The work on black holes immersed in external fields is reviewed in both test-field approximation and within exact solutions. In particular we pay attention to the effect of the expulsion of the flux of external fields across charged and rotating black holes which are approaching extremal states. Recently this effect has been shown to occur for black hole solutions in string theory. We also discuss black holes surrounded by rings and disks and rotating black holes accelerated by strings.

Studying the threshold of black hole formation via numerical evolution has led to the discovery of fascinating nonlinear phenomena. Power-law mass scaling, aspects of universality, and self-similarity have now been found for a large variety of models. However, questions remain. Here I briefly review critical phenomena, discuss some recent results, and describe a model which demonstrates similar phenomena without gravity.

This survey intends to cover recent approaches to black hole entropy which attempt to go beyond the standard semiclassical perspective. Quantum corrections to the semiclassical Bekenstein-Hawking area law for black hole entropy, obtained within the quantum geometry framework, are treated in some detail. Their ramification for the holographic entropy bound for bounded stationary spacetimes is discussed. Four dimensional supersymmetric extremal black holes in string-based N=2 supergravity are also discussed, albeit more briefly.

An outstanding problem in gravitation theory and relativistic astrophysics today is to understand the final outcome of an endless gravitational collapse. Such a continual collapse would take place when stars more massive than few times the mass of the sun collapse under their own gravity on exhausting their nuclear fuel. According to the general theory of relativity, this results either in a black hole, or a naked singularity — which can communicate with far away observers in the universe. While black holes are (almost) being detected and are increasingly used to model high energy astrophysical phenomena, naked singularities have turned into a topic of active discussion, aimed at understanding their structure and implications. Recent developments here are reviewed, indicating future directions.

Rotating neutron stars are one of the important sources of gravitational waves (GW) for the ground based as well as space based detectors. Since the waves are emitted continuously, the source is termed as a continuous gravitational wave (CGW) source. The expected weakness of the signal requires long integration times (∼year). The data analysis problem involves tracking the phase coherently over such large integration times, which makes it the most computationally intensive problem among all GW sources envisaged. In this article, the general problem of data analysis is discussed, and more so, in the context of searching for CGW sources orbiting another companion object. The problem is important because there are several pulsars, which could be deemed to be CGW sources orbiting another companion star. Differential geometric techniques for data analysis are described and used to obtain computational costs. These results are applied to known systems to assess whether such systems are detectable with current (or near future) computing resources.

This talk presents a brief overview of recent results pertaining to the cosmological constant ‘A’. I summarize the observational situation focussing on observations of high redshift Type Ia supernovae which suggest A > 0. Observations of small angular anisotropies in the cosmic microwave background complement Type Ia supernovae observations and both CMB and Sn can be combined to place strong constraints on the value of A. The presence of a small A-term increases the age of the universe and slows down the formation of large scale structure. I also review recent theoretical attempts to generate a small A-term at the current epoch and a model independent approach for determining the cosmic equation of state.

Magnetic fields are observed not only in stars, but in galaxies, clusters, and even high redshift Lyman-α systems. In principle, these fields could play an important role in structure formation and also affect the anisotropies in the cosmic microwave background radiation (CMB). The study of cosmological magnetic fields aims not only to quantify these effects on large-scale structure and the CMB, but also to answer one of the outstanding puzzles of modern cosmology: when and how do magnetic fields originate? They are either primoridial, i.e. created before the onset of structure formation, or they are generated during the process of structure formation itself.

This is a summary of the papers presented in session W1 on the papers submitted to the workshop I on the classical aspects of black holes and compact objects were classified into three categories: (i) theoretical aspects; (ii) astrophysical aspects; (iii) gravitational radiation. The three sessions were devoted each to one of the above categories. The chairmen of the workshop were J Bičák, Charles University, Prague (Czech Republic) and C V Vishveshwara, Indian Institute of Astrophysics, India.

This is a summary of the papers presented in session W2 on a fairly wide-ranging variety of topics in the area of black hole physics and quantum aspects of gravity, including quantum field and string theory in curved spacetimes. In addition, experts in a couple of topical subjects were invited to present short surveys on the subjects of their specialization. The invited speakers were: Mitra, who surveys recent research on the very topical area of AdS black holes, and Date, who presents a comparative perspective on trapping and isolated horizons. Among the contributed papers, the first, by Jassal, is an attempt to understand the dynamics of strings near a black hole horizon. This is followed by a paper by Barve et al on a calculation of the quantum stress tensor for a background that includes a naked singularity. Following this we have Singh on radial oscillations of quark stars in strong magnetic fields. The next paper by Goyal and Dahiya, discusses chiral symmetry restoration in a linear sigma model in the presence of a magnetic field. The following paper, by Horwitz, offers new perspectives on the intriguing question of primordial black holes. Finally, Madhavan discusses issues pertaining to the classical limit of kinematical quantum gravity.

The topics on which there were presentations in this workshop can broadly be divided into the following categories: Observational aspects of large-scale structures in the universities; phase transitions in the early universe; cosmic microwave background radiation; observational cosmology.

Due to its subject matter, this workshop included a number of rather disjointed contributions in a number of areas, including exact solutions, mathematical cosmology and alternative theories. We shall therefore give a brief summary of each talk in this section in alphabetical order.

It is an attempt to explore non-singular cosmological solutions with non-rotating perfect fluids with p=κρ. The investigation strongly indicates that there is no solution of the above type other than already known. It is hoped that this result may be rigorously proved in future.

We discuss ways of quantifying structuration in relativistic cosmological settings, by employing a family of covariant density constrast indicators. We study the evolution of these indicators with time in the context of inhomogeneous Szekeres models. We find that different observers (having either different spatial locations or different indicators) see different evolutions for the density contrast, which may or may not be monotonically increasing with time. We also find that monotonicity seems to be related to the initial conditions of the model, which may be of potential interest in connection with debates regarding gravitational entropy and the arrow of time.

The introduction of time dependence through a scale factor in a non-conformally flat static cosmological model whose spacetime can be embedded in a five demensional flat spacetime is shown to give rise to two spherical models of universe filled with perfect fluid acompannied with radial heat flux without any Big Bang type singularity. The first model describes an ever existing universe which witnesses a transition from state of contraction to that of ever expansion. The second model represents a universe oscillating between two regular states.