arXiv subjects

Kumar S. Gupta

Publications and source records attributed to Kumar S. Gupta.

At least 55 records · Page 3Linked to original sources

arXiv2007

Universal near-horizon conformal structure and black hole entropy

It is shown that a massless scalar probe reveals a universal near-horizon conformal structure for a wide class of black holes, including the BTZ. The central charge of the corresponding Virasoro algebra contains information about the black hole. With a suitable quantization condition on the central charge, the CFT associated with the black hole in our approach is consistent with the recent observation of Witten, where the dual theory for the BTZ in the AdS/CFT framework has been identified with the construction of Frenkel, Lepowsky and Meurman. This CFT admits the Fischer-Griess monster group as its symmetry. The logarithm of the dimension of a specific representation of the monster group has been identified by Witten as the entropy of the BTZ black hole. Our algebraic approach shows that a wide class of black holes share the same near-horizon conformal structure as that for the BTZ. With a suitable quantization condition, the CFT's for all these black holes in our formalism can be identified with the FLM model, although not through the AdS/CFT correspondence. The corresponding entropy for the BTZ provides a lower bound for the entropy of this entire class of black holes.

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arXiv2007

Electron Capture and Scaling Anomaly in Polar Molecules

We present a new analysis of the electron capture mechanism in polar molecules, based on von Neumann's theory of self-adjoint extensions. Our analysis suggests that it is theoretically possible for polar molecules to form bound states with electrons, even with dipole moments smaller than the critical value D_0 given by 1.63\times10^{-18} esu cm. This prediction is consistent with the observed anomalous electron scattering in H_2S and HCl, whose dipole moments are smaller than the critical value D_0. We also show that for a polar molecule with dipole moment less than D_0, typically there is only a single bound state, which is in qualitative agreement with observations. We argue that the quantum mechanical scaling anomaly is responsible for the formation of these bound states.

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arXiv2006

Noncommutative BTZ Black Hole and Discrete Time

We search for all Poisson brackets for the BTZ black hole which are consistent with the geometry of the commutative solution and are of lowest order in the embedding coordinates. For arbitrary values for the angular momentum we obtain two two-parameter families of contact structures. We obtain the symplectic leaves, which characterize the irreducible representations of the noncommutative theory. The requirement that they be invariant under the action of the isometry group restricts to $R\times S^1$ symplectic leaves, where $R$ is associated with the Schwarzschild time. Quantization may then lead to a discrete spectrum for the time operator.

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arXiv2006

Black Holes, Holography and Moduli Space Metric

String theory can accommodate black holes with the black hole parameters related to string moduli. It is a well known but remarkable feature that the near horizon geometry of a large class of black holes arising from string theory contains a BTZ part. A mathematical theorem (Sullivan's Theorem) relates the three dimensional geometry of the BTZ metric to the conformal structures of a two dimensional space, thus providing a precise kinematic statement of holography. Using this theorem it is possible to argue that the string moduli space in this region has to have negative curvature from the BTZ part of the associated spacetime. This is consistent with a recent conjecture of Ooguri and Vafa on string moduli space.

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arXiv2006

Asymptotic Quasinormal Modes of d-Dimensional Schwarzschild Black Hole with Gauss-Bonnet Correction

We obtain an analytic expression for the highly damped asymptotic quasinormal mode frequencies of the $d\geq 5$-dimensional Schwarzschild black hole modified by the Gauss-Bonnet term, which appears in string derived models of gravity. The analytic expression is obtained under the string inspired assumption that there exists a minimum length scale in the system and in the limit when the coupling in front of the Gauss-Bonnet term in the action is small. Although there are several similarities of this geometry with that of the Schwarzschild black hole, the asymptotic quasinormal mode frequencies are quite different. In particular, the real part of the asymptotic quasinormal frequencies for this class of single horizon black holes in not proportional to log(3).

