The raychaudhuri type equations that we obtain in the paper, lead us to results on the evolution of both the 4d expansion and the 5d expansion in a 5d universe. Raychaudhuri, indian academy of sciences, bangalore. It was shown recently that replacing classical geodesics with quantal bohmian trajectories gives rise to a quantum corrected raychaudhuri equation qre. Historically speaking, it is the equation for one of the quantitites the expansion, which is termed as the raychaudhuri equation. This item does not appear to have any files that can be experienced. Reaksi ini disebut reaksi hipersensitif tipe cepat raychaudhuri equation pdf immediate type hypersensitivity. Even though the applications of the raychaudhuri equations are mostly confined to the domain of gr, it is. Lecture notes on general relativity matthiasblau albert einstein center for fundamental physics institut fu. Abstract as a homage to a k raychaudhuri, i derive in a straightforward way his famous equation and also indicate the problems he was last engaged in.
Howard percy robertson, was born in hoquiam, washington, on january 27, 1903, the oldest of five children of george duncan robertson, an engineer who built bridges in washington state, and anna mcleod, a nurse. Write out the raychaudhuri equation for the geodesics of comoving matter in the flrw universe and show that it is reduced to the second friedman equation. Pdf derivation of the raychaudhuri equation researchgate. Generalized raychaudhuris equation for null hypersurfaces. Raychaudhuri equation at the crossroads, a volume in honour of a. Raychaudhuris equation is fundamental for the analysis of behaviour of geodesic congruences. Pada pemeriksaan histopatologi akan nampak sebukan sel eosinofil. Kodama time, entropy bounds, the raychaudhuri equation, and. We describe the generalisation to congruences of solutions of arbitrary secondorder ordinary differential equations on a manifold. From this equation, we can infer that expansion decelerates in a universe dominated by ordinary matter or. General relativity, while ultimately based on the einstein equations, also allows one to quantitatively study. Energy conditions and the raychaudhuri equation universe in.
Beginning with a summary of the essential features of the original article by raychaudhuri and subsequent work of numerous authors, we move on to a discussion of the equations in the context of alternate nonriemannian spacetimes as well as other theories of gravity, with a special mention on the equations in spacetimes with torsion. A recent generalisation of the raychaudhuri equations for timelike geodesic congruences to. Userguided cytometric data analysis for largescale immunoprofiling studies. Pdf as a homage to a k raychaudhuri, i derive in a straightforward way his famous equation and also indicate the problems he was last. Raychaudhuri equation in the finslerranders spacetime and. The raychaudhuri equation enables to examine the whole spacetime structure without specific solutions of einsteins equations, playing a central role for the understanding of the gravitational. What links here related changes upload file special pages permanent link page information wikidata item cite this page. Kinematic quantities and raychaudhuri equations in a 5d. In the menu at the top, select view make sure thumbnails is checked in the dropdown menu. Trapped surfaces are spacelike 2surface in 4d whose ingoing and outgoing null. See section iv for derivation of the general form of raychaudhuri equations for three kinematical. Is the big bang singularity due to the strong symmetry of the friedmann lemaitrerobertsonwalker models due to the strong symmetry assumptions. Shortest distance along great circle longest distance along great circle conjugate points a b maximal geodesics predicted by global arguments, on the other hand.
Singularity theorems conjugate points due to raychaudhuri equation. These geometrical notions of the theory provide an insight to the nature of more general spacetimes. The most recent of which is the quantum raychaudhuri equation qre 3. Generalized raychaudhuri equations for strings and membranes sayan kar yz institute of physics, sachivalaya marg, bhubaneswar751005, india abstract a recent generalisation of the raychaudhuri equations for timelike geodesic. In general relativity, the raychaudhuri equation, or landau raychaudhuri equation, 1 is a fundamental result describing the motion of nearby bits of matter. Gravitational wave memory in cosmological spacetimes. In this thesis, the raychaudhuri equation, the choice of the coordinate system, the notions of surface gravity and of entropy, and restrictions on negative energy densities on the form of the quantum interest conjecture, will be discussed. The aim is to utilize this equation for investigating the dynamics of astrophysical high temperature abelian and nonabelian plasmas. If your open pdf has more than a single page, select a thumbnail in the lefthand side where you want to insert another pdf file. In general relativity, the raychaudhuri equation, or landau raychaudhuri equation, is a fundamental result describing the motion of nearby bits of matter the equation is important as a fundamental lemma for the penrosehawking singularity theorems and for the study of exact solutions in general relativity, but has independent interest, since it offers a simple and general validation of our.
