arXiv subjects
Publications and source records attributed to Sashideep Gutti.
We study radiation reaction in a Lorentz violating electrodynamics [1]. We explore the possible modification whatsoever present in the radiation reaction force experienced by an accelerating charge in the modified Maxwell theory. However it turns out that radiation reaction receives no change due to Lorentz violation whereas electromagnetic mass manifests anisotropy.
We study the response of a rotating monopole detector that is coupled to a massless scalar field which is described by a non-linear dispersion relation in flat spacetime. Since it does not seem to be possible to evaluate the response of the rotating detector analytically, we resort to numerical computations. Interestingly, unlike the case of the uniformly accelerated detector that has been considered recently, we find that defining the transition probability rate of the rotating detector poses no difficulties. Further, we show that the response of the rotating detector can be computed {\it exactly}\vee (albeit, numerically) even when it is coupled to a field that is governed by a non-linear dispersion relation. We also discuss the response of the rotating detector in the presence of a cylindrical boundary on which the scalar field is constrained to vanish. While super-luminal dispersion relations hardly affect the standard results, we find that sub-luminal dispersion relations can lead to relatively large modifications.
Previous papers dealt with the quantization of the Lemaitre-Tolman-Bondi (LTB) model for vanishing cosmological constant $Λ$. Here we extend the analysis to the case $Λ>0$. Our main goal is to present solutions of the Wheeler-DeWitt equation, to give their interpretation, and to derive Hawking radiation from them. We restrict ourselves to a discussion of those points that are different from the $Λ=0$-case. These have mainly to do with the occurrence of two horizons.
In a recent publication we developed a canonical quantization program describing the gravitational collapse of a spherical dust cloud in 2+1 dimensions with a negative cosmological constant $-Λ\equiv -l^{-2}<0$. In this paper we address the quantization of the Banados--Teitelboim--Zanelli (BTZ) black hole. We show that the mass function describing the black hole is made of two pieces, a constant non-vanishing boundary contribution and a discrete spectrum of the form $μ_n = \frac{\hbar}{l}(n+ \frac 12)$. The discrete spectrum is obtained by applying the Wheeler--DeWitt equation with a particular choice of factor ordering and interpreted as giving the energy levels of the collapsed matter shells that form the black hole. Treating a black hole microstate as a particular distribution of shells among the levels, we determine the canonical entropy of the BTZ black hole. Comparison with the Bekenstein--Hawking entropy shows that the boundary energy is related to the central charge of the Virasoro algebra that generates the asymptotic symmetry group of the three-dimensional anti-de Sitter space AdS$_3$. This gives a connection between the Wheeler--DeWitt approach and the conformal field theory approach.
We study the collapse of a spherically symmetric dust distribution in $d$-dimensional AdS spacetime. We investigate the role of dimensionality, and the presence of a negative cosmological constant, in determining the formation of trapped surfaces and the end state of gravitational collapse. We obtain the self-similar solution for the case of zero cosmological constant, and show that one cannot construct a self-similar solution when a cosmological constant is included.
We develop the canonical theory of gravitational collapse in 2+1 dimensions with a negative cosmological constant and obtain exact solutions of the Wheeler--DeWitt equation regularized on a lattice. We employ these solutions to derive the Hawking radiation from black holes formed in all models of dust collapse. We obtain an (approximate) Planck spectrum near the horizon characterized by the Hawking temperature $T_{\mathrm H}=\hbar\sqrt{GΛM}/2π$, where $M$ is the mass of a black hole that is presumed to form at the center of the collapsing matter cloud and $-Λ$ is the cosmological constant. Our solutions to the Wheeler-DeWitt equation are exact, so we are able to reliably compute the greybody factors that result from going beyond the near horizon region.
We investigate the quantum particle creation during the circularly symmetric collapse of a 2+1 dust cloud, for the cases when the cosmological constant is either zero or negative. We derive the Ford-Parker formula for the 2+1 case, which can be used to compute the radiated quantum flux in the geometric optics approximation. It is shown that no particles are created when the collapse ends in a naked singularity, unlike the 3+1 case. When the collapse ends in a BTZ black hole, we recover the expected Hawking radiation.
We examine the gravitational collapse of spherically symmetric inhomogeneous dust in (2+1) dimensions, with cosmological constant. We obtain the analytical expressions for the interior metric. We match the solution to a vacuum exterior. We discuss the nature of the singularity formed by analyzing the outgoing radial null geodesics. We examine the formation of trapped surfaces during the collapse.
If there exists a formulation of quantum mechanics which does not refer to a background classical spacetime manifold, it then follows as a consequence, (upon making one plausible assumption), that a quantum description of gravity should be necessarily non-linear. This is true independent of the mathematical structure used for describing such a formulation of quantum mechanics. A specific model which exhibits this non-linearity is constructed, using the language of noncommutative geometry. We derive a non-linear Schrodinger equation for the quantum dynamics of a particle; this equation reduces to the standard linear Schrodinger equation when the mass of the particle is much smaller than Planck mass. It turns out that the non-linear equation found by us is very similar to a non-linear Schrodinger equation found by Doebner and Goldin in 1992 from considerations of unitary representaions of the infinite-dimensional group of diffeomorphisms in three spatial dimensions. Our analysis suggests that the diffusion constant introduced by Doebner and Goldin depends on the mass of the particle, and that this constant tends to zero in the limit in which the particle mass is much smaller than Planck mass, so that in this limit the non-linear theory reduces to standard linear quantum mechanics. A similar effective non-linear Schrodinger equation was also found for the quantum dynamics of a system of D0-branes, by Mavromatos and Szabo.
We examine the gravitational collapse of an infinite cylindrical distribution of time like dust. In order to simplify the calculation we make an assumption that the axial and azimuthal metric functions are equal. It is shown that the resulting solution describes homogeneous collapse. We show that the interior metric can be matched to a time dependent exterior. We also discuss the nature of the singularity in the matter region and show that it is covered.