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arXiv2005

Waves on Noncommutative Spacetimes

Waves on ``commutative'' spacetimes like R^d are elements of the commutative algebra C^0(R^d) of functions on R^d. When C^0(R^d) is deformed to a noncommutative algebra {\cal A}_θ(R^d) with deformation parameter θ({\cal A}_0 (R^d) = C^0(R^d)), waves being its elements, are no longer complex-valued functions on R^d. Rules for their interpretation, such as measurement of their intensity, and energy, thus need to be stated. We address this task here. We then apply the rules to interference and diffraction for d \leq 4 and with time-space noncommutativity. Novel phenomena are encountered. Thus when the time of observation T is so brief that T \leq 2 θw, where w is the frequency of incident waves, no interference can be observed. For larger times, the interference pattern is deformed and depends on \frac{θw}{T}. It approaches the commutative pattern only when \frac{θw}{T} goes to 0. As an application, we discuss interference of star light due to cosmic strings.

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arXiv2005

Geometric Finiteness and Non-quasinormal Modes of the BTZ Black Hole

The BTZ black hole is geometrically finite. This means that its three dimensional hyperbolic structure as encoded in its metric is in 1-1 correspondence with the Teichmuller space of its boundary, which is a two torus. The equivalence of different Teichmuller parameters related by the action of the modular group therefore requires the invariance of the monodromies of the solutions of the wave equation around the inner and outer horizons in the BTZ background. We show that this invariance condition leads to the non-quasinormal mode frequencies discussed by Birmingham and Carlip.

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arXiv2004

On the Real Spectra of Calogero Model with Complex Coupling

We study the eigenvalue problem of the rational Calogero model with the coupling of the inverse-square interaction as a complex number. We show that although this model is manifestly non-invariant under the combined parity and time-reversal symmetry ${\cal{PT}}$, the eigenstates corresponding to the zero value of the generalized angular momentum have real energies.

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arXiv2003

Quantum Inverse Square Interaction

Hamiltonians with inverse square interaction potential occur in the study of a variety of physical systems and exhibit a rich mathematical structure. In this talk we briefly mention some of the applications of such Hamiltonians and then analyze the case of the N-body rational Calogero model as an example. This model has recently been shown to admit novel solutions, whose properties are discussed.

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arXiv2003

Black Hole Decay as Geodesic Motion

We show that a formalism for analyzing the near-horizon conformal symmetry of Schwarzschild black holes using a scalar field probe is capable of describing black hole decay. The equation governing black hole decay can be identified as the geodesic equation in the space of black hole masses. This provides a novel geometric interpretation for the decay of black holes. Moreover, this approach predicts a precise correction term to the usual expression for the decay rate of black holes.

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arXiv2003

Near-Horizon States of Black Holes and Calogero Models

We find self-adjoint extensions of the rational Calogero model in presence of the harmonic interaction. The corresponding eigenfunctions may describe the near-horizon quantum states of certain types of black holes.

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arXiv2003

Inequivalent Quantizations of the Rational Calogero Model

We show that the rational Calogero model with suitable boundary condition admits quantum states with non-equispaced energy levels. Such a spectrum generically consists of infinitely many positive energy states and a single negative energy state. The new states appear for arbitrary number of particles and for specific ranges of the coupling constant. These states owe their existence to the self-adjoint extensions of the corresponding Hamiltonian, which are labelled by a real parameter z. Each value of z corresponds to a particular spectrum, leading to inequivalent quantizations of the model.

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arXiv2003

Novel Quantum States of the Rational Calogero Models Without the Confining Interaction

We show that the N-particle A_{N-1} and B_N rational Calogero models without the harmonic interaction admit a new class of bound and scattering states. These states owe their existence to the self-adjoint extensions of the corresponding Hamiltonians, labelled by a real parameter z. It is shown that the new states appear for all values of N and for specific ranges of the coupling constants. Moreover, they are shown to exist even in the excited sectors of the Calogero models. The self-adjoint extension generically breaks the classical scaling symmetry, leading to quantum mechanical scaling anomaly. The scaling symmetry can however be restored for certain values of the parameter z. We also generalize these results for many particle systems with classically scale invariant long range interactions in arbitrary dimensions.

