General Relativity and Quantum Cosmology (gr-qc)

Abstract: We study the geometrically thick non-self gravitating equilibrium tori orbiting the static spherically symmetric dyonic black hole with quasi-topological electromagnetic electromagnetism. Our results show that the electric and magnetic charges together with the coupling parameter in the quasi-topological electromagnetic electromagnetism lead to a much richer class of equilibrium tori. There is a range of parameters which allows for the existence of double tori. The properties of the double equilibrium tori and the accretion in the double tori become far richer. Moreover, the transitions between single torus and double tori solutions can occur by changing the specific angular momentum of the fluid. These richer properties of equilibrium tori could help to understand the dyonic black hole and its thick accretion disk.

Abstract: We quantize the Oppenheimer-Snyder model of black hole using the integral quantization method. We treat spatial and temporal coordinates on the same footing both at classical and quantum levels. Our quantization resolves or smears the singularities of the classical curvature invariants. Quantum trajectories with bounces can replace singular classical ones. The considered quantum black hole may have finite lifetime. As a byproduct, we obtain the resolution of the gravitational singularity of the Schwarzschild black hole at quantum level.

Abstract: We present the component form of the multipole tidal phase for the gravitational waveform of compact binary coalescences (MultipoleTidal), which consists of the mass quadrupole, the current quadrupole, and the mass octupole moments. We demonstrate the phase evolution and the phase difference between the tidal multipole moments (MultipoleTidal) and the mass quadrupole (PNTidal) as well as the numerical-relativity calibrated model (NRTidalv2). We find the MultipoleTidal gives a larger phase shift than the PNTidal, and is closer to the NRTidalv2. We compute the matches between waveform models to see the impact of the tidal multipole moments on the gravitational wave phases. We find the MultipoleTidal gives larger matches to the NRTidalv2 than the PNTidal, in particular, for high masses and large tidal deformabilities. We also apply the MultipoleTidal model to binary neutron star coalescence events GW170817 and GW190425. We find that the current quadrupole and the mass octupole moments give no significant impact on the inferred tidal deformability.

Abstract: Future space-based gravitational-wave detectors will detect gravitational waves with high sensitivity in the millihertz frequency band, which provides more opportunities to test theories of gravity than ground-based ones. The study of quasinormal modes (QNMs) and their application to testing gravity theories have been an important aspect in the field of gravitational physics. In this study, we investigate the capability of future space-based gravitational wave detectors such as LISA, TaiJi, and TianQin to constrain the dimensionless deviating parameter for Einstein-dilaton-Gauss-Bonnet (EdGB) gravity with ringdown signals from the merger of binary black holes. The ringdown signal is modeled by the two strongest QNMs in EdGB gravity. Taking into account time-delay interferometry, we calculate the signal-to-noise ratio (SNR) of different space-based detectors for ringdown signals to analyze their capabilities. The Fisher information matrix is employed to analyze the accuracy of parameter estimation, with particular focus on the dimensionless deviating parameter for EdGB gravity. The impact of the parameters of gravitational wave sources on the estimation accuracy of the dimensionless deviating parameter has also been studied. We find that the constraint ability of EdGB gravity is limited because the uncertainty of the dimensionless deviating parameter increases with the decrease of the dimensionless deviating parameter. LISA and TaiJi has more advantages to constrain the dimensionless deviating parameter to a more accurate level for the massive black hole, while TianQin is more suitable for less massive black holes. Bayesian inference method is used to perform parameter estimation on simulated data, which verifies the reliability of the conclusion.

Abstract: Early during the era of cosmic inflation, rotational invariance may have been broken, only later emerging as a feature of low-energy physics. This motivates ongoing searches for residual signatures of anisotropic space-time, for example in the power spectrum of the cosmic microwave background. We propose that dipolar Bose-Einstein condensates (BECs) furnish a laboratory quantum simulation platform for the anisotropy evolution of fluctuation spectra during inflation, exploiting the fact that the speed of dipolar condensate sound waves depends on direction. We construct the anisotropic analogue space-time metric governing sound, by linking the time-varying strength of dipolar and contact interactions in the BEC to the scale factors in different coordinate directions. Based on these, we calculate the dynamics of phonon power spectra during an inflation that renders the initially anisotropic universe isotropic. We find that the expansion speed provides an experimental handle to control and study the degree of final residual anisotropy. Gravity analogues using dipolar condensates can thus provide tuneable experiments for a field of cosmology that was until now confined to a single experiment, our universe.

