Research Publications
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Item Stationary states in a quantum gravity model(Elsevier Science Publishers, 1981-05-05) Padmanabhan, T.; Narlikar, J. V.A model theory for quantized gravity is discussed whereonly selected degrees of freedomare quantized. The concept of stationary states is introduced. It is shown that the Planck length arises as a lower bound to the space—time length scale in a natural way.Item Inflation from quantum gravity(Elsevier Science Publishers, 1984-08-27) Padmanabhan, T.A model for inflation based on a quantum gravity scenario is presented. The process allows inflation of a Planck size bubble to the observed universe.Item Holographic Gravity and the Surface term in the Einstein-Hilbert Action(Springer, 2005-06-12) Padmanabhan, T.Certain peculiar features of Einstein-Hilbert (EH) action provide clues towards a holographic approach to gravity which is independent of the detailed microstructure of spacetime. These features of the EH action include: (a) the existence of second derivatives of dynamical variables; (b) a non trivial relation between the surface term and the bulk term; (c) the fact that surface term is non analytic in the coupling constant, when gravity is treated as a spin-2 perturbation around flat spacetime and (d) the form of the variation of the surface term under infinitesimal coordinate transformations. The surface term can be derived directly from very general considerations and using (d) one can obtain Einstein’s equations just from the surface term of the action. Further one can relate the bulk term to the surface term and derive the full EH action based on purely thermodynamic considerations. The features (a), (b) and (c) above emerge in a natural fashion in this approach. It is shown that action Agrav splits into two terms -S+βE in a natural manner in any stationary spacetime with horizon, where E is essentially an integral over ADM energy density and S arises from the integral of the surface gravity over the horizon. This analysis shows that the true degrees of freedom of gravity reside in the surface term of the action, making gravity intrinsically holographic. It also provides a close connection between gravity and gauge theories, and highlights the subtle role of the singular coordinate transformations.Item Gravity as elasticity of spacetime: A paradigm to understand horizon thermodynamics and cosmological constant(World Scientific Publishing Company, 2004-05-20) Padmanabhan, T.It is very likely that the quantum description of spacetime is quite di erent from what we perceive at large scales, l (G~=c3)1=2. The long wavelength description of spacetime, based on Einstein's equations, is similar to the description of a continuum solid made of a large number of microscopic degrees of freedom. This paradigm provides a novel interpretation of coordinate transformations as deformations of \spacetime solid" and allows one to obtain Einstein's equations as a consistency condition in the long wave- length limit. The entropy contributed by the microscopic degrees of freedom reduces to a pure surface contribution when Einstein's equations are satis ed. The horizons arises as \defects" in the \spacetime solid" (in the sense of well-de ned singular points) and contributes an entropy which is one quarter of the horizon area. Finally, the response of the microstructure to vacuum energy leads to a near cancellation of the cosmological constant, leaving behind a tiny uctuation which matches with the observed value.Item Gravity: A new holographic perspective(World Scientific Publishing Company, 2005-12-15) Padmanabhan, T.A general paradigm for describing classical (and semiclassical) gravity is presented. This approach brings to the centre-stage a holographic relationship between the bulk and surface terms in a general class of action functionals and provides a deeper insight into several aspects of classical gravity which have no explanation in the conventional approach. After highlighting a series of unresolved issues in the conventional approach to gravity, I show that (i) principle of equivalence, (ii) general covariance and (iii)a reasonable condition on the variation of the action functional, suggest a generic Lagrangian for semiclassical gravity of the form L=QabcdRabcd with ∇b Qabcd=0. The expansion of Qabcd in terms of the derivatives of the metric tensor determines the structure of the theory uniquely. The zeroth order term gives the Einstein-Hilbert action and the first order correction is given by the Gauss-Bonnet action. Any such Lagrangian can be decomposed into a surface and bulk terms which are related holographically. The equations of motion can be obtained purely from a surface term in the gravity sector. Hence the field equations are invariant under the transformation Tab → Tab + λ gab and gravity does not respond to the changes in the bulk vacuum energy density. The cosmological constant arises as an integration constant in this approach. The implications are discussed.Item Mach's principle and the notion of time(Indian Academy of Sciences, 2009-09-12) Padmanabhan, T.The role of time coordinate in the realization of March's principles is highlighted. It is shown that Mach's principle is linked to the definition of a 'particle'. These results a deep connection between quantum gravity an Mach's principle.Item Limitations on the operational definition of spacetime events and quantum gravity(IOP Publishing, 1987-01-12) Padmanabhan, T.Using simple arguments from general relativity and quantum theory we show that it is not possible to devise experiments (or operational procedures) which will measure the position of a particle to an accuracy better than the Planck length (Gh/c3) = cm. It is also impossible to synchronise clocks to a precision better than Planck time. The implications of the result are discussed.Item Zero-point length from string fluctuations(Elsevier Science Publishers, 2005-12-19) Fontanini, Michele; Spallucci, Euro; Padmanabhan, T.One of the leading candidates for quantum gravity, viz. string theory, has the following features incorporated in it. (i) The full spacetime is higher-dimensional, with (possibly) compact extra-dimensions; (ii) there is a natural minimal length below which the concept of continuum spacetime needs to be modified by some deeper concept. On the other hand, the existence of a minimal length (zero-point length) in four-dimensional spacetime, with obvious implications as UV regulator, has been often conjectured as a natural aftermath of any correct quantum theory of gravity. We show that one can incorporate the apparently unrelated pieces of information—zero-point length, extra-dimensions, string T -duality—in a consistent framework. This is done in terms of a modified Kaluza–Klein theory that interpolates between (high-energy) string theory and (low-energy) quantum field theory. In this model, the zero-point length in four dimensions is a “virtual memory” of the length scale of compact extra-dimensions. Such a scale turns out to be determined by T -duality inherited from the underlying fundamental string theory. From a low energy perspective short distance infinities are cutoff by a minimal length which is proportional to the square root of the string slope, i.e.,√α . Thus, we bridge the gap between the string theory domain and the low energy arena of point-particle quantum field theory.Item Topological interpretation of the horizon temperature(World Scientific Publishing Company, 2003-08-23) Padmanabhan, T.Item Entropy of horizons, complex paths and quantum tunneling(World Scientific Publishing Company, 2004-07-01) Padmanabhan, T.In any spacetime, it is possible to have a family of observers following a congruence of timelike curves such that they do not have access to part of the spacetime. This lack of information suggests associating a (congruence dependent) notion of entropy with the horizon that blocks the information from these observers. While the blockage of information is absolute in classical physics, quantum mechanics will allow tunneling across the horizon. This process can be analysed in a simple, yet general, manner and we show that the probability for a system with energy E to tunnel across the horizon is P(E)∝exp[-(2π/κ)E) where κ is the surface gravity of the horizon. If the surface gravity changes due to the leakage of energy through the horizon, then one can associate an entropy S(M) with the horizon where dS = [ 2π / κ (M) ] dM and M is the active gravitational mass of the system.