General Relativity and Quantum Cosmology (gr-qc)

Abstract: An extended gravity theory is used to explore the possibility of non-exotic matter traversable wormholes. In the extended gravity theory, additional terms linear and quadratic in the trace of the energy momentum tensor are considered in the Einstein-Hilbert action. Obviously, such an addition leads to violation of the energy-momentum tensor. The model parameters are constrained from the structure of the field equations. Non-exotic matter wormholes tend to satisfy the null energy conditions. We use two different traversable wormhole geometries namely an exponential and a power law shape functions to model the wormholes. From a detailed analysis of the energy conditions, it is found that, the existence of non-exotic matter traversable wormholes is not obvious in the model considered and its possibility may depend on the choice of the wormhole geometry. Also, we found that, non-exotic wormholes are possible within the given squared trace extended gravity theory for a narrow range of the chosen equation of state parameter.

Abstract: Huygens principle violation in a spacetime of odd dimensions leads to the fact that the retarded massless fields of localised sources depend on their history of motion preceding the retarded time. This non-local character of retarded fields should result into the formation of tail signals in the radiation of localised sources. In particular, in gravity theories with odd number of extra spacetime dimensions the gravitational radiation of binary systems should contain the tail terms. In this work, we demonstrate the presence of tail signal in radiation within a simple model of scalar field interacting with the point charge moving on elliptical orbit in three dimensions. We find that the tail term results into the characteristic dependence of radiation power of the charge on time. In particular, its extremum points do not correspond to the moments when the charge passes the pericenter and apocenter of the orbit, in contrast with the four-dimensional theory. We obtain the formulae for the shifts of radiation power extremum points up to the contributions quadratic in the orbital eccentricity. We also compute the spectral distribution of radiation power of the charge. We find that in three dimensions the charge on elliptical orbit radiates into the lower harmonics of the spectrum, compared to the four-dimensional theory. We conjecture that in higher dimensions the character of spectral distributions is opposite - the charge mainly radiates into the higher harmonics of the spectrum.

Abstract: Spin-induced quadrupole moments provide an important characterization of compact objects, such as black holes, neutron stars and black hole mimickers inspired by additional fields and/or modified theories of gravity. Black holes in general relativity have a specific spin-induced quadrupole moment, with other objects potentially having differing values. Different values of this quadrupole moment lead to modifications of the spin precession dynamics, and consequently modifications to the inspiral waveform. Based on the spin-dynamics and the associated precessing waveform developed in our previous work, we assess the prospects of measuring spin-induced moments in various black hole, neutron star, and black-hole mimicker binaries. We focus on binaries in which at least one of the objects is in the mass-gap (similar to the $2.6 M_\odot$ object found in GW190814). We find that for generic precessing binaries, the effect of the spin-induced quadrupole moments on the precession is sensitive to the nature of the mass-gap object, i.e., whether it is a light black hole or a massive neutron star. So that this is a good probe of the nature of these objects. For precessing black-hole mimicker binaries, this waveform also provides significantly tighter constraints on their spin-induced quadrupole moments than the previous results obtained without incorporating the precession effects of spin-induced quadrupole moments. We apply the waveform to sample events in GWTC catalogs to obtain better constraints on the spin-induced quadrupole moments, and discuss the measurement prospects for events in the O$4$ run of the LIGO-Virgo-KAGRA collaboration.

Abstract: The stationary black hole solution of a Chern-Simons model based on the semi-simple extension of the Poincar\'e gauge group is studied. The solution resembles the metric properties of the BTZ geometry but contains, in addition, non-vanishing torsion. The global structure of spacetime is characterized by three conserved charges: two associated with the mass and angular momentum and one extra constant triggered by spacetime torsion. Consequently, we show that the entropy deviates from the standard Bekenstein-Hawking value and discuss the implications of torsional charges in the context of black hole thermodynamics.

Abstract: From a theoretical perspective, matter accretion processes around compact objects are highly relevant as they serve as a natural laboratory to test general relativity in the strong field regime. This enables us to validate fundamental concepts such as the no-hair theorem, the cosmic censorship hypothesis, and the existence of alternative solutions to Einstein's equations that mimic the effects of black holes. In this study, we analyze the emission spectra of geometrically thick accretion disks, referred to as Polish doughnuts, around naked singularities described by the $q$-metric. To begin, we revisit the construction of equilibrium configurations of magnetized tori in this spacetime and evaluate the role of the deformation parameter over these configurations. Once we have systematically studied the disks in this spacetime, we use the \texttt{OSIRIS} code to perform a backward ray-tracing method, resulting in the first simulations of the intensity map and emission profiles of magnetized tori within this metric. Furthermore, we validate the effect of both the quadrupole moment and the angular momentum on observable quantities such as flux and intensity for optically thin and thick disks, since for values of $ q < 0$, which correspond to objects with prolate deformation, and which in turn, are constructed with higher values of angular momentum, the emission spectrum exhibits higher intensity than that obtained for Schwarzschild's spacetime. Hence, we find a first differential feature that distinguishes tori formed around naked singularities from those around static black holes.

Abstract: The determination of the polarization modes of gravitational waves (GWs), and of their dispersion relations is decisive to scrutinize the viability of extended theories of gravity. A tool to investigate the polarization states of GWs is the Newman-Penrose (NP) formalism. However, if the speed of GWs is smaller than the speed of light, the number of NP variables is greater than the number of polarizations. To overpass this inconvenience we use the Bardeen formalism to describe the six possible polarization modes of GWs considering different general dispersion relations for the modes. The definition of a new gauge-invariant quantity enables an unambiguous description of the scalar longitudinal polarization mode. We apply the formalism to General Relativity, scalar-tensor theories, and $f(R)$-gravity. To obtain a bridge between theory and experiment, we derive an explicit relation between a physical observable (the derivative of the frequency shift of an electromagnetic signal) with the gauge-invariant variables. From this relation, we find an analytical formula for the Pulsar Timing rms response to each polarization mode. To estimate the sensitivity of a single Pulsar Timing we focus on the case of a dispersion relation of a massive particle. The sensitivity curves of the scalar longitudinal and vector polarization modes change significantly depending on the value of the effective mass. The detection (or absence of detection) of the polarization modes using the Pulsar Timing technique has decisive implications for alternative theories of gravity. Finally, the investigation of a cutoff frequency in the Pulsar Timing band can lead to a more stringent bound on the graviton mass than that presented by ground-based interferometers.

Abstract: Reduced general relativity for four-dimensional spherically-symmetric stationary space-times, more simply called the black hole mini-superspace, was shown in previous work to admit a symmetry under the three-dimensional Poincar\'e group ISO(2,1). Such a non-semi-simple symmetry group usually signals that the system is a special case of a more general model admitting a semi-simple Lie group symmetry. We explore here possible modifications of the Hamiltonian constraint of the mini-superspace. We identify in particular a continuous deformation of the dynamics that lifts the degeneracy of the Poincar\'e group and leads to a SO(3,1) or SO(2,2) symmetry. This deformation is not related to the cosmological constant. We show that the deformed dynamics can be represented as the superposition of two non-interacting homogeneous FRW cosmologies, with flat slices filled with perfect fluid. The resulting modified black hole metrics are found to be non-singular.