General Relativity and Quantum Cosmology (gr-qc)

Abstract: We construct a generic asymptotic solution for modified gravity near a sudden singularity. This solution contains a fluid source with no equation of state and is function-counting stable, that is it has eleven independent arbitrary functions of the spatial coordinates as dictated by the Cauchy problem of the theory. We further show that near the sudden singularity the solution has a shock wave character with the same number of free functions in the Jordan and Einstein frame.

Abstract: Starting from the most general action in Einstein-Dilaton-Nonlinear Electrodynamics (NED) theory, we obtain the field equations. We apply the field equations for the specific NED known as the square root model coupled nonminimally to the dilaton scalar field whose self-interacting is in the Liouville type plus a cosmological constant and solve the field equations. In static spherically symmetric spacetime and a magnetic monopole sitting at the origin, the field equations are exactly solvable provided the integration constants of the solutions and the theory constants appearing in the action are linked through two constraints. As it is known, such an exact solution in the absence of dilaton i.e., gravity coupled to square root NED dosen't exist. Therefore, the presence of the dilaton gives additional freedom to solve the field equations. The obtained spacetime is singular and non-asymptotically flat and depending on the free parameters it may be a black hole or a cosmological object. For the black hole spacetime, we study the thermal stability of the spacetime and show that the black hole is thermally stable provided its size is larger than a critical value.

Abstract: Some form of approximately exponential inflation is generally assumed to be the origin of our present universe. The inflation is thought to be driven by a scalar field potential where the field first slowly slides along the potential and then comes to a steep slope where the field rapidly falls and then oscillates around zero transforming into particles. The slowly sliding scalar field inflation leads to an exponentially expanding de Sitter space. A scalar field as well as the deSitter space are both Lorentz invariant. Thus no global frame of rest can be established in this scenario, while particle creation requires a preferred frame of rest. Observations of the cosmic microwave background show, when the redshift is corrected for our local velocity, a very even temperature and redshift distribution requiring a global preferred frame of rest. We suggest here that a density dependent equilibrium relation between matter/radiation and a scalar energy density could maintain a preferred frame of rest throughout the bounce and inflation and thereby solve the problem.

Abstract: In this paper we focus on the effect of mass transfer between compact binary stars like neutron star-neutron star (NS-NS) system and neutron star-white dwarf (NS-WD) system. We adopt mass quadrupole formula with post-Newtonian approximation to calculate the gravitational wave (GW) radiation and orbit evolution. Two kinds of mass transfer process are considered here. One is the tidal disruption model where the less dense star orbits into the Roche limit and its mass flows toward to the other star as a beam of incompressible fluid, and the other is common envelope model where we divide the transferring mass into the mass-inflow of envelope and the the envelope itself winding in the Roche lobe of the binary stars. Viewing the envelope as a background, the GW by its spin can be calculated as a pulsar. Assuming a mass-inflow parameter, we eventually obtain the radiation power and corrected gravitational wave form (GWF) templates for different initial mass ratios, which are mainly captured by the inspiral duration and strain and of the GWs.

Abstract: The study of charged particle dynamics in the combined gravitational and magnetic field can provide important theoretical insight into astrophysical processes around black holes. In this paper, we explore the charged particle dynamics in parabolic magnetic field configuration around Schwarzschild black hole, since the paraboloidal shapes of magnetic field lines around black holes are well motivated by the numerical simulations and supported by observations of relativistic jets. Analysing the stability of bounded orbits and using the effective potential approach, we show the possibility of existence of stable circular off-equatorial orbits around the symmetry axis. We also show the influence of radiation reaction force on the dynamics of charged particles, in particular on the chaoticity of the motion and Poincar\'{e} sections, oscillatory frequencies, and emitted electromagnetic spectrum. Applied to Keplerian accretion disks, we show that in parabolic magnetic field configuration, the thin accretion configurations can be either destroyed or transformed into a thick toroidal structure given the radiation reaction and electromagnetic-disk interactions included. Calculating the Fourier spectra for radiating charged particle trajectories, we find that the radiation reaction force does not affect the main frequency peaks, however, it lowers the higher harmonics making the spectrum more flat and diluted in high frequency range.

Abstract: The precise knowledge of the gravitational phase of compact binaries is crucial to the data analysis for gravitational waves. Until recently, it was known analytically (for non-spinning systems) up to the 3.5 post-Newtonian (PN) order, i.e. up to the $(v/c)^7$ correction beyond the leading order. If this precision is sufficient for the data analysis of the current generation of detectors, the next ones (notably LISA and ET) may require higher accuracy. Using a post-Newtonian-multipolar-post-Minkowskian matching algorithm, we have pushed the accuracy to the next level, namely the 4PN order. This derivation involved challenging technical issues, due to the appearance of non-physical divergences, that have to be properly regularized, as well as non-linear interaction terms.