Abstract: We study inflation in scalar-tensor perturbative quantum gravity driven by a one-loop effective potential. We consider effective potentials generated by three models. The first model describes a single scalar field with a non-vanishing mass. The second model describes a massless scalar field with non-minimal coupling to the Einstein tensor. The third model describes a single scalar field with quadratic and quartic interaction terms. All models develop a small tensor-to-scalar ratio, but the tilt of the scalar spectrum is too large to be consistent with the observational data. We discuss ways to extend these models to account for other quantum effects.

Abstract: We consider the stability of six-dimensional singly rotating Myers-Perry black holes under massive scalar perturbations. Using Leaver's continued fraction method, we compute the quasinormal modes of the massive scalar fields. All modes found are damped under the quasinormal boundary conditions. It is also found that long-living modes called quasiresonances exist for large scalar masses as in the four-dimensional Kerr black hole case. Our numerical results provide a direct and complement evidence for the stability of six-dimensional MP black holes under massive scalar perturbation.

Abstract: In the framework of scalar-tensor gravity, we consider non-flat interacting quintessence cosmology where a scalar field is interacting with dark matter. Such a scalar field can be a standard or a phantom one. We use the Noether Symmetry Approach to obtain general exact solutions for cosmological equations and to select scalar-field self-interaction potentials. It turns out that the found solutions can reproduce the accelerated expansion of the Universe, and are compatible with observational dataset, as the SNeIa Pantheon data, gamma ray bursts Hubble diagram, and direct measurements of the Hubble parameter.

Abstract: It is shown that in the presence of virtual wormholes, the vacuum is unstable, which leads to a series of phase transitions in the early Universe. Then the standard Kibble scenario predicts the formation of defects such as domain walls. An unusual feature of virtual wormholes is that they generate defects with negative energy density. Such defects have macroscopic dimensions and can support the necks of already real primary wormholes, which gives reason to consider relic wormholes as realistic astrophysical objects.

Abstract: The recent gravitational wave signal detected by NANOGrav, Parkers Pulsar Timing Array, European Pulsar Timing Array, and Chinese Pulsar Timing Array collaborations can be explained by scalar induced secondary gravitational waves. The waveforms of scalar induced secondary gravitational waves exhibit a near-model-independent behavior in the infrared region $k\ll k_p$, $h^2\Omega_\text{GW} = A_\text{GW}\left(k/k_{\rm ref}\right)^{n_{\mathrm{GW}}}$, where the index $n_{\mathrm{GW}}$ is $n_{\mathrm{GW}} = 2 n_1$ for $n_1<3/2$, $n_{\mathrm{GW}} = 3-3/ \ln(k_p/k)$ for $n_1=3/2$, and $n_{\mathrm{GW}} =3-2/ \ln(k_p/k)$ for $n_1>3/2$ if the primordial curvature perturtation is parameterized as a power-law with the index $n_1$. Through Bayesian analysis, we discuss the parameter space that characterizes the behavior of scalar induced gravitational waves in the infrared region. The mean values and one sigma confidence intervals of parameters are $\log_{10} A_\mathrm{GW} = -7.18^{+0.24}_{-0.26}$ and $n_1 = 0.94^{+0.17}_{-0.17}$ for $n_1<3/2$, $\log_{10} A_\mathrm{GW} = -6.96^{+0.27}_{-0.30}$ and $\log_{10} k_p/ {\rm Mpc}^{-1} = 8.24^{+1.48}_{-0.58}$ for $n_1=3/2$, and $\log_{10} A_\mathrm{GW} = -6.77^{+0.19}_{-0.22}$ and $\log_{10} k_p/ {\rm Mpc}^{-1} = 8.37^{+1.69}_{-0.68}$ for $n_1>3/2$. Comparing with the interpretation of the detected signal as stochastic background from massive black hole binaries, the results for $n_1<3/2$, $n_1=3/2$, and $n_1>3/2$ give the support of scalar induced gravitational waves with the Bayes factor $\ln \mathcal{B}= 2.8$, $\ln \mathcal{B}= 2.9$, and $\ln \mathcal{B} = 1.8$, respectively.

Abstract: In this paper, we investigate nonlinearly charged AdS black holes in four-dimensional critical gravity and study more exact black hole thermodynamics under the effect of small statistical fluctuations. We compute the correction to the thermodynamics of nonlinearly charged AdS black hole up to the leading order. We discuss the stability of black holes under the circumstances of fluctuation and find that fluctuation causes instability in the black holes. Moreover, both the isothermal and adiabatic compressibilities are also derived. Finally, we estimate the role of small fluctuations on the equation of states and study the $P-v$ diagram of nonlinearly charged AdS black hole.