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arXiv2003

Hidden Degeneracy in the Brick Wall Model of Black Holes

Quantum field theory in the near-horizon region of a black hole predicts the existence of an infinite number of degenerate modes. Such a degeneracy is regulated in the brick wall model by the introduction of a short distance cutoff. In this Letter we show that states of the brick wall model with non zero energy admit a further degeneracy for any given finite value of the cutoff. The black hole entropy is calculated within the brick wall model taking this degeneracy into account. Modes with complex frequencies however do not exhibit such a degeneracy.

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arXiv2002

Near-Horizon Conformal Structure and Entropy of Schwarzschild Black Holes

Near-horizon conformal structure of a massive Schwarzschild black hole of mass M is analyzed using a scalar field as a simple probe of the background geometry. The near-horizon dynamics is governed by an operator which is related to the Virasoro algebra and admits a one-parameter family of self-adjoint extensions described by a real parameter z. When z satisfies a suitable contraint, the corresponding wavefunctions exhibit scaling behaviour in a band-like region near the horizon of the black hole. This formalism is consistent with the Bekenstein-Hawking entropy formula and naturally produces the -3/2 log M^2 correction term to the black hole entropy with other subleading corrections exponentially suppressed. This precise form for the black hole entropy is expected on general grounds in any conformal field theoretic description of the problem. The presence of the Virasoro algebra and the scaling properties of the associated wavefunctions in the near-horizon region together with the appearance of the logarithmic correction to the Bekenstein-Hawking entropy provide strong evidence for the near-horizon conformal structure in this system.

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arXiv2001

Further Evidence for the Conformal Structure of a Schwarzschild Black Hole in an Algebraic Approach

We study the excitations of a massive Schwarzschild black hole of mass M resulting from the capture of infalling matter described by a massless scalar field. The near-horizon dynamics of this system is governed by a Hamiltonian which is related to the Virasoro algebra and admits a one-parameter family of self-adjoint extensions described by a parameter z \in R . The density of states of the black hole can be expressed equivalently in terms of z or M, leading to a consistent relation between these two parameters. The corresponding black hole entropy is obtained as S = S(0) - 3/2 log S(0) + C, where S(0) is the Bekenstein-Hawking entropy, C is a constant with other subleading corrections exponentially suppressed. The appearance of this precise form of the black hole entropy within our formalism, which is expected on general grounds in any conformal field theoretic description, provides strong evidence for the near-horizon conformal structure in this system.

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arXiv2001

Bound States in One-Dimensional Quantum N-Body Systems with Inverse Square Interaction

We investigate the existence of bound states in a one-dimensional quantum system of $N$ identical particles interacting with each other through an inverse square potential. This system is equivalent to the Calogero model without the confining term. The effective Hamiltonian of this system in the radial direction admits a one-parameter family of self-adjoint extensions and the negative energy bound states occur when most general boundary conditions are considered. We find that these bound states exist only when $N=3,4$ and for certain values of the system parameters. The effective Hamiltonian for the system is related to the Virasoro algebra and the bound state wavefunctions exhibit a scaling behaviour in the limit of small inter-particle separation.

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arXiv2001

Near-Horizon Conformal Structure of Black Holes

The near-horizon properties of a black hole are studied within an algebraic framework, using a scalar field as a simple probe to analyze the geometry. The operator H governing the near-horizon dynamics of the scalar field contains an inverse square interaction term. It is shown that the operators appearing in the corresponding algebraic description belong to the representation space of the Virasoro algebra. The operator H is studied using the representation theory of the Virasoro algebra. We observe that the wave functions exhibit scaling behaviour in a band-like region near the horizon of the black hole.

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