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Sandipan Sengupta

Publications and source records attributed to Sandipan Sengupta.

33 records · Page 2Linked to original sources
arXiv2017

A degenerate extension of the Schwarzschild exterior

We present vacuum spacetime solutions of first order gravity, which are described by the exterior Schwarzschild geometry in one region and by degenerate tetrads in the other. The invertible and noninvertible phases of the tetrad meet at an intermediate boundary across which the components of the metric, affine connection and field-strength are all continuous. Within the degenerate spacetime region, the noninvertibility of the tetrad leads to nonvanishing torsion. In contrast to the Schwarzschild spacetime which is the unique spherically symmetric solution of Einsteinian gravity, all the field-strength components associated with these vacuum geometries remain finite everywhere.

gr-qc↗
arXiv2016

New solutions in pure gravity with degenerate tetrads

In first order formulation of pure gravity, we find a new class of solutions to the equations of motion represented by degenerate four-geometries. These configurations are described by non- invertible tetrads with two zero eigenvalues and admit non-vanishing torsion. The homogeneous ones among these infinitely many degenerate solutions admit a geometric classification provided by the three fundamental geometries that a closed two-surface can accomodate, namely, E^2 , S^2 and H^2.

gr-qc↗
arXiv2016

Degenerate spacetimes in first order gravity

We present a systematic framework to obtain the most general solutions of the equations of motion in first order gravity theory with degenerate tetrads. There are many possible solutions. Generically, these exhibit non-vanishing torsion even in the absence of any matter coupling. These solutions are shown to contain a special set of eight configurations which are associated with the homogeneous model three-geometries of Thurston.

gr-qc↗
arXiv2015

Dark Energy From The Gravity Vacuum

We propose a new solution to the cosmological constant problem building on a nonperturbative quantum theory of gravity with torsional instantons. These pseudoparticles, which were recently found to exist in a first order formulation of Giddings-Strominger axionic gravity, carry nontrivial Nieh-Yan topological charge. The nonperturbative ground state as generated due to tunneling effects is shown to be stable under quantum fluctuations. Within this framework, the associated vacuum angle, namely the Barbero-Immirzi topological parameter, gets fixed to a numerical value determined by the Hubble constant.

gr-qc↗
arXiv2015

Torsional instanton effects in quantum gravity

We show that, in the first order gravity theory coupled to axions, the instanton number of the Giddings-Strominger wormhole can be interpreted as the Nieh-Yan topological index. The axion charge of the baby universes is quantized in terms of the Nieh-Yan integers. Tunneling between universes of different Nieh-Yan charges implies a nonperturbative vacuum state. The associated topological vacuum angle can be identified with the Barbero-Immirzi parameter.

gr-qc↗
arXiv2014

Asymptotic Flatness and Quantum Geometry

We construct a canonical quantization of the two dimensional theory of a parametrized scalar field on noncompact spatial slices. The kinematics is built upon generalized charge-network states which are labelled by smooth embedding spacetimes, unlike the standard basis states carrying only discrete labels. The resulting quantum geometry corresponds to a nondegenerate vacuum metric, which allows a consistent realization of the asymptotic conditions on the canonical fields. Although the quantum counterpart of the classical symmetry group of conformal isometries consists only of continuous global translations, Lorentz invariance can still be recovered in an effective sense. The quantum spacetime as characterized by a gauge invariant state is shown to be made up of discrete strips at the interior, and smooth at asymptotia. The analysis here is expected to be particularly relevant for a canonical quantization of asymptotically flat gravity based on generalized spin-network states labelled by smooth geometries.

gr-qc↗
arXiv2013

Quantum geometry with a nondegenerate vacuum: a toy model

Motivated by a recent proposal (by Koslowski-Sahlmann) of a kinematical representation in Loop Quantum Gravity (LQG) with a nondegenerate vacuum metric, we construct a polymer quantization of the parametrised massless scalar field theory on a Minkowskian cylinder. The dif- feomorphism covariant kinematics is based on states which carry a continuous label corresponding to smooth embedding geometries, in addition to the discrete embedding and matter labels. The physical state space, obtained through group averaging procedure, is nonseparable. A physical state in this theory can be interpreted as a quantum spacetime, which is composed of discrete strips and supercedes the classical continuum. We find that the conformal group is broken in the quantum theory, and consists of all Poincare translations. These features are remarkably different compared to the case without a smooth embedding. Finally, we analyse the length operator whose spectrum is shown to be a sum of contributions from the continuous and discrete embedding geometries, being in perfect analogy with the spectra of geometrical operators in LQG with a nondegenerate vacuum geometry.

