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# Spacetime and Geometry: An Introduction to General Relativity

Classical and Quantum Gravity (Impact Factor: 3.1). 10/2005; 22(20):4385. DOI: 10.1088/0264-9381/22/20/B01

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**ABSTRACT:**We study the pseudoduality transformation in supersymmetric sigma models. We generalize the classical construction of pseudoduality transformation to supersymmetric case. We perform this both by component expansion method on manifold and by orthonormal coframe method on manifold . The component expansion method yields the result that pseudoduality tranformation is not invertible at all points and occurs from all points on one manifold to only one point where Riemann normal coordinates are valid on the second manifold. Torsion of the sigma model on must vanish while it is nonvanishing on , and curvatures of the manifolds must be constant and the same. In the case of super-WZW sigma models, pseudoduality equations result in three different pseudoduality conditions; identity, chiral and antichiral pseudoduality.International Journal of Modern Physics A 01/2012; 25(15). · 1.09 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**We consider a freely falling holographic screen for the Schwarzschild and Reissner–Nordström black holes and evaluate the entropic force à la Verlinde. When the screen crosses the event horizon, the temperature of the screen agrees to the Hawking temperature and the entropic force gives rise to the surface gravity for both of the black holes.Modern Physics Letters A 11/2011; 25(33). · 1.34 Impact Factor -
##### Article: Scope of Raychaudhuri equation in cosmological gravitational focusing and space-time singularities

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**ABSTRACT:**Indian scientist Amal Kumar Raychaudhuri established ‘Raychaudhuri equation’ in 1955 to describe gravitational focusing properties in cosmology. This equation is extensively used in general relativity, quantum field theory, string theory and the theory of relativistic membranes. This paper investigates the issue of the final fate of a gravitationally collapsing massive star and the associated cosmic censorship problems and space-time singularities therein with the help of Raychaudhuri equation. It is conjecture that the universe is emerged from a big bang singularity where all the known laws of physics break down. On the other hand, when the star is heavier than a few solar masses, it could undergo an endless gravitational collapse without achieving any equilibrium state. This happens when the star has exhausted its internal nuclear fuel which provides the outwards pressure against the inwards pulling gravitational forces. Then for a wide range of initial data, a space-time singularity must develop. It is conjecture that such a singularity of gravitational collapse from a regular initial surface must always be hidden behind the event horizon of gravity; this is called the cosmic censorship hypothesis. Thus cosmic censorship implies that the final outcome of gravitational collapse of a massive star must necessarily be a black hole which covers the resulting space-time singularity. So, causal message from the singularity cannot reach the external observer at infinity. Raychaudhuri equation plays a pioneer role in cosmology to describe the gravitational focusing and space-time singularities.Peak Journal of Physical and Environmental Science Research. 12/2013; 1(7):106-114.

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