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The inner regions of the most massive compact stellar objects might be occupied by a phase of quarks. Since the observations of the massive pulsars PSR J1614-2230 and of PSR J0348+0432 with about two solar masses, the equations of state constructing relativistic stellar models have to be constrained respecting these new limits. We discuss stable hybrid stars, i.e. compact objects with an outer layer composed of nuclear matter and with a core consisting of quark matter (QM). For the outer nuclear layer we utilise a density-dependent nuclear equation of state and we use a chiral SU(3) Quark-Meson model with a vacuum energy pressure to describe the object’s core.

The appearance of a disconnected mass-radius branch emerging from the hybrid star branch implies the existence of a third family of compact stars, so called “twin” stars. Twin stars did not emerge as the transition pressure has to be relatively small with a large jump in energy density, which could not be satisfied within our approach. This is, among other reasons, due to the fact that the speed of sound in QM has to be relatively high, which can be accomplished by an increase of the repulsive coupling. This increase on the other hand yields too high transition pressures for twins stars to appear.

I would review the contributions to GR from Indian scientists of which the prominent ones are Datt’s homogeneous collapse, Raychaudhuri equation, Vaidya’s and Majumdar’s solutions, and so on.

Moving from the consideration that matter fields must be treated in terms of their fundamental quantum counterparts, we show straightforward arguments, within the framework of ordinary quantum mechanics and quantum field theory, in order to convince readers that cosmological perturbations must be addressed in term of the semiclassical limit of the expectation value of the quantum fields. We first take into account cosmological perturbations originated by a quantum scalar field, and then extend our treatment in order to account for the expectation values of bilinears of Dirac fermion fields. The latter can indeed transform as scalar quantities under diffeomorphisms, as well as all the other bilinear Dirac fermion elements of the Clifford algebra. Phenomenological consequences follow, including the possibility of generating cross-correlation spectra from fermion perturbations. We then discuss how the macroscopic state for matter we propose can be interpreted as a non-Bunch-Davies vacuum, and then generalise this construction likening it to representation theory. Phenomenological consequences of this identification are then outlined.

We study transitions of hadronic matter to three-flavour quark matter (3QM) locally both for shock-induced and diffusion-induced conversions. The former is the transition via two-flavour quark matter triggered by a rapid density rise in a shock wave and the latter is induced by diffusions of a seed 3QM. Not only the jump condition on both sides of the conversion front but the structures inside the front are also considered by taking into account what happens during the conversion processes on the time scale of weak interactions. We demonstrated that the combustion will occur in the so-called endothermic regime which has been ignored in the discussion so far. We also find that the deflagration front is unstable in the exothermic regime but stable in the endothermic regime, which is quite contrary to the ordinary combustion. It is also confirmed that strong detonation and weak deflagration are always obtained for shock-induced and diffusion-induced combustion, respectively, regardless of whether in exothermic or endothermic regime.

Extended theories of gravity represent a straightforward generalisation of Einstein theories aimed to cure its shortcomings at ultra-violet and infra-red scales. Here we review some theoretical aspects of metric and metric affine extended theories of gravity in view of astrophysical application. In particular, after a general exposition, we discuss some exact black hole solutions, gravitational waves and stellar structures.

In the characteristic formalism, coordinates are based on null cones generated by radial null geodesics. The Einstein equations take hierarchical form, and so can easily be written as a system suitable for numerical evolution. In numerical relativity, the major interest in the characteristic formalism is for gravitational wave estimation by Cauchy characteristic extraction, but it is also useful in cosmology.

The characteristic formalism is applicable to cosmology, since nearly all data is a result of observations on our past null cone. It is in principle possible to measure the initial data required in order to calculate an evolution into the interior of the past null cone, and codes have been implemented to perform the evolution. In the case of spherical symmetry, it is now possible to apply this process using real data.

We study the the spatial development of the kink instability along helically magnetized rotating, relativistic jets using special relativistic MHD code “RAISHIN”. Using non-periodic computational box, the spatial growth of the kink instability is triggered by a precessional perturbation at the inlet. Currently we are studying light as well as heavy jets depending on density profile besides different set of angular velocity amplitude parameters are also provided. The jets do appear to be collimated by magnetic field lines and the magnetic acceleration is also seen due to conversion of electromagnetic energy into kinetic energy of the jet. We also briefly discuss the role of magnetic reconnection at the location of kink instability along the jet.

Analytical solutions of the Einstein field equations heavily rely on symmetries imposed on the underlying spacetime. Due to the complexity of these non-linear coupled partial differential equations, finding more general solutions is a difficult task. In cosmology the most considerations are based on the well known FLRW metric or on perturbations of the latter, although the observed universe departs greatly from the underlying assumptions on smaller scales.

To address this issues, the framework of Regge calculus and its possible use for cosmology is examined. In this formalism the spacetime is approximated by finite sized simplices, building a simplicial complex and upon it a numerical time evolution scheme can be constructed. An introduction to the concepts in this field is presented together with an original method to account for the dynamical effects of the cosmological constant $\Lambda$. A new numerical library is briefly described. Finally, as an application, it is shown that the time evolution of the Kasner and $\Lambda$-vacuum spacetime can be reproduced.

In this talk, I will present results of our recent 3D GRHD simulations of thick accretion disks around tilted Kerr black holes.  We investigate the effects of the tilt angle between the disk angular momentum vector and black hole spin on the dynamics of these systems, being particularly interested in a possible imprint of the tilt angle in the gravitational wave pattern as the torus evolves in the tilted spacetime. We find that Papalouizou-Pringle unstable models still develop the PPI when the central BH is tilted. For the models where the PPI saturates abruptly, the central BH is given a mild kick. We simulate the systems using the Einstein Toolkit, using the thorn McLachlan for the evolution of the spacetime via the BSSN formalism and the thorn GRHydro for the evolution of the hydrodynamics, using a 3D Cartesian mesh with adaptive mesh refinement (AMR).