IUCAA Preprints
Permanent URI for this communityhttp://localhost:4000/handle/11007/149
Browse
9 results
Search Results
Item Formal analysis of two dimensional gravity(2015-03-11) Engineer, Sunu; Srinivasan, K.; Padmanabhan, T.Several investigations in the study of cosmological structure formation use numerical simulations in both two and three dimensions. In this paper we address the subtle question of ambiguities in the nature of two dimensional gravity in an expanding background. We take a detailed and formal approach by deriving the equations describing gravity in (D + 1) dimensions using the action principle of Einstein. We then consider the Newtonian limit of these equations and finally obtain the necessary fluid equations required to describe structure formation. These equations are solved for the density perturbation in both the linearised form and in the spherical top hat model of nonlinear growth. We find that, when the special case of D = 2 is considered, no structures can grow. We therefore conclude that, within the frame work of Einstein's theory of gravity in (2 + 1) dimensions, formation of structures cannot take place. Finally, we indicate the different possible ways of getting around this difficulty so that growing structures can be obtained in two dimensional cosmological gravitational simulations and discuss their implications.Item Cosmological solution of Machian gravity(IUCAA, 2015-02) Das, SantanuItem Machian gravity and the giant galactic forces(IUCAA, 2015-02) Das, SantanuItem Radiating Kerr-Newman black hole in f(R) gravity(IUCAA, 2015-02) Ghosh, S. G.; Maharaj, S. D.; Papnoi, UmaItem Subtle is the gravity(2001-07-05) Dadhich, NareshIn this lecture I build up the motivation for relativity and grav- itation based on general principles and common sense considera- tions which should fall in the sphere of appreciation of a general reader. There is a novel way of looking at things and understanding them in a more direct physical terms which should be of interest to fellow relativists as well as physicists in general.Item Holography of gravity encoded in a relation between entropy, horizon area and action for gravity(2002-05-20) Padmanabhan, T.I provide a general proof of the conjecture that one can attribute an en- tropy to the area of any horizon. This is done by constructing a canonical ensemble of a subclass of spacetimes with a fixed value for the temperature T = β−1 and evaluating the exact partition function Z(β). For spherically symmetric spacetimes with a horizon at r = a, the partition function has the generic form Z ∝ exp[S −βE], where S = (1/4)4πa2 and |E| = (a/2). Both S and E are determined entirely by the properties of the metric near the horizon. This analysis reproduces the conventional result for the black-hole spacetimes and provides a simple and consistent interpretation of entropy and energy for De Sitter spacetime. For the Rindler spacetime the entropy per unit transverse area turns out to be (1/4) while the energy is zero. Further, I show that the relationship between entropy and area allows one to construct the action for the gravitational field on the bulk and thus the full theory. In this sense, gravity is intrinsically holographic.Item Classical electron model with negative energy density in Einstein-Cartan theory of gravitation(2011-07-05) Ray, Saibal; Bhadra, SumanaExperimental result regarding the maximum limit of the radius of the electron ∼ 10−16 cm and a few of the theoretical works suggest that there might have some negative energy density regions within the particle in general theory of relativity. It is argued in the present investigation that such a negative energy density also can be obtained with a better physical interpretation in the framework of Einstein-Cartan theory.Item From Gravitons to Gravity: Myths and Reality(2011-07-06) Padmanabhan, T.email: nabhan@iucaa.ernet.in There is a general belief, reinforced by statements in standard textbooks, that: (i) one can obtain the full non-linear Einstein’s theory of gravity by coupling a massless, spin-2 field hab self-consistently to the total energy momentum tensor, including its own; (ii) this procedure is unique and leads to Einstein-Hilbert action and (iii) it only uses standard concepts in Lorentz invariant field theory and does not involve any geometrical assumptions. After providing several reasons why such beliefs are suspect — and critically re-examining several previous attempts — we provide a detailed analysis aimed at clarifying the situation. First, we prove that it is impossible to obtain the Einstein-Hilbert (EH) action, starting from the standard action for gravitons in linear theory and iterating repeatedly. This result follows from the fact that EH action has a part (viz. the surface term arising from second derivatives of the metric tensor) which is non-analytic in the coupling constant, when expanded in terms of the graviton field. Thus, at best, one can only hope to obtain the remaining, quadratic, part of the EH Lagrangian (viz. the Γ2 lagrangian) if no additional assumptions are made. Second, we use the Taylor series expansion of the action for Einstein’s theory, to identify the tensor Sab , to which the graviton field hab couples to the lowest order (through a term of the form Sab hab in the lagrangian). We show that the second rank tensor Sab is not the conventional energy momentum tensor Tab of the graviton and provide an explanation for this feature. Third, we construct the full nonlinear Einstein’s theory with the source being spin-0 field, spin-1 field or relativistic particles by explicitly coupling the spin-2 field to this second rank tensor Sab order by order and summing up the infinite series. Finally, we construct the theory obtained by self consistently coupling hab to the conventional energy momentum tensor Tab order by order and show that this does not lead to Einstein’s theory. The implications are discussed.Item Manybody treatment of white dwarf and neutron stars on the brane(2005-07-01) Azam, Mofazzal; Sami, M.Brane-World models suggest modification of Newton’s law of gravity on the 3-brane at submillimeter scales. The brane-world induced corrections are in higher powers of inverse distance and appear as additional terms with the Newtonian potential. The average inter-particle distance in white dwarf and neutron stars are 10−10 cms and 10−13 cms respectively, and therefore, the effect of submillimeter corrections needs to be investigated. We show, by carrying out simple manybody calculations, that the mass and mass-radius relationship of the white dwarf and neutron stars are not effected by submillimeter corrections. However, our analysis shows that the correction terms in the effective theory give rise to force akin to surface tension in normal liquids.