Maxwell Electrodynamics in terms of Physical Potentials

A fully relativistically covariant and manifestly gauge invariant formulation of classical Maxwell electrodynamics is presented, purely in terms of gauge invariant potentials without entailing any gauge fixing. We show that the inhomogeneous equations satisfied by the physical scalar and vector potentials (originally discovered by Maxwell) have the same symmetry as the isometry of Minkowski spacetime, thereby reproducing Einstein's incipient approach leading to his discovery of special relativity as a spacetime symmetry. To arrive at this conclusion, we show how the Maxwell equations for the potentials follow from stationary electromagnetism by replacing the Laplacian operator by the d'Alembertian operator, while making all variables dependent on space and time. We also establish consistency of these equations by deriving them from the standard Maxwell equations for the field strengths, showing that there is a unique projection operator which projects onto the physical potentials. Properties of the physical potentials are elaborated through their iterative N\"other coupling to a charged scalar field leading to the Abelian Higgs model, and through a sketch of the Aharonov-Bohm effect, where dependence of the Aharonov-Bohm phase on the physical vector potential is highlighted.Comment: 9 pages Latex2e. arXiv admin note: contains material formerly in arXiv:1801.0760

Gravitational Waves with Orbital Angular Momentum

Compact orbiting binaries like the black hole binary system observed in GW150914 carry large amount of orbital angular momentum. The post-ringdown compact object formed after merger of such a binary configuration has only spin angular momentum, and this results in a large orbital angular momentum excess. One significant possibility is that the gravitational waves generated by the system carry away this excess orbital angular momentum. An estimate of this excess is made. Arguing that plane gravitational waves cannot possibly carry any orbital angular momentum, a case is made in this paper for gravitational wave beams carrying orbital angular momentum, akin to optical beams. Restricting to certain specific beam-configurations, we predict that such beams may produce a new type of strain, in addition to the longitudinal strains measured at aLIGO for GW150914 and GW170817. Current constraints on post-ringdown spins, derived within the planewave approximation of gravitational waves, therefore stand to improve. The minimal modification that might be needed on a laser-interferometer detector (like aLIGO or VIRGO) to detect such additional strains is also briefly discussed.Comment: 8 pages, 4 figures Version to appear in EPJ

Non-parametric inference of the population of compact binaries from gravitational wave observations using binned Gaussian processes

The observation of gravitational waves from multiple compact binary coalescences by the LIGO-Virgo-KAGRA detector networks has enabled us to infer the underlying distribution of compact binaries across a wide range of masses, spins, and redshifts. In light of the new features found in the mass spectrum of binary black holes and the uncertainty regarding binary formation models, non-parametric population inference has become increasingly popular. In this work, we develop a data-driven clustering framework that can identify features in the component mass distribution of compact binaries simultaneously with those in the corresponding redshift distribution, from gravitational wave data in the presence of significant measurement uncertainties, while making very few assumptions on the functional form of these distributions. Our generalized model is capable of inferring correlations among various population properties such as the redshift evolution of the shape of the mass distribution itself, in contrast to most existing non-parametric inference schemes. We test our model on simulated data and demonstrate the accuracy with which it can re-construct the underlying distributions of component masses and redshifts. We also re-analyze public LIGO-Virgo-KAGRA data from events in GWTC-3 using our model and compare our results with those from some alternative parametric and non-parametric population inference approaches. Finally, we investigate the potential presence of correlations between mass and redshift in the population of binary black holes in GWTC-3 (those observed by the LIGO-Virgo-KAGRA detector network in their first 3 observing runs), without making any assumptions about the specific nature of these correlations.Comment: Upload accepted versio

Measuring Gravitational Wave Speed and Lorentz Violation with the First Three Gravitational-Wave Catalogs

