Ayan Chatterjee

Laws of black hole mechanics from the Holst action

The formulation of weak isolated horizons (WIH) based on the standard isolated horizon formulation of black hole horizons has been reconsidered in the context of the Holst action. Both the zeroth and the first laws of WIH mechanics have been derived. While the zeroth law follows directly from the WIH boundary conditions, first law depends on the action chosen. We construct the covariant phase space of the Holst action for a space-time having WIH as the inner boundary. This requires the introduction of new potential functions so that the symplectic structure is foliation independent. We show that a precise cancellation among various terms leads to the usual first law. Subsequently, we show from the same covariant phase space that for spherically symmetric horizons, the effective theory on the inner boundary is a U(1) Chern-Simons theory.

Hawking radiation from dynamical horizons

In completely local settings, we establish that a dynamically evolving black hole horizon can be assigned a Hawking temperature. Moreover, we calculate the Hawking flux and show that the radius of the horizon shrinks.

Kalb-Ramond field interactions in a braneworld scenario

Electromagnetic and (linearized) gravitational interactions of the Kalb-Ramond (KR) field, derived from an underlying ten-dimensional heterotic string in the zero slope limit, are studied in a five-dimensional background Randall-Sundrum I spacetime with standard model fields confined to the visible brane having negative tension. The warp factor responsible for generating the gauge hierarchy in the Higgs sector is seen to appear inverted in the KR field couplings, when reduced to four dimensions. This leads to dramatically enhanced rotation, far beyond observational bounds, of the polarization plane of electromagnetic and gravitational waves, when scattered by a homogeneous KR background. Possible reasons for the conflict between theory and observation are discussed.

Generic weak isolated horizons

Weak isolated horizon boundary conditions have been relaxed supposedly to their weakest form so that both zeroth and first laws of black hole mechanics hold. This makes the formulation more amenable for applications in both analytic and numerical relativities. It also unifies the phase spaces of non-extremal and extremal black holes.

Gauge invariant coupling of fields to torsion: A string inspired model

In a consistent heterotic string theory, the Kalb-Ramond field, which is the source of space-time torsion, is augmented by Yang-Mills and gravitational Chern-Simons terms. When compactified to 4 dimensions and in the field theory limit, such additional terms give rise to interactions with interesting astrophysical predictions like rotation of plane of polarization for electromagnetic and gravitational waves. On the other hand, if one is also interested in coupling 2- or 3-form (Abelian or non-Abelian) gauge fields to torsion, one needs another class of interaction. In this paper, we shall study this interaction and offer some astrophysical and cosmological predictions. We explicitly calculate the Coleman-Weinberg potential for this theory. We also comment on the possibility of such terms in loop quantum gravity where, if the Barbero-Immirzi parameter is promoted to a field, acts as a source for torsion.

Horizon mechanics and asymptotic symmetries with an Immirzi-like parameter in 2 + 1 dimensions

Starting with a generalized theory of 2  + 1 gravity containing an Immirzi-like parameter, we derive the modified laws of black hole mechanics using the formalism of weak isolated horizons. Definitions of the horizon mass and angular momentum emerge naturally in this framework. We further go on to analyse the asymptotic symmetries, as first discussed by Brown and Henneaux, and analyse their implications in a completely covariant phase space framework.

Quasilocal rotating conformal Killing horizons

The formulation of quasi-local conformal Killling horizons(CKH) is extended to include rotation. This necessitates that the horizon be foliated by 2-spheres which may be distorted. Matter degrees of freedom which fall through the horizon is taken to be a real scalar field. We show that these rotating CKHs also admit a first law in differential form.

Quasilocal conformal Killing horizons: Classical phase space and the first law

In realistic situations, black hole spacetimes do not admit a global timelike Killing vector field. However, it is possible to describe the horizon in a quasilocal setting by introducing the notion of a quasilocal boundary with certain properties which mimic the properties of a black hole horizon. Isolated horzons and Killing horizons are examples of such kind. In this paper, we construct a boundary of spacetime which is null and admits a conformal Killing vector field. Furthermore we construct the space of solutions (in general theory of relativity) which admits such quasilocal conformal Killing boundaries. We also establish a form of first law for these quasilocal horizons.

Non-minimally coupled scalar fields, Holst action and black hole mechanics

Abstract The paper deals with the extension of the Weak Isolated Horizon (WIH) formulation of black hole horizons to the non-minimally coupled scalar fields. In the early part of the paper, we introduce an appropriate Holst type action to incorporate scalar fields non-minimally coupled to gravity and construct the covariant phase space of the theory. Using this phase space, we proceed to prove the laws of black hole mechanics. Further, we show that with a gauge fixing, the symplectic structure on the horizon reduces to that of a U(1) Chern–Simons theory. The level of the Chern–Simons theory is shown to depend on the non-minimally coupled scalar field.

Weak Isolated Horizons

Weak Isolated Horizon (WIH) is the most general definition of a black hole horizon so far i.e. WIH is defined through the weakest possible set of boundary conditions imposed on a generic null surface. We will also show that the laws of black hole mechanics can be derived for these horizons. In addition, the definition enables us to put the extremal and non‐extremal black holes on the same phase‐space so that one can make sense of extremal limit.