The recent discovery of the accelerated cosmic expansion suggests that our Universe may be endowed with a positive cosmological constant Λ. In addition, even though general relativity (GR) is a very successful and well-tested theory, it could be that it is not the final theory of gravity. Brans-Dicke theory is one of the first and simplest modifications of Einstein’s theory. During this talk, I will present the study of cosmic structures in Brans-Dicke-like theories in the presence of a positive cosmological constant. I will discuss the validity of the no-hair theorem in the context of such theories. Moreover, I will show that, the black hole solutions in these theories are no different from those in GR and also that the presence of a stationary cosmological event horizon rules out any regular spherical stationary solution, appropriate for the description of a star.

# Category: Uncategorized

## Stable hybrid stars within a SU(3) Quark-Meson-Model

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.

## Indian contributions to GR: a centenary review

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.

## On the semi-classicality of cosmological perturbations and the non-Bunch-Davies vacua

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.

## Hydrodynamical study on the conversion of hadronic matter to quark matter

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.

## General Relativity and Beyond

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.

## Observations on past null cones, numerical relativity, and cosmology

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.

## Spatial growth of the current-driven instability in rotating, relativistic jets and the role of magnetic reconnection

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.

## Cosmology on Simplicial Complexes

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.