The speed of gravitational waves $v_g$ can be measured with the time delay between gravitational-wave detectors. Our study provides a more precise measurement of $v_g$ using gravitational-wave signals only, compared with previous studies. We select 52 gravitational-wave events that were detected with high confidence by at least two detectors in the first three observing runs (O1, O2, and O3) of Advanced LIGO and Advanced Virgo. We use Markov chain Monte Carlo and nested sampling to estimate the $v_g$ posterior distribution for each of those events. We then combine their posterior distributions to find the 90% credible interval of the combined $v_g$ distribution for which we obtain $0.99^{+0.02}_{-0.02}c$ without the use of more accurate sky localization from the electromagnetic signal associated with GW170817. Restricting attention to the 50 binary black hole events generates the same result, while the use of the electromagnetic sky localization for GW170817 gives a tighter constraint of $0.99^{+0.01}_{-0.02}c$. The abundance of gravitational wave events allows us to apply hierarchical Bayesian inference on the posterior samples to simultaneously constrain all nine coefficients for Lorentz violation in the nondispersive, nonbirefringent limit of the gravitational sector of the Standard-Model Extension test framework. We compare the hierarchical Bayesian inference method with other methods of combining limits on Lorentz violation in the gravity sector that are found in the literature.Comment: 17 pages, 4 figures, 3 table

When to Point Your Telescopes: Gravitational Wave Trigger Classification for Real-Time Multi-Messenger Followup Observations

We develop a robust and self-consistent framework to extract and classify gravitational wave candidates from noisy data, for the purpose of assisting in real-time multi-messenger follow-ups during LIGO-Virgo-KAGRA's fourth observing run~(O4). Our formalism implements several improvements to the low latency calculation of the probability of astrophysical origin~(\PASTRO{}), so as to correctly account for various factors such as the sensitivity change between observing runs, and the deviation of the recovered template waveform from the true gravitational wave signal that can strongly bias said calculation. We demonstrate the high accuracy with which our new formalism recovers and classifies gravitational wave triggers, by analyzing replay data from previous observing runs injected with simulated sources of different categories. We show that these improvements enable the correct identification of the majority of simulated sources, many of which would have otherwise been misclassified. We carry out the aforementioned analysis by implementing our formalism through the \GSTLAL{} search pipeline even though it can be used in conjunction with potentially any matched filtering pipeline. Armed with robust and self-consistent \PASTRO{} values, the \GSTLAL{} pipeline can be expected to provide accurate source classification information for assisting in multi-messenger follow-up observations to gravitational wave alerts sent out during O4.Comment: v2 upload was accidental. revert back to v

Performance of the low-latency GstLAL inspiral search towards LIGO, Virgo, and KAGRA's fourth observing run

GstLAL is a stream-based matched-filtering search pipeline aiming at the prompt discovery of gravitational waves from compact binary coalescences such as the mergers of black holes and neutron stars. Over the past three observation runs by the LIGO, Virgo, and KAGRA (LVK) collaboration, the GstLAL search pipeline has participated in several tens of gravitational wave discoveries. The fourth observing run (O4) is set to begin in May 2023 and is expected to see the discovery of many new and interesting gravitational wave signals which will inform our understanding of astrophysics and cosmology. We describe the current configuration of the GstLAL low-latency search and show its readiness for the upcoming observation run by presenting its performance on a mock data challenge. The mock data challenge includes 40 days of LIGO Hanford, LIGO Livingston, and Virgo strain data along with an injection campaign in order to fully characterize the performance of the search. We find an improved performance in terms of detection rate and significance estimation as compared to that observed in the O3 online analysis. The improvements are attributed to several incremental advances in the likelihood ratio ranking statistic computation and the method of background estimation.Comment: 19 pages, 21 figure

Background gravity correction to the limiting mass of white dwarfs

Abstract While computing the Fermi degeneracy pressure of electrons in a white dwarf star within the framework of hydrostatic equilibrium, we depart from the extant practice of treating the electrons as a free fermion gas, by including the effect of the background gravitational potential experienced by the electrons in the star, resulting from the mass of its constituent atoms (being the mass of all nucleons). Modifying the free particle Hamiltonian with this effective potential, we employ first order quantum mechanical perturbation theory to compute the degeneracy pressure, in order to study the effect of inclusion of this self-gravity of the star on the limiting mass. The final effect is found to be non-trivial, but perhaps a shade too small to alter any major observational result