General Relativity and Quantum Cosmology (gr-qc)

Abstract: The concept of entropy forms the backbone of the principles of thermodynamics. R.C. Tolman initiated a correlation between gravity and thermodynamics. The development of black hole thermodynamics and the generalized second law of thermodynamics led to Penrose's conjecture that the Weyl tensor should serve as a measure of the entropy of the free gravitational field. This entropy reflects the degrees of freedom associated with the free gravitational field. The proposition of gravitational entropy justifies the initial entropy of the universe. This entropy function had to be associated with the dynamics of the free gravitational field from the time of the big bang, so that a gravity-dominated evolution of the universe preserves the second law of thermodynamics. Moreover, the concept of black hole entropy emerges as a particular case of the entropy of the free gravitational field. However, a self-consistent notion of gravitational entropy in the context of cosmological structure formation has eluded us till today. Various proposals have been put forward, initially based on Penrose's Weyl Curvature Hypothesis, and subsequently modified to fit the needs of specific geometries and matter distributions. Such proposals were basically geometric in nature. A few years back a new definition of gravitational entropy was proposed from the considerations of the relativistic Gibb's equation and based on the square root of the Bel-Robinson tensor, the simplest divergence-free tensor derived from the Weyl tensor. Even this proposal is valid only for a restricted class of spacetimes. A complete self-consistent description of gravitational entropy encompassing black hole physics and cosmological dynamics is yet to emerge. In this article, we gather an overview of the concept of gravitational entropy, following it up with the development of the various proposals of gravitational entropy.

Abstract: Using the tool of Hodge-Morrey decomposition of forms, we prove a new decomposition of symmetric rank-2 tensors on flat manifolds with boundary. Using this we reconstruct a new cosmological perturbation theory that allows for the scalar-vector-tensor type separation of the linearized Einstein equations with general boundary conditions. We discuss gauge transformations, gauge invariant quantities and as an example how the new decomposition works out in the single-field inflation scenario. For the scalar modes we get two copies of Mukhanov-Sasaki equation, one of them with a slight modification. Additionally we run a Weinberg-like argument for the existence adiabatic modes, and find some gauge-invariant solutions to the perturbations that exists whatever the constituents of the universe are.

Abstract: A universal method to solve the differential equations of light-like geodesics is developed. The validity of this method depends on a new theorem, which is introduced for light-like geodesics in analogy to Beltrami's "geometrical" method for time-like geodesics. we apply the method to the Schwarzschild and Kerr spacetime as two examples. The general solutions of the light-like geodesic equations in the two spacetimes are derived straightforwadly. After setting $\theta=\pi/2$, the general light-like geodesics in Schwarzschild spacetime reduce to the same expression as that in literatures. The method developed and results obtained in this paper may be useful in modeling dynamical phenomena in strong gravitaional fields like black holes since the solutions are expressed in terms of elliptic integrals, which can be calculated effectively.

Abstract: Recently there has been an interest in exploring black holes that are regular in that the central curvature singularity is avoided. Here, we give a recipe to obtain a regular black hole spacetime from the unhindered gravitational collapse from regular initial data of a spherically symmetric perfect fluid. While the classic Oppenheimer-Snyder collapse model necessarily produces a black hole with a Schwarzschild singularity at the centre, we show here that there are classes of regular initial conditions when collapse gives rise to a regular black hole.

Abstract: GW170817 - GRB 170817A provided the first observation of gravitational waves from a neutron star merger with associated transient counterparts across the entire electromagnetic spectrum. This discovery demonstrated the long-hypothesized association between short gamma-ray bursts and neutron star mergers. More joint detections are needed to explore the relation between the parameters inferred from the gravitational wave and the properties of the gamma-ray burst signal. We developed a joint multi-messenger analysis of LIGO, Virgo, and Fermi/GBM data designed for detecting weak gravitational-wave transients associated with weak gamma-ray bursts. As such, it does not start from confident (GWTC-1) events only. Instead, we take the full list of existing compact binary coalescence triggers generated with the PyCBC pipeline from the second Gravitational-Wave Observing Run (O2), and reanalyze the entire set of public Fermi/GBM data covering this observing run to generate a corresponding set of gamma-ray burst candidate triggers. We then search for coincidences between the gravitational-wave and gamma-ray burst triggers without requiring a confident detection in any channel. The candidate coincidences are ranked according to a statistic combining each candidate's strength in gravitational-wave and gamma-ray data, their time proximity, and the overlap of their sky localization. The ranking is then converted to a false-alarm rate using time shifts between the gravitational-wave and gamma-ray burst triggers. We present the results using O2 triggers which allowed us to check the validity of our method against GW170817 - GRB 170817A. We also discuss the different configurations tested to maximize the significance of the joint detection.

Abstract: Gravitational waves (GWs) from stellar-mass compact binary coalescences (CBCs) are expected to be strongly lensed when encountering large agglomerations of matter, such as galaxies or clusters. Searches for strongly lensed GWs have been conducted using data from the first three observing runs of the LIGO-Virgo GW detector network. Although no confirmed detections have been reported, interesting candidate lensed pairs have been identified. In this work, we delineate a preliminary analysis that rapidly identifies pairs to be further analyzed by more sophisticated Bayesian parameter estimation (PE) methods. The analysis relies on the Gaussian/Fisher approximation to the likelihood and compares the corresponding approximate posteriors on the chirp masses of the candidate pair. It additionally cross-correlates the rapidly produced localization sky areas (constructed by Bayestar sky-localization software). The analysis was used to identify pairs involving counterparts from targeted sub-threshold searches to confidently detected super-threshold CBC events. The most significant candidate ``super-sub'' pair deemed by this analysis was subsequently found, by more sophisticated and detailed joint-PE analyses, to be among the more significant candidate pairs, but not sufficiently significant to suggest the observation of a lensed event [1].

Abstract: Palatini $f(R)$ gravity is probably the simplest extension of general relativity (GR) and the simplest realization of a metric-affine theory. It has the same number of degrees of freedom as GR and, in vacuum, it is straightforwardly mapped into GR with a cosmological constant. The mapping between GR and Palatini $f(R)$ inside matter is possible but at the expense of reinterpreting the meaning of the matter fields. The physical meaning and consequences of such mapping will depend on the physical context. Here we consider three such cases within the weak field limit: Solar System dynamics, planetary internal dynamics (seismology), and galaxies. After revising our previous results on the Solar System and Earth's seismology, we consider here the possibility of $f(R)$ Palatini as a dark matter candidate. For any $f(R)$ that admits a polynomial approximation in the weak field limit, we show here, using SPARC data and a recent method that we proposed, that the theory cannot be used to replace dark matter in galaxies. We also show that the same result applies to the Eddington-inspired Born-Infeld gravity. Differently from the metric $f(R)$ case, the rotation curve data are sufficient for this conclusion. This result does not exclude a combination of modified gravity and dark matter.

Abstract: Ultra-high frequency gravitational waves in the MHz to THz regime promise a unique possibility to probe the very early universe, particle physics at very high energies and exotic astrophysical objects - but achieving the sensitivity required for detection is an immense challenge. This is a brief summary of recent progress in electromagnetic high-frequency gravitational wave searches, which are based on classical electromagnetism in a space-time perturbed by gravitational waves. A particular focus is given to synergies with axion searches and atomic precision measurements. This article was prepared as proceedings for Moriond EW 2023.