Testing the Kerr nature of intermediate-mass and supermassive black hole binaries using spin-induced multipole moment measurements

The gravitational wave measurements of spin-induced multipole moment coefficients of a binary black hole system can be used to distinguish black holes from other compact objects [N. V. Krishnendu et al., PRL 119, 091101 (2017)]. Here, we apply the idea proposed in [N. V. Krishnendu et al., PRL 119, 091101 (2017)] to binary systems composed of intermediate-mass and supermassive black holes and derive the expected bounds on their Kerr nature using future space-based gravitational wave detectors. Using astrophysical models of binary black hole population, we study the measurability of the spin-induced quadrupole and octupole moment coefficients using LISA and DECIGO. The errors on spin-induced quadrupole moment parameter of the binary system are found to be { $\leq 0.1$ for almost $3\%$ of the total supermassive binary black hole population which is detectable by LISA whereas it is $\sim 46\%$ for the intermediate-mass black hole binaries observable by DECIGO at its design sensitivity.} We find that { errors on} {\it both} the quadrupole and octupole moment parameters can be estimated to { be} $\leq 1$ for $\sim 2\%$ and $\sim 50\%$ {of the population} respectively for LISA and DECIGO detectors. { Our findings suggest that a subpopulation of binary black hole events, with the signal to noise ratio thresholds greater than 200 and 100 respectively for LISA and DECIGO detectors, would permit tests of black hole nature to 10\% precision.}Comment: 7 pages, 6 figure

Testing general relativity with gravitational waves: An overview

The detections of gravitational-wave (GW) signals from compact binary coalescence by ground-based detectors have opened up the era of GW astronomy. These observations provide opportunities to test Einstein's general theory of relativity at the strong-field regime. Here we give a brief overview of the various GW-based tests of General Relativity (GR) performed by the LIGO-Virgo collaboration on the detected GW events to date. After providing details for the tests performed in four categories, we discuss the prospects for each test in the context of future GW detectors. The four categories of tests include the consistency tests, parametrized tests for GW generation and propagation, tests for the merger remnant properties, and GW polarization tests.Comment: 21 pages, 7 figures, review article contributed as part of the Special Issue on Current and Future Tests of General Relativity of the journal Univers

Constraining the nature of dark compact objects with spin-induced octupole moment measurement

Various theoretical models predict the existence of exotic compact objects that can mimic the properties of black holes (BHs). Gravitational waves (GWs) from the mergers of compact objects have the potential to distinguish between exotic compact objects and BHs. The measurement of spin-induced multipole moments of compact objects in binaries provides a unique way to test the nature of compact objects. The observations of GWs by LIGO and Virgo have already put constraints on the spin-induced quadrupole moment, the leading order spin-induced moment. In this work, we develop a Bayesian framework to measure the spin-induced octupole moment, the next-to-leading order spin-induced moment. The precise measurement of the spin-induced octupole moment will allow us to test its consistency with that of Kerr BHs in general relativity and constrain the allowed parameter space for non-BH compact objects. For various simulated compact object binaries, we explore the ability of the LIGO and Virgo detector network to constrain spin-induced octupole moment of compact objects. We find that LIGO and Virgo at design sensitivity can constrain the symmetric combination of component spin-induced octupole moments of binary for dimensionless spin magnitudes $\sim 0.8$. Further, we study the possibility of simultaneously measuring the spin-induced quadrupole and octupole moments. Finally, we perform this test on selected GW events reported in the third GW catalog. These are the first constraints on spin-induced octupole moment using full Bayesian analysis.Comment: 13 pages, 8 figure

Gap equation in scalar field theory at finite temperature

We investigate the two-loop gap equation for the thermal mass of hot massless $g^2\phi^4$ theory and find that the gap equation itself has a non-zero finite imaginary part. This indicates that it is not possible to find the real thermal mass as a solution of the gap equation beyond $g^2$ order in perturbation theory. We have solved the gap equation and obtain the real and the imaginary part of the thermal mass which are correct up to $g^4$ order in perturbation theory.Comment: 13 pages, Latex with axodraw, Minor corrections, Appendix adde

Unveiling Microlensing Biases in Testing General Relativity with Gravitational Waves