Abstract: Recently, the piercing of a mini boson star by a black hole was studied, with tidal capture and the discovery of a "gravitational atom" being reported ( arXiv:2206.00021 [gr-qc] ). Building on this research, we extend the study by including a hexic solitonic potential and explore the piercing of a solitonic boson star by a black hole. Notably, the solitonic boson star can reach higher compactness, which one might expect could alter the dynamics in this context. Our findings suggest that even when the black hole's size approaches the test particle limit, the solitonic boson star is easily captured by the black hole due to an extreme tidal capture process. Regardless of the black hole initial mass and velocity, our results indicate that over 85% of the boson star material is accreted. Thus, the self-interaction does not alter the qualitative behavior of the system.

Abstract: Consistent coupling of quantum and classical degrees of freedom exists so long as there is both diffusion of the classical degrees of freedom and decoherence of the quantum system. In this paper, we derive the Newtonian limit of such classical-quantum (CQ) theories of gravity. Our results are obtained both via the gauge fixing of the recently proposed path integral theory of CQ general relativity and via the CQ master equation approach. In each case, we find the same weak field dynamics. We find that the Newtonian potential diffuses by an amount lower bounded by the decoherence rate into mass eigenstates. We also present our results as an unravelled system of stochastic differential equations for the trajectory of the hybrid classical-quantum state and provide a series of kernels for constructing figures of merit, which can be used to rule out part of the parameter space of classical-quantum theories of gravity by experimentally testing it via the decoherence-diffusion trade-off. We compare and contrast the weak field limit to previous models of classical Newtonian gravity coupled to quantum systems. Here, we find that the Newtonian potential and quantum state change in lock-step, with the flow of time being stochastic.

Abstract: The dynamics of spin in external electromagnetic, gravitational, and axion fields is analysed in the framework of the gravitoelectromagnetism approach in Einstein's general relativity theory. We consistently extend the recent studies from the flat Minkowski geometry to the curved spacetime manifolds, contributing to the discussion of the possible new role of a precessing spin as an ``axion antenna'' that can be used to detect the hypothetical axion-like dark matter. The formalism developed helps to clarify the subtle influence of the gravitational/inertial and axion fields in the ultra-sensitive high-energy spin experiments with charged particles and neutrons at accelerators and storage rings devoted to testing fundamental physical symmetries, including attempts to establish the nature of dark matter in the Universe.

Abstract: This dissertation examines the impact of quantum gravity on electromagnetism and its backreaction, using perturbative general relativity as an effective field theory. Our analysis involves quantum-correcting Maxwell's equations to obtain a gauge-independent, real, and causal effective field equation that describes quantum gravitational effects on electromagnetism. Additionally, we present a perturbative mechanism through which quantum gravity induces a dimension six coupling between a massive scalar and electromagnetism. To investigate the effects of electromagnetism on the gravitational sector, we derive an exact, dimensionally regulated, Fourier mode sum for the Lorentz gauge propagator of a massive photon on an arbitrary cosmological background supported by a scalar inflaton. This allows us to calculate the effective potential induced by photons. Finally, we use a similar Fourier mode sum for a time-dependent mass to study the effective force on the inflaton 0-mode and its impact on reheating.

Abstract: This thesis aims to explore the properties of the motion of finite size, compact test bodies around a Kerr black hole in the small mass-ratio approximation. The small body is modelled as a perturbation of Kerr geometry, neglecting its gravitational back-reaction but including deviations from a purely geodesic motion by allowing it to possess a non-trivial internal structure. Such a body can be accurately described by a worldline endowed with a collection of multipole moments. Hereafter, we shall always consider the multipole expansion truncated at quadrupole order. Moreover, only spin-induced quadrupole moment will be taken into account, thus discarding the presence of any tidal-type deformation. For astrophysically realistic objects, this approximation is consistent with expanding the equations of motion up to second order in the body's spin magnitude. The text is structured as follows. The first part is devoted to an extended review of geodesic motion in Kerr spacetime, including Hamiltonian formulation and classification of timelike geodesics, with a particular emphasis put on near-horizon geodesics of high spin black holes. The second part introduces the equations of motion for extended test bodies in generic curved spacetime, also known as Mathisson-Papapetrou-Dixon (MPD) equations. The third part discusses conserved quantities for the MPD equations in Kerr spacetime, restricting to the aforementioned quadrupole approximation. Finally, the covariant Hamiltonian formulation of test body motion in curved spacetime is presented, and an Hamiltonian reproducing the spin-induced quadrupole MPD equations is derived. It is shown that the constants of motion obtained in the previous part directly arise while solving the Hamilton-Jacobi equation at first order in the spin magnitude. Some expectations regarding the computation at quadratic order close the discussion.

