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. PACS numbers: 04.20.Jb, 04.2.Cv, 98.80 Dr Let us consider a collection of bodies falling freely under their own gravity. They would all attract each other and would tend to converge. If they are expanding or contracting and their gravitational potential e...

This review is concerned with the gravitational self-force acting on a mass particle in orbit around a large black hole. Renewed interest in this old problem is driven by the prospects of detecting gravitational waves from strongly gravitating binaries with extreme mass ratios. We begin here with a summary of recent advances in the theory of gravitational self-interaction in curved spacetime, a...

Abstract Inspirals of stellar-mass objects into massive black holes will be important sources for the space-based gravitational-wave detector LISA. Modelling these systems requires calculating metric perturbation due to a point particle orbiting Kerr hole. Currently, linear is obtained with reconstruction procedure that puts it in ‘no-string’ radiation gauge which singular on surface surroundin...

The interaction of mass will determine the curvature of space-time, may determine that events proceed at different rates of time at each point in space, so each has a corresponding gravitational potential time. So we can find different values of gravity (g), corresponding to different times (t), thus making a "map of time in space." The space-time is curved by present mass, causing a force of a...

Gravitational Thomas Precession ( GTP ) is the name given to the Thomas Precession when the acceleration is caused by a gravitational force field. In continuation of our discussion on the idea of a GTP, in this note by way of considering the motion of a planet around the Sun, the GTP is shown to be a gravitomagnetic effect that a planet might experience while moving through a gravitational fiel...

In this paper, we propose a color image segmentation method based on gravitational clustering using neighbor relations in the spatial domain and distance information in RGB space among pixels. Most clustering-based segmentation algorithms use only color space distances after pixels are mapped from the spatial domain to color space, ignoring their neighbor relations; but we use both information....