Gravitational waves (GW) from chirping binary black holes (BBHs) provide unique opportunities to test general relativity (GR) in the strong-field regime. However, testing GR can be challenging when incomplete physical modeling of the expected signal gives rise to systematic biases. In this study, we investigate the potential influence of wave effects in gravitational lensing (which we refer to as microlensing) on tests of GR using GWs for the first time. We utilize an isolated point-lens model for microlensing with the lens mass ranging from $10-10^5~$M$_\odot$ and base our conclusions on an astrophysically motivated population of BBHs in the LIGO-Virgo detector network. Our analysis centers on two theory-agnostic tests of gravity: the inspiral-merger-ringdown consistency test (IMRCT) and the parameterized tests. Our findings reveal two key insights: First, microlensing can significantly bias GR tests, with a confidence level exceeding $5\sigma$. Notably, substantial deviations from GR $(\sigma > 3)$ tend to align with a strong preference for microlensing over an unlensed signal, underscoring the need for microlensing analysis before claiming any erroneous GR deviations. Nonetheless, we do encounter scenarios where deviations from GR remain significant ($1 < \sigma < 3$), yet the Bayes factor lacks the strength to confidently assert microlensing. Second, deviations from GR correlate with pronounced interference effects, which appear when the GW frequency ($f_\mathrm{GW}$) aligns with the inverse time delay between microlens-induced images ($t_\mathrm{d}$). These false deviations peak in the wave-dominated region and fade where $f_\mathrm{GW}\cdot t_\mathrm{d}$ significantly deviates from unity. Our findings apply broadly to any microlensing scenario, extending beyond specific models and parameter spaces, as we relate the observed biases to the fundamental characteristics of lensing.Comment: 21 pages, 12 figure

Antioxidant Properties of Bitter Gourd (Momordica Charantia L.)

Bitter gourd is regarded as an antioxidant rich vegetable with beneficial properties for the circulatory, respiratory, digestive and nervous systems according to the Indian indigenous system of medicine. Several methods have been used to determine antioxidant activity of plants. The present study, therefore, involved four various established methods to evaluate anti oxidative activity of bitter gourd fruit, namely, total antioxidant capacity, DPPH radical scavenging activity, hydroxyl radical scavenging activity and super oxide anion radical scavenging activity by using different types of solvents like petroleum ether, acetone, ethanol and methanol. The present study revealed that light green big sample had the highest DPPH activity with an IC50 value of 50.88 µg/ ml in methanol solvent. In the case of bitter gourd dried samples, highest DPPH activity with an IC50 value of 50.10 µg/ ml was reported in light green big type. The hydroxyl radical scavenging activity of light green big was found to be highest both in the case of fresh and dried bitter gourd samples with an IC50 values of 50.95 µg/ml and 50.10 µg/ml respectively. Light green small sample showed higher superoxide anion radical scavenging activity with an IC50 value of 50.36 µg/ ml in fresh samples and 49.76 µg/ ml in dried samples, in solvents like petroleum ether and acetone respectively. Antioxidant activity ranged with an IC50 value of 50.09 µg/ml to 61.90 µg/ml in fresh bitter gourd samples and maximum antioxidant capacity was observed in light green big (50.09 µg/ ml) whereas dried samples, the highest antioxidant activity was observed in light green dried (50.07 µg/ ml) in acetone solvent

Constraining mass of the graviton with GW170817

We consider the massive graviton phenomenological model based on the graviton's dispersion terms included into phase of gravitational wave's waveform. Such model was already considered in many works but it was based on a single leading-order dispersion term only. Here we derive a relation between relativistic gravitons emission and absorption time intervals computed up to ${\cal O}(\gamma^{-6})$, where $\gamma$ is the Lorentz factor. Including the dispersion terms into the phase of gravitational wave's waveform results in two non-GR parameters of the $1^{st}$ and the $-2^{nd}$ post-Newtonian orders whose posteriors are used to put a constraint on the graviton's rest mass. We use the TaylorF2 waveform model to analyse the event GW170817 and report the following $95\%$-confidence upper bounds on the graviton's rest mass: $m^{Low\,Spin}_{g}\leq1.305\times10^{-54}$g and $m^{High\,Spin}_{g}\leq2.996\times10^{-54}$g for the high and low spin priors

Investigating the relation between gravitational wave tests of general relativity

Gravitational wave observations of compact binary coalescences provide precision probes of strong-field gravity. There is thus now a standard set of null tests of general relativity (GR) applied to LIGO-Virgo detections and many more such tests proposed. However, the relation between all these tests is not yet well understood. We start to investigate this by applying a set of standard tests to simulated observations of binary black holes in GR and with phenomenological deviations from GR. The phenomenological deviations include self-consistent modifications to the energy flux in an effective-one-body (EOB) model, the deviations used in the second post-Newtonian (2PN) TIGER and FTA parameterized tests, and the dispersive propagation due to a massive graviton. We consider four types of tests: residuals, inspiral-merger-ringdown consistency, parameterized (TIGER and FTA), and modified dispersion relation. We also check the consistency of the unmodeled reconstruction of the waveforms with the waveform recovered using GR templates. These tests are applied to simulated observations similar to GW150914 with both large and small deviations from GR and similar to GW170608 just with small deviations from GR. We find that while very large deviations from GR are picked up with high significance by almost all tests, more moderate deviations are picked up by only a few tests, and some deviations are not recognized as GR violations by any test at the moderate signal-to-noise ratios we consider. Moreover, the tests that identify various deviations with high significance are not necessarily the expected ones. We also find that the 2PN (1PN) TIGER and FTA tests recover much smaller deviations than the true values in the modified EOB (massive graviton) case. Additionally, we find that of the GR deviations we consider, the residuals test is only able to detect extreme deviations from GR. (Abridged