The Structure of the Gravitational Action and its relation with Horizon Thermodynamics and Emergent Gravity Paradigm

If gravity is an emergent phenomenon, as suggested by several recent results, then the structure of the action principle for gravity should encode this fact. With this motivation we study several features of the Einstein-Hilbert action and establish direct connections with horizon thermodynamics. We begin by introducing the concept of holographically conjugate variables (HCVs) in terms of which the surface term in the action has a specific relationship with the bulk term. In addition to g_{ab} and its conjugate momentum \sqrt{-g} M^{cab}, this procedure allows us to (re)discover and motivate strongly the use of f^{ab}=\sqrt{-g}g^{ab} and its conjugate momentum N^c_{ab}. The gravitational action can then be interpreted as a momentum space action for these variables. We also show that many expressions in classical gravity simplify considerably in this approach. For example, the field equations can be written in a form analogous to Hamilton's equations for a suitable Hamiltonian if we use these variables. More importantly, the variation of the surface term, evaluated on any null surface which acts a local Rindler horizon can be given a direct thermodynamic interpretation. The term involving the variation of the dynamical variable leads to T\delta S while the term involving the variation of the conjugate momentum leads to S\delta T. We have found this correspondence only for the choice of variables (g_{ab}, \sqrt{-g} M^{cab}) or (f^{ab}, N^c_{ab}). We use this result to provide a direct thermodynamical interpretation of the boundary condition in the action principle, when it is formulated in a spacetime region bounded by the null surfaces. We analyse these features from several different perspectives and provide a detailed description, which offers insights about the nature of classical gravity and emergent paradigm.Comment: 31 pages, published version with typos fixe

Gravitational field equations near an arbitrary null surface expressed as a thermodynamic identity

Previous work has demonstrated that the gravitational field equations in all Lanczos-Lovelock models imply a thermodynamic identity TdS=dE+PdV (where the variations are interpreted as changes due to virtual displacement along the affine parameter) in the near-horizon limit in static spacetimes. Here we generalize this result to any arbitrary null surface in an arbitrary spacetime and show that certain components of the Einstein's equations can be expressed in the form of the above thermodynamic identity. We also obtain an explicit expression for the thermodynamic energy associated with the null surface. Under appropriate limits, our expressions reduce to those previously derived in the literature. The components of the field equations used in obtaining the current result are orthogonal to the components used previously to obtain another related result, viz. that some components of the field equations reduce to a Navier-Stokes equation on any null surface, in any spacetime. We also describe the structure of Einstein's equations near a null surface in terms of three well-defined projections and show how the different results complement each other.Comment: v2, 25 pages, no figures, to appear in JHE

A Boundary Term for the Gravitational Action with Null Boundaries

Constructing a well-posed variational principle is a non-trivial issue in general relativity. For spacelike and timelike boundaries, one knows that the addition of the Gibbons-Hawking-York (GHY) counter-term will make the variational principle well-defined. This result, however, does not directly generalize to null boundaries on which the 3-metric becomes degenerate. In this work, we address the following question: What is the counter-term that may be added on a null boundary to make the variational principle well-defined? We propose the boundary integral of $2 \sqrt{-g} \left( \Theta+\kappa \right)$ as an appropriate counter-term for a null boundary. We also conduct a preliminary analysis of the variations of the metric on the null boundary and conclude that isolating the degrees of freedom that may be fixed for a well-posed variational principle requires a deeper investigation.Comment: 47 pages, no figures, title change

Network of Recurrent events - A case study of Japan

A recently proposed method of constructing seismic networks from 'record breaking events' from the earthquake catalog of California (Phy. Rev. E, 77 6,066104, 2008) was successfull in establishing causal features to seismicity and arrive at estimates for rupture length and its scaling with magnitude. The results of our implementation of this procedure on the earthquake catalog of Japan establishes the robustness of the procedure. Additionally, we find that the temporal distributions are able to detect heterogeneties in the seismicity of the region.Comment: 13 pages, 6 figures, 1 tabl

Vela, its X-ray nebula, and the polarization of pulsar radiation

The recent identification of the perpendicular mode of radio polarization as the primary one in the Vela pulsar by Lai et al. (2001) is interpreted in terms of the maser mechanism proposed by Luo & Melrose (1995). We suggest that such a mechanism may also be operative for the parallel mode which opens up the possibility of accounting for all types of polarization observed in pulsars. We propose an alternative interpretation of the arcs in the nebular X-radiation observed by Pavlov et al.(2000) & Helfand et al. (2001) with the Chandra Observatory, and interpreted by the latter as an equatorial wind. We interpret the arcs as traces of the particle beams from the two magnetic poles at the shock front. We also propose that the alignment with the rotation axis of the jet-like feature bisecting the arcs is an effect of projection on the sky plane and that there is no physical jet along the axis of rotation.Comment: 7 pages, 3 figures; version 2; accepted for publication in A&

Electroluminescence from Strained Ge membranes and Implications for an Efficient Si-Compatible Laser

We demonstrate room-temperature electroluminescence (EL) from light-emitting diodes (LED) on highly strained germanium (Ge) membranes. An external stressor technique was employed to introduce a 0.76% bi-axial tensile strain in the active region of a vertical PN junction. Electrical measurements show an on-off ratio increase of one order of magnitude in membrane LEDs compared to bulk. The EL spectrum from the 0.76% strained Ge LED shows a 100nm redshift of the center wavelength because of the strain-induced direct band gap reduction. Finally, using tight-binding and FDTD simulations, we discuss the implications for highly efficient Ge lasers.Comment: 4 Pages, 5 figure

A Pulsational Model for the Orthogonal Polarization Modes in Radio Pulsars

In an earlier paper, we introduced a model for pulsars in which non-radial oscillations of high spherical degree (\el) aligned to the magnetic axis of a spinning neutron star were able to reproduce subpulses like those observed in single-pulse measurements of pulsar intensity. The model did not address polarization, which is an integral part of pulsar emission. Observations show that many pulsars emit radio waves that appear to be the superposition of two linearly polarized emission modes with orthogonal polarization angles. In this paper, we extend our model to incorporate linear polarization. As before, we propose that pulsational displacements of stellar material modulate the pulsar emission, but now we apply this modulation to a linearly-polarized mode of emission, as might be produced by curvature radiation. We further introduce a second polarization mode, orthogonal to the first, that is modulated by pulsational velocities. We combine these modes in superposition to model the observed Stokes parameters in radio pulsars.Comment: 19 pages, 4 figures accepted Ap

Multidimensional effects on dissociation of N-2 on Ru(0001)

Theoretical Chemistr