necessary to frame our discussion within an appropriate regularization and renormalization scheme. Pauli-Villars avoids some of the drawbacks of adiabatic subtraction and dimensional regularization and is particularly convenient in this context. In some cases, we can predict the evolution of the energy density irrespectively of the quantum state of the field modes. To further illustrate our results we focus however on the {\it in} vacuum, the preferred quantum state singled out by inflation, and explore to what extent the latter determines the subsequent evolution of the energy density regardless of the unknown details of reheating. We contrast this discussion with examples of transitions to radiation domination that avoid some of the problems of the one commonly studied in the literature, and point out some instances in which the particle production or the classical field approximations lead to the incorrect energy density. Along the way, we also elaborate on the connection of our analysis to dynamical dark energy models and axion-like dark matter candidates.

Abstract: One of the most challenging open questions in physics today is discovering the nature of dark matter. In this work we study the imaging formation in dark matter (DM) halos due to an external light source using some DM profiles for comparison with astronomical observations. Approaching these models on a small scale, we analyze the images generated on the lens plane by obtaining the analytical scaled surface mass densities $\Sigma_{*}(x)$ and their corresponding deflection angles $\alpha_{*}(x)$, for later applying a method for ray tracing using the gravitational refraction law. The method is able to locate the positions of the images on the lens plane, by mapping fringes that represent possible sources (such as other galaxies), placed on the source plane. The regions where the strong lensing occurs for each profile, are determined by fixing the $\lambda$ parameter that establishes the ray tracing process. It is shown that the presence of Einstein rings generated by each profile is directly related with the central branch of the caustic. This method gives us a possible alternative way to distinguish between different DM candidates by observing imaging from external sources.