9,078 research outputs found
Derivation of the Raychaudhuri Equation
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.Comment: 8 pages, latex file, Pedagogical, One technical incorrect statement
corrected and some minor rephrasin
Universal Velocity and Universal Force
In his monumental discoveries, the driving force for Einstein was, I believe,
consistency of concept and principle rather than conflict with experiment.
Following this Einsteinian dictum, we would first argue that homogeneity
(universal character) of space and time characterizes 'no force' (absence of
force) and leads to existence of a universal velocity while inhomogeneity
(again a universal property) characterizes curved spacetime and presence of a
universal force which is present everywhere and always. The former gives rise
to Special Relativity while the latter to General Relativity.Comment: 12 pages, latex. arXiv admin note: substantial text overlap with
physics/050509
The gravitational equation in higher dimensions
Like the Lovelock Lagrangian which is a specific homogeneous polynomial in
Riemann curvature, for an alternative derivation of the gravitational equation
of motion, it is possible to define a specific homogeneous polynomial analogue
of the Riemann curvature, and then the trace of its Bianchi derivative yields
the corresponding polynomial analogue of the divergence free Einstein tensor
defining the differential operator for the equation of motion. We propose that
the general equation of motion is for dimensions with the single coupling constant
, and is the usual Einstein equation. It turns out that
gravitational behavior is essentially similar in the critical dimensions for
all . All static vacuum solutions asymptotically go over to the Einstein
limit, Schwarzschild-dS/AdS. The thermodynamical parameters bear the same
relation to horizon radius, for example entropy always goes as and
so for the critical dimensions it always goes as . In terms of
the area, it would go as . The generalized analogues of the Nariai and
Bertotti-Robinson solutions arising from the product of two constant curvature
spaces, also bear the same relations between the curvatures and
respectively.Comment: latex, 5pages, Contribution to the Proceedings of the Conference,
Relativity and Gravitation: 100 years after Einstein in Prague, June 25-28,
201
On the quantum f-relative entropy and generalized data processing inequalities
We study the fundamental properties of the quantum f-relative entropy, where
f(.) is an operator convex function. We give the equality conditions under
monotonicity and joint convexity, and these conditions are more general than,
since they hold for a class of operator convex functions, and different for
f(t) = -ln(t) from, the previously known conditions. The quantum f-entropy is
defined in terms of the quantum f-relative entropy and we study its properties
giving the equality conditions in some cases. We then show that the
f-generalizations of the Holevo information, the entanglement-assisted
capacity, and the coherent information also satisfy the data processing
inequality, and give the equality conditions for the f-coherent information.Comment: 24 page
Black hole : Equipartition of matter and potential energy
Black hole horizon is usually defined as the limit for existence of timelike
worldline or when a spatially bound surface turns oneway (it is crossable only
in one direction). It would be insightful and physically appealing to find its
characterization involving an energy consideration. By employing the Brown-York
[1] quasilocal energy we propose a new and novel characterization of the
horizon of static black hole. It is the surface at which the Brown-York energy
equipartitions itself between the matter and potential energy. It is also
equivalent to equipartitioning of the binding energy and the gravitational
charge enclosed by the horizon.