Parthasarathi Majumdar

Logarithmic correction to the Bekenstein-Hawking entropy

The exact formula derived by us earlier for the entropy of a four dimensional nonrotating black hole within the quantum geometry formulation of the event horizon in terms of boundary states of a three dimensional Chern-Simons theory is reexamined for large horizon areas. In addition to the semiclassical Bekenstein-Hawking contribution proportional to the area obtained earlier, we find a contribution proportional to the logarithm of the area together with subleading corrections that constitute a series in inverse powers of the area.

General logarithmic corrections to black hole entropy

We compute leading-order corrections to the entropy of any thermodynamic system due to small statistical fluctuations around equilibrium. When applied to black holes, these corrections are shown to be of the form −k ln(Area). For BTZ black holes, k = 3/2, as found earlier. We extend the result to anti-de Sitter Schwarzschild and Reissner–Nordstrom black holes in arbitrary dimensions. Finally we examine the role of conformal field theory in black-hole entropy and its corrections.

Universal Canonical Black Hole Entropy

Nonrotating black holes in three and four dimensions are shown to possess a canonical entropy obeying the Bekenstein-Hawking area law together with a leading correction (for large horizon areas) given by the logarithm of the area with a universal finite negative coefficient, provided one assumes that the quantum black hole mass spectrum has a power-law relation with the quantum area spectrum found in nonperturbative canonical quantum general relativity. The thermal instability associated with asymptotically flat black holes appears in the appropriate domain for the index characterizing this power-law relation, where the canonical entropy (free energy) is seen to turn complex.

Quantum black hole entropy

We derive an exact formula for the dimensionality of the Hilbert space of the boundary states of SU(2) Chern-Simons theory, which, according to the recent work of Ashtekar et al., leads to the Bekenstein-Hawking entropy of a four dimensional Schwarzschild black hole. Our result stems from the relation between the (boundary) Hilbert space of the Chern-Simons theory with the space of conformal blocks of the Wess-Zumino model on the boundary 2-sphere.

A New holographic entropy bound from quantum geometry

A new entropy bound, tighter than the standard holographic bound due to Bekenstein, is derived for space-times with nonrotating isolated horizons from the quantum geometry approach, in which the horizon is described by the boundary degrees of freedom of a three dimensional Chern-Simons theory.

Mass and charge fluctuations and black hole entropy

The effects of thermal fluctuations of the mass (horizon area) and electric charge, on the entropy of nonrotating charged macroscopic black holes, are analyzed using a grand canonical ensemble. Restricting to Gaussian fluctuations around equilibrium, and assuming a power-law type of relation between the black hole mass, charge and horizon area, characterized by two real positive indices, the grand canonical entropy is shown to acquire a logarithmic correction with a positive coefficient proportional to the sum of the indices. However, the root mean squared fluctuations of mass and charge relative to the mean values of these quantities turn out to be independent of the details of the assumed mass-area relation. We also comment on possible cancellation between log (area) corrections arising due to fixed area quantum spacetime fluctuations and that due to thermal fluctuations of the area and other quantities.

Parity-violating gravitational coupling of electromagnetic fields

A manifestly gauge-invariant formulation of the coupling of the Maxwell theory with an Einstein-Cartan geometry is given, where the spacetime torsion originates from a massless Kalb-Ramond field augmented by suitable U(1) Chern-Simons terms. We focus on the situation where the torsion violates parity, and relate it to earlier proposals for gravitational parity violation.

Parity-violating Kalb–Ramond–Maxwell interactions and CMB anisotropy in a braneworld

Following up on a recent paper by two of us (DM and SS), demonstrating the large enhancement in observable optical activity in radiation from high red-shift sources arising from the string-based coupling of bulk Kalb–Ramond field to the Maxwell–Chern–Simons three-form on the brane in a Randall–Sundrum braneworld, we exhibit here a similar enhancement in parity-violating temperature–polarization correlations, as yet unseen, in the CMB anisotropy due to a generalized parity-violating Kalb–Ramond axion–photon interaction proposed earlier by one of us (PM). The non-observation of such correlations in CMB anisotropies would necessitate unnatural fine tuning of the Kalb–Ramond axion parameters. As a stringy realization of the Randall–Sundrum braneworld scenario is yet to be understood properly, our work indicates the need for a careful investigation to establish the connection between string-based phenomenological models and the Randall–Sundrum braneworld scenario.

Does a Kalb--Ramond field make spacetime optically active?

Abstract. A spacetime with torsion produced by a Kalb–Ramond field coupled gravitationally to the Maxwell field, in accordance with a recent proposal by two of us (PM and SS), is argued to lead to optical activity in synchrotron radiation from cosmologically distant radio sources. We show that this indicates a very small, but possibly observable rotation of the plane of polarization of the radiation, above and beyond the Faraday rotation due to magnetized galactic plasma. Implications for heterotic string theory are outlined.

Superspace geometry from D = 4, N = 1 heterotic superstrings

Abstract The presence of classical κ -supersymmetry invariance is shown to be consistent with an off-shell D = 4, N = 1 conformal supergravity background in the presence of a tensor multiplet. We derive a suitable set of constraints, via super Weyl rescaling, for a heterotic superstring in such a background. Starting from the geometry of 16-16 supergravity and gauging the R -symmetry with a composite connection, we derive a geometrical structure similar to that of new minimal supergravity.