Abstract: In this paper, we attempt to explore the possibility of a obtaining a viable emergent universe scenario supported by a type of fluid known as the extended Chaplygin gas, which extends a modification to the equation of state of the well known modified Chaplygin gas by considering additional higher order barotropic fluid terms. We consider quadratic modification only. Such a fluid is capable of explaining the present cosmic acceleration and is a possible dark energy candidate. We construct a theoretical model of the emergent universe assuming it is constituted from such a fluid. It interestingly turns out that the theoretical constraints we obtain on the extended Chaplygin gas parameters from our emergent universe model are well in agreement with the observational constraint on these parameters from BICEP2 data. Our model is found to replicate the late time behaviour really well and reproduces $\Lambda$-CDM like behaviour, as evident from the analysis of the statefinder parameters. Moreover, the Hubble parameter analysis shows that for theoretically constrained values of the ECG parameters, the Hubble tension can be resolved yielding higher values of the present Hubble parameter $H_0$ in all possible cases. Also, the value of $H(z)$ at a redshift $z=2.34$ fits better than $\Lambda-CDM$ with recent observations in some cases. This leads us to the realization that such a fluid is not only a probable candidate for dark energy, but also supports an emergent universe unlike modified Chaplygin gas and the initial singularity problem can be resolved in a flat universe within the standard relativistic context.

Abstract: In this paper we have explored the possibility of constructing a traversable wormhole on the Shtanov-Sahni braneworld with a timelike extra dimension. We find that the Weyl curvature singularity at the throat of the wormhole can be removed with physical matter satisfying the NEC $\rho+p \geq 0$, even in the absence of any effective $\Lambda$-term or any type of charge source on the brane. (The NEC is however violated by the effective matter description on the brane arising due to effects of higher dimensional gravity.) Besides satisfying NEC the matter constituting the wormhole also satisfies the Strong Energy Condition (SEC), $\rho+3p \geq 0$, leading to the interesting possibility that normal matter on the brane may be harnessed into a wormhole. Incidentally, these conditions also need to be satisfied to realize a non-singular bounce and cyclic cosmology on the brane\cite{Sahni4} where both past and future singularities can be averted. Thus, such a cyclic universe on the brane, constituted of normal matter can naturally contain wormholes. The wormhole shape function on the brane with a time-like extra dimension represents the tubular structure of the wormhole spreading out at large radial distances much better than in wormholes constructed in a braneworld with a spacelike extra dimension and have considerably lower mass resulting in minimization of the amount of matter required to construct a wormhole. Wormholes in the Shtanov-Sahni (SS) braneworld also have sufficiently low tidal forces, facilitating traversability. Additionally they are found to be stable and exhibit a repulsive geometry. We are left with the intriguing possibilty that both types of curvature singularity can be resolved with the SS model, which we discuss at the end of the concluding section.

Abstract: This paper examines the issue of the existence and nature of time-like geodesics in asymptotically flat spacetimes and proposes a novel generalized topological criterion for the existence of time-like geodesics. Its validity is proved using theorems such as the Jordan-Brouwer Separation Theorem, the Raychaudhuri Equation, and key elements of Differential Geometry. More specifically, the proof primarily hinges on a closed, simply-connected subset of the spacetime manifold and a continuous map, causing a non-trivial induction on the first homology groups, from the boundary of this subset to a unit circle. The mathematical analysis conclusively affirms the presence of these geodesics, intersecting transversally within the said subset of spacetime. Findings underscore these geodesics' significant implications for the structure of asymptotically flat spacetimes, including stability, and hypothetical existence of wormholes. The generalized topological criterion also has implications on the problem of obstructions for the existence of Lorentzian metrics, and Einstein's Constraint Equations. Future research should extend this topological criterion to other classes of spacetimes, including those with non-trivial topologies or non-zero cosmological constants. Also, the criterion's application to study complex dynamical systems, such as gravitational waves or rotating black holes, could offer significant insights.