Saurav Samanta

Topics in Noncommutative Geometry Inspired Physics

In this review article we discuss some of the applications of noncommutative geometry in physics that are of recent interest, such as noncommutative many-body systems, noncommutative extension of Special Theory of Relativity kinematics, twisted gauge theories and noncommutative gravity.

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 a 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 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.

Hawking Radiation due to Photon and Gravitino Tunneling

Abstract Applying the Hamilton–Jacobi method we investigate the tunneling of photon across the event horizon of a static spherically symmetric black hole. The necessity of the gauge condition on the photon field, to derive the semiclassical Hawking temperature, is explicitly shown. Also, the tunneling of photon and gravitino beyond this semiclassical approximation are presented separately. Quantum corrections of the action for both cases are found to be proportional to the semiclassical contribution. Modifications to the Hawking temperature and Bekenstein–Hawking area law are thereby obtained. Using this corrected temperature and Hawking’s periodicity argument, the modified metric for the Schwarzschild black hole is given. This corrected version of the metric, up to ℏ order is equivalent to the metric obtained by including one loop back reaction effect. Finally, the coefficient of the leading order correction of entropy is shown to be related to the trace anomaly.

P-V criticality of AdS black holes in a general framework

In black hole thermodynamics, it has been observed that AdS black holes behave as van der Waals system if one interprets the cosmological constant as a pressure term. Also the critical exponents for the phase transition of AdS black holes and the van der Waals systems are same. Till now this type of analysis is done by two steps. In the first step one shows that a particular metric allows phase transition and in the second step, using this information, one calculates the exponents. Here, we present a different approach based on two universal inputs (the general forms of the Smarr formula and the first law of thermodynamics) and one assumption regarding the existence of van der Waals like critical point for a metric. We find that the same values of the critical exponents can be obtained by this approach. Thus we demonstrate that, though the existence of van der Waals like phase transition depends on specific metrics, the values of critical exponents are then fixed for that set of metrics.

Killing symmetries and Smarr formula for black holes in arbitrary dimensions

We calculate the effective Komar conserved quantities for the

Thermogeometric phase transition in a unified framework

N+1

Effective Values of Komar Conserved Quantities and Their Applications

dimensional charged Myers-Perry spacetime. At the event horizon we derive a new identity

Entropy corresponding to the interior of a Schwarzschild black hole

{K}_{{\ensuremath{\chi}}^{\ensuremath{\mu}}}=2ST

Gravitational surface Hamiltonian and entropy quantization

where the left hand side is the Komar conserved quantity corresponding to the null Killing vector

STUDY ON THE NONCOMMUTATIVE REPRESENTATIONS OF GALILEAN GENERATORS

{\ensuremath{\chi}}^{\ensuremath{\mu}}