Geodesic deviation, raychaudhuri equation, and tidal forces in modified gravity with an arbitrary curvaturematter coupling. Jul 31, 2007 the raychaudhuri equation is central to the understanding of gravitational attraction in astrophysics and cosmology, and in particular underlies the famous singularity theorems of general relativity theory. The raychaudhuri equation is central to the understanding of gravitational attraction in astrophysics and cosmology, and in particular underlies the famous singular. Expansion, rotation, shear what quantities characterise a. In general relativity, the raychaudhuri equation, or landauraychaudhuri equation, is a.
Amalgamated codazzi raychaudhuri identity for foliation. It is an intrinsic property of the volume expansion. In doing so, we introduce two families of observers. The derived relation between the parameters appears to depend on the relative scale of the system black hole, which could be. The raychaudhuri equations indian academy of sciences. Spacetime singularities and raychaudhuri equations core.
We generalize the raychaudhuri equation for the evolution of a self gravitating fluid to include an abelian and nonabelian hybrid magneto fluid at a finite. Pdf in general relativity, gravity is universally attractive, a feature embodied by the raychaudhuri equation which requires that the. It may be worthwhile to point out precisely, the work of landau, in relation to this equation. Jun 28, 2011 friends, i am studying the raychaudhuri equation. The derived relation between the parameters appears to depend on the relative scale of the system black hole, which could be read as a beta function equation for the quadratic. As of today we have 75,612,618 ebooks for you to download for free.
On the other hand, by the raychaudhuri equation we have e 4tr j j2 tr. In general relativity, the raychaudhuri equation, or landauraychaudhuri equation, is a fundamental result describing the motion of nearby bits of matter the equation is important as a fundamental lemma for the penrosehawking singularity theorems and for the study of exact solutions in general relativity, but has independent interest, since it offers a simple and general validation of our. It is shown how a pure background tensor formalism provides a concise but explicit and highly. Raychaudhuri, the raychaudhuri equation and its role in modern cosmology. Introduction to the application of dynamical systems theory. We study the evolution of timelike geodesics for two dimensional black hole spacetimes arising in string theory and general theory of relativity by solving the raychaudhuri equation for expansion. Say v is the timelike unit tangent vector of congruence of timelike geodesic. Joshi, 1996, global aspects in gravitation and cosmology, clarendon press oup, oxford the international series of monographs on physics, vol 87. As a homage to a k raychaudhuri, i derive in a straightforward way his famous equation and also indicate the problems he was last engaged in. Kodama time, entropy bounds, the raychaudhuri equation, and the.
However, in this article, we will refer to the full set of equations as raychaudhuri equations. Raychaudhuri equation this equation has the special characteristic that it is true without reference to the einstein equations. Pdf towards the raychaudhuri equation beyond general relativity. In this thesis, the raychaudhuri equation, the choice of the coordinate system, the notions of surface gravity and of. However, in view of the einstein equations see section 4. Beginning with a summary of the essential features of the original article by raychaudhuri and subsequent work of numerous authors, we move. On a raychaudhuri equation for hot gravitating fluids. The qre is derived from considering the pilot wave theory of quantum mechanics to assign to each particle moving in the congruence a semi. This essay follows the lecture which was given in honor of this great indian scientist and teacher on december 26, 2005 in puri, india. Pdf as a homage to a k raychaudhuri, i derive in a straightforward way his famous equation and also indicate the problems he was last engaged in.
On a raychaudhuri equation for hot gravitating fluids core. The raychaudhuri equation is sometimes referred to as the landauraychaudhuri equation. The raychaudhuri equation gives a sufficient condition to ensure that detgij 0, and therefore that a focal point or maybe a spacetime singularity develops. Submitted on 23 nov 2005, last revised 28 nov 2005 this version, v2 abstract. Pdf geodesic deviation, raychaudhuri equation, and tidal. On the raychaudhuri equation george f r ellis mathematics department, university of cape town, rondebosch, cape town, south africa email. But landau also deduced this equation, in independent way. Sergei winitzkis projects topics in general relativity. In general relativity, the raychaudhuri equation, or landau raychaudhuri equation, 1 is a fundamental result describing the motion of nearby bits of matter the equation is important as a fundamental lemma for the penrosehawking singularity theorems and for the study of exact solutions in general relativity, but has independent interest, since it offers a simple and general validation of. Raychaudhuris equation is one of the most important tools in investigating the evolution of such geodesics. Raychaudhuri, i derive in a straightforward way his famous equation. Llog 0 are determined from g, we deduce that tr is also determined. Raychaudhuri equation in the finslerranders spacetime and generalized scalartensor theories. The gup and quantum raychaudhuri equation sciencedirect.
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