gr-qc↗
arXiv2013

Gravity Asymptotics with Topological Parameters

In four dimensional gravity theory, the Barbero-Immirzi parameter has a topological origin, and can be identified as the coefficient multiplying the Nieh-Yan topological density in the gravity Lagrangian, as proposed by Date et al.[1]. Based on this fact, a first order action formulation for spacetimes with boundaries is introduced. The bulk Lagrangian, containing the Nieh-Yan density, needs to be supplemented with suitable boundary terms so that it leads to a well-defined variational principle. Within this general framework, we analyse spacetimes with and without a cosmological constant. For locally Anti de Sitter (or de Sitter) asymptotia, the action principle has non-trivial implications. It admits an extremum for all such solutions provided the SO(3,1) Pontryagin and Euler topological densities are added to it with fixed coefficients. The resulting Lagrangian, while containing all three topological densities, has only one independent topological coupling constant, namely, the Barbero-Immirzi parameter. In the final analysis, it emerges as a coefficient of the SO(3,2) (or SO(4,1)) Pontryagin density, and is present in the action only for manifolds for which the corresponding topological index is non-zero.

gr-qc↗
arXiv2011

SU(2) gauge theory of gravity with topological invariants

The most general gravity Lagrangian in four dimensions contains three topological densities, namely Nieh-Yan, Pontryagin and Euler, in addition to the Hilbert-Palatini term. We set up a Hamiltonian formulation based on this Lagrangian. The resulting canonical theory depends on three parameters which are coefficients of these terms and is shown to admit a real SU(2) gauge theoretic interpretation with a set of seven first-class constraints. Thus, in addition to the Newton's constant, the theory of gravity contains three (topological) coupling constants, which might have non-trivial imports in the quantum theory.

gr-qc↗
arXiv2011

Topological parameters in gravity

We present the Hamiltonian analysis of the theory of gravity based on a Lagrangian density containing Hilbert-Palatini term along with three topological densities, Nieh-Yan, Pontryagin and Euler. The addition of these topological terms modifies the symplectic structure non-trivially. The resulting canonical theory develops a dependence on three parameters which are coefficients of these terms. In the time gauge, we obtain a real SU (2) gauge theoretic description with a set of seven first class constraints corresponding to three SU (2) rotations, three spatial diffeomorphism and one to evolution in a timelike direction. Inverse of the coefficient of Nieh-Yan term, identified as Barbero-Immirzi parameter, acts as the coupling constant of the gauge theory.

gr-qc↗
arXiv2010

Quantum realizations of Hilbert-Palatini second-class constraints

In a classical theory of gravity, the Barbero-Immirzi parameter ($η$) appears as a topological coupling constant through the Lagrangian density containing the Hilbert-Palatini term and the Nieh-Yan invariant. In a quantum framework, the topological interpretation of $η$ can be captured through a rescaling of the wavefunctional representing the Hilbert-Palatini theory, as in the case of the QCD vacuum angle. However, such a rescaling cannot be realized for pure gravity within the standard (Dirac) quantization procedure where the second-class constraints of Hilbert-Palatini theory are eliminated beforehand. Here we present a different treatment of the Hilbert-Palatini second-class constraints in order to set up a general rescaling procedure (a) for gravity with or without matter and (b) for any choice of gauge (e.g. time gauge). The analysis is developed using the Gupta-Bleuler and the coherent state quantization methods.

gr-qc↗
arXiv2009

Canonical supergravity with Barbero-Immirzi parameter

A canonical formulation of the N=1 supergravity theory containing the topological Nieh-Yan term in its Lagrangian density is developed. The constraints are analysed without choosing any gauge. In the time gauge, the theory is shown to be described in terms of real SU(2) variables.

hep-th↗
arXiv2009

Effective Actions from Loop Quantum Cosmology: Correspondence with Higher Curvature Gravity

Quantum corrections of certain types and relevant in certain regimes can be summarised in terms of an effective action calculable, in principle, from the underlying theory. The demands of symmetries, local form of terms and dimensional considerations limit the form of the effective action to a great extent leaving only the numerical coefficients to distinguish different underlying theories. The effective action can be restricted to particular symmetry sectors to obtain the corresponding, {\em reduced effective action}. Alternatively, one can also quantize a classically (symmetry) reduced theory and obtain the corresponding effective action. These two effective actions can be compared. As an example, we compare the effective action(s) known in isotropic loop quantum cosmology with the Lovelock actions, as well as with more general actions, specialized to homogeneous isotropic space-times and find that the $\barμ$-scheme is singled out.

gr-qc↗
arXiv2008

Topological Interpretation of Barbero-Immirzi Parameter

We set up a canonical Hamiltonian formulation for a theory of gravity based on a Lagrangian density made up of the Hilbert-Palatini term and, instead of the Holst term, the Nieh-Yan topological density. The resulting set of constraints in the time gauge are shown to lead to a theory in terms of a real SU(2) connection which is exactly the same as that of Barbero and Immirzi with the coefficient of the Nieh-Yan term identified as the inverse of Barbero-Immirzi parameter. This provides a topological interpretation for this parameter. Matter coupling can then be introduced in the usual manner, {\em without} changing the universal topological Nieh-Yan term.

gr-qc↗