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Rabin Banerjee

Publications and source records attributed to Rabin Banerjee.

At least 73 records · Page 4Linked to original sources
arXiv2012

Trivial symmetries in a 3D topological torsion model of gravity

We study the gauge symmetries in a Mielke-Baekler type model of gravity in 2+1 dimensions. The model is built in a Poincare gauge theory framework where localisation of Poincare symmetries lead to gravity. However, explicit construction of gauge symmetries in the model through a Hamiltonian procedure yields an apparently different set of symmetries, as has been noted by various authors. Here, we show that the two sets of symmetries are actually equivalent in a canonical sense, their difference being just a set of trivial symmetries.

gr-qc↗
arXiv2012

A unified picture of phase transition: from liquid-vapour systems to AdS black holes

Based on fundamental concepts of thermodynamics we examine phase transitions in black holes defined in Anti-de Sitter (AdS) spaces. The method is in line with that used a long ago to understand the liquid-vapour phase transition where the first order derivatives of Gibbs potential are discontinuous and Clausius-Clapeyron equation is satisfied. The idea here is to consider the AdS black holes as grand-canonical ensembles and study phase transition defined by the discontinuity of second order derivatives of Gibbs potential. We analytically check that this phase transition between the `smaller' and `larger' mass black holes obey Ehrenfest relations defined at the critical point and hence confirm a second order phase transition. This include both the rotating and charged black holes in Einstein gravity.

gr-qc↗
arXiv2012

Dual composition of odd-dimensional models

A general way of interpreting odd dimensional models as a doublet of chiral models is discussed. Based on the equations of motion this dual composition is illustrated. Examples from quantum mechanics, field theory and gravity are considered. Specially the recently advocated topologically massive gravity is analysed in some details.

hep-th↗
arXiv2012

Critical behavior of Born Infeld AdS black holes in higher dimensions

Based on a canonical framework, we investigate the critical behavior of Born-Infeld AdS black holes in higher dimensions. As a special case, considering the appropriate limit, we also analyze the critical phenomena for Reissner Nordstrom AdS black holes. The critical points are marked by the divergences in the heat capacity at constant charge. The static critical exponents associated with various thermodynamic entities are computed and shown to satisfy the thermodynamic scaling laws. These scaling laws have also been found to be compatible with the static scaling hypothesis. Furthermore, we show that the values of these exponents are universal and do not depend on the spatial dimensionality of the AdS space. We also provide a suggestive way to calculate the critical exponents associated with the spatial correlation which satisfy the scaling laws of second kind.

gr-qc↗
arXiv2012

Critical phenomena in Born-Infeld AdS black holes

We investigate the thermodynamics of critical phenomena in Born-Infeld AdS black holes using a canonical ensemble. The critical behavior has been studied near the critical point which is characterized by a discontinuity in the heat capacity at constant charge. We explicitly calculate the critical exponents of the relevant thermodynamic quantities. These exponents satisfy all the thermodynamic scaling laws. We also check the Generalized Homogeneous Function (GHF) hypothesis (or the scaling hypothesis) which is shown to be compatible with the thermodynamic scaling laws. Finally we check the validity of the scaling laws of second kind which include the critical exponents associated with the spatial correlation. In the appropriate limit our results also provide the corresponding expressions for the Reissner Nordstrom AdS case.

gr-qc↗
arXiv2011

Poincaré gauge symmetries, hamiltonian symmetries and trivial gauge transformations

We resolve a problem of finding the Poincare symmetries from hamiltonian gauge symmetries constructed through a canonical procedure of handling constrained systems. Through the use of Noether identities corresponding to the symmetries, we motivate a procedure of finding the map between the hamiltonian and Poincare gauge parameters. Using this map, we show that the Poincare and hamiltonian gauge symmetries are equivalent, modulo trivial gauge transformations.

gr-qc↗
arXiv2011

Thermodynamics of phase transition in higher dimensional AdS black holes

We investigate the thermodynamics of phase transition for $ (n+1) $ dimensional Reissner Nordstrom (RN)-AdS black holes using a grand canonical ensemble. This phase transition is characterized by a discontinuity in specific heat. The phase transition occurs from a lower mass black hole with negative specific heat to a higher mass black hole with positive specific heat. By exploring Ehrenfest's scheme we show that this is a second order phase transition. Explicit expressions for the critical temperature and critical mass are derived. In appropriate limits the results for $ (n+1) $ dimensional Schwarzschild AdS black holes are obtained.

gr-qc↗
arXiv2011

Hamiltonian analysis of symmetries in a massive theory of gravity

We construct the generator of hamiltonian gauge symmetries in a 2+1 dimensional massive theory of gravity, proposed recently, through a systematic off-shell algorithm. Using a field dependant map among gauge parameters we show that the symmetries obtained from this generator are on-shell equivalent to the Poincaré gauge symmetries. We also clarify certain subtle issues concerning the implementation of this map.

gr-qc↗
arXiv2011

Second Order Phase Transition and Thermodynamic Geometry in Kerr-AdS Black Hole

We discuss a scheme based on Ehrenfest like equations to exhibit and classify transitions between two phases (with "smaller" and "larger" masses) of Kerr AdS black holes. We show that for fixed angular velocity this phase transition is of second order as both Ehrenfest's equations are satisfied. Finally we make a close connection of the results found from this analysis with those obtained from the thermodynamic state space geometry approach.

hep-th↗
arXiv2011

Gauge symmetry and W-algebra in higher derivative systems

The problem of gauge symmetry in higher derivative Lagrangian systems is discussed from a Hamiltonian point of view. The number of independent gauge parameters is shown to be in general {\it{less}} than the number of independent primary first class constraints, thereby distinguishing it from conventional first order systems. Different models have been considered as illustrative examples. In particular we show a direct connection between the gauge symmetry and the W-algebra for the rigid relativistic particle.

hep-th↗
arXiv2011

Symmetries of Snyder--de Sitter space and relativistic particle dynamics

We study the deformed conformal-Poincare symmetries consistent with the Snyder--de Sitter space. A relativistic particle model invariant under these deformed symmetries is given. This model is used to provide a gauge independent derivation of the Snyder--de Sitter algebra. Our results are valid in the leading order in the parameters appearing in the model.

hep-th↗
arXiv2011

New approach to phase transitions in black holes

We develop an analogy between fluids and black holes to study phase transitions in the latter. The entropy-temperature graph shows the onset of a phase transition without any latent heat. The nature of this continuous (higher order) phase transition is examined in details. We find that the second order derivatives of the free energy diverge at the critical temperature. Also, the transition is smeared instead of sharp, so that the usual Ehrenfest's scheme breaks down. A generalised version of this scheme is formulated which is shown to be consistent with the phase transition curves.

gr-qc↗
arXiv2010

New type of phase transition in Reissner Nordström - AdS black hole and its thermodynamic geometry

The phase transition of a RN-AdS black hole is studied in details using Ehrenfest's equations. There is no discontinuity in entropy which signals a lack of any first order phase transition. We then show that although Ehrenfest's first equation is satisfied, the second is not, so that a true second order phase transition is also ruled out. However this deviation from the second Ehrenfest's equation, for a certain range of the black hole charge, indicates the existence of a new glassy type transition. We finally study the thermodynamic behaviour using state space geometry and find that the scalar curvature diverges exactly at those points where the heat capacity diverges.

gr-qc↗
arXiv2010

Killing Symmetries and Smarr Formula for Black Holes in Arbitrary Dimensions

We calculate the effective Komar conserved quantities for the $N+1$ dimensional charged Myers-Perry spacetime. At the event horizon we derive a new identity $K_{χ^μ}=2ST$ where the left hand side is the Komar conserved quantity corresponding to the null Killing vector $χ^μ$ while in the right hand side $S,~T$ are the black hole entropy and Hawking temperature. From this identity we also derive the generalized Smarr formula connecting the macroscopic parameters $M,~J,~Q$ of the black hole with its surface gravity and horizon area. The consistency of this new formula is established by an independent algebraic approach.

gr-qc↗
arXiv2010

A Note on the Lower Bound of Black Hole Area Change in Tunneling Formalism

In the framework of tunneling mechanism and employing Bekenstein's general expression for the variation of the black hole area, we determine the area quantum up to a constant. Depending on the value of this constant one can get either Bekenstein's lower bound or Hod's one for the change in the black hole area.

hep-th↗
arXiv2010

Glassy Phase Transition and Stability in Black Holes

Black hole thermodynamics, confined to the semi-classical regime, cannot address the thermodynamic stability of a black hole in flat space. Here we show that inclusion of correction beyond the semi-classical approximation makes a black hole thermodynamically stable. This stability is reached through a phase transition. By using Ehrenfest's scheme we further prove that this is a glassy phase transition with a Prigogine-Defay ratio close to 3. This value is well placed within the desired bound (2 to 5) for a glassy phase transition. Thus our analysis indicates a very close connection between the phase transition phenomena of a black hole and glass forming systems. Finally, we discuss the robustness of our results by considering different normalisations for the correction term.

hep-th↗
arXiv2010

Quantum gravitational correction to the Hawking temperature from the Lemaitre-Tolman-Bondi model

We solve the quantum constraint equations of the Lemaitre-Tolman-Bondi model in a semiclassical approximation in which an expansion is performed with respect to the Planck length. We recover in this way the standard expression for the Hawking temperature as well as its first quantum gravitational correction. We then interpret this correction in terms of the one-loop trace anomaly of the energy-momentum tensor and thereby make contact with earlier work on quantum black holes.

gr-qc↗