Searcharxiv⌕ Search

arXiv subjects

Amit Ghosh

Publications and source records attributed to Amit Ghosh.

At least 37 records · Page 2Linked to original sources
arXiv2012

The scaling of black hole entropy in loop quantum gravity

We discuss some general properties of black hole entropy in loop quantum gravity from the perspective of local stationary observers at distance l from the horizon. The present status of the theory indicates that black hole entropy differs from the low energy (IR) expected value A/(4G) (in natural units) in the deep Planckian regime (UV). The partition function is well defined if the number of non-geometric degrees of freedom g_M (encoding the degeneracy of the area a_p eigenvalue at a puncture p) satisfy the holographic bound g_M < exp(ap/(4G)). Our framework provides a natural renormalization mechanism such that S_UV ---> S_IR=A/(4 G) as the scale l flows.

gr-qc↗
arXiv2012

The number of roots of polynomials of large degree in a prime field

We establish asymptotic upper bounds on the number of zeros modulo $p$ of certain polynomials with integer coefficients, with $p$ prime numbers arbitrarily large. The polynomials we consider have degree of size $p$ and are obtained by truncating certain power series with rational coefficients that satisfy simple differential equations.

math.NT↗
arXiv2012

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.

gr-qc↗
arXiv2012

Near-extremal black holes

We present a new formulation of deriving Hawking temperature for near-extremal black holes using distributions. In this paper the near-extremal Reissner-Nordstrom and Kerr black holes are discussed. It is shown that the extremal solution as a limit of non-extremal metric is well-defined. The pure extremal case is also discussed separately.

gr-qc↗
arXiv2011

Black hole entropy and isolated horizons thermodynamics

We present a statistical mechanical calculation of the thermodynamical properties of (non rotating) isolated horizons. The introduction of Planck scale allows for the definition of an universal horizon temperature (independent of the mass of the black hole) and a well-defined notion of energy (as measured by suitable local observers) proportional to the horizon area in Planck units. The microcanonical and canonical ensembles associated with the system are introduced. Black hole entropy and other thermodynamical quantities can be consistently computed in both ensembles and results are in agreement with Hawking's semiclassical analysis for all values of the Immirzi parameter.

gr-qc↗
arXiv2011

A local first law for black hole thermodynamics

We first show that stationary black holes satisfy an extremely simple local form of the first law δE=κ(l) δA/(8 π) where the thermodynamical energy E=A/(8πl) and (local) surface gravity κ(l)=1/l, where A is the horizon area and l is a proper length characterizing the distance to the horizon of a preferred family of local observers suitable for thermodynamical considerations. Our construction is extended to the more general framework of isolated horizons. The local surface gravity is universal. This has important implications for semiclassical considerations of black hole physics as well as for the fundamental quantum description arising in the context of loop quantum gravity.

gr-qc↗
arXiv2011

Real zeros of holomorphic Hecke cusp forms

This note is concerned with the zeros of holomorphic Hecke cusp forms of large weight on the modular surface. The zeros of such forms are symmetric about three geodesic segments and we call those zeros that lie on these segments, real. Our main results give estimates for the number of real zeros as the weight goes to infinity.

math.NT↗
arXiv2010

Local symmetries of non-expanding horizons

Local symmetries of a non-expanding horizon has been investigated in the 1st order formulation of gravity. When applied to a spherically symmetric isolated horizon only a U(1) subgroup of the Lorentz group survives as residual local symmetry that one can make use of in constructing an effective theory on the horizon.

gr-qc↗
arXiv2009

Laws of Black Hole Mechanics from Holst Action

The formulation of Weak Isolated Horizons (WIH) based on the Isolated Horizon formulation of black hole horizons is reconsidered. The first part of the paper deals with the derivation of laws of mechanics of a WIH. While the zeroth law follows from the WIH boundary conditions, first law depends on the action chosen. We construct the covariant phase space for a spacetime having an WIH as inner boundary for the Holst action. 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 for WIH. Subsequently, we show from the same covariant phase space that for spherical horizons, the topological theory on the inner boundary is a U(1) Chern-Simons theory.

gr-qc↗
arXiv2006

Generic weak isolated horizons

Weak isolated horizon boundary conditions have been relaxed supposedly to their weakest form such that both zeroth and the first law of black hole mechanics still emerge, thus making the formulation more amenable for applications in both analytic and numerical Relativity. As an additional gain it explicitly brings the non-extremal and extremal black holes at the same footing.

gr-qc↗
arXiv2004

On the log correction to the black hole area law

Various approaches to black hole entropy yield the area law with logarithmic corrections, many involving a coefficient 1/2, and some involving 3/2. It is pointed out here that the standard quantum geometry formalism is not consistent with 3/2 and favours 1/2.

gr-qc↗
arXiv2001

Black hole entropy calculations based on symmetries

Symmetry based approaches to the black hole entropy problem have a number of attractive features; in particular they are very general and do not depend on the details of the quantization method. However we point out that, of the two available approaches, one faces conceptual problems (also emphasized by others), while the second contains certain technical flaws. We correct these errors and, within the new, improved scheme, calculate the entropy of 3-dimensional black holes. We find that, while the new symmetry vector fields are well-defined on the ``stretched horizon,'' and lead to well-defined Hamiltonians satisfying the expected Lie algebra, they fail to admit a well-defined limit to the horizon. This suggests that, although the formal calculation can be carried out at the classical level, its real, conceptual origin probably lies in the quantum theory.

hep-th↗
arXiv2000

Statistical Entropy of Schwarzschild Black Strings and Black Holes

The statistical entropy of a Schwarzschild black string in five dimensions is obtained by counting the black string states which form a representation of the near-horizon conformal symmetry with a central charge. The statistical entropy of the string agrees with its Bekenstein-Hawking entropy as well as that of the Schwarzschild black hole in four dimensions. The choice of the string length which gives the Virasoro algebra also reproduces the precise value of the Bekenstein-Hawking entropy and lies inside the stability bound of the string.

hep-th↗
arXiv1996

QED_2 in Curved Backgrounds

Here we discuss the two dimensional quantum electrodynamics in curved space-time, especially in the background of some black holes. We first show the existence of some new quantum mechanical solution which has interesting properties. Then for some special black holes we discuss the fermion-black hole scattering problem. The issue of confinement is intimately connected with these solutions and we also comment on this in this background. Finally, the entanglement entropy and the Hawking radiation are also discussed in this background from a slightly different viewpoint.

hep-th↗
arXiv1995

S-DUALITY AND THE ENTROPY OF BLACK HOLES IN HETEROTIC STRING THEORY

Four dimensional heterotic string effective action is known to admit non-rotating electrically and magnetically charged black hole solutions. It is shown that the partition functions and entropies in both the cases are identical when these black hole solutions are related by S-duality transformations. The entropy is computed and is vanishing for each black hole in the extremal limit.

hep-th↗
arXiv1994

Entropy for extremal Reissner- Nordstrøm black holes

We reinterpret recent work on extremal Reissner- Nordstrøm black holes to argue that the mass is a measure of the gravitational entropy. We also find that the entropy of scalar fields in this background has a stronger divergence than usual.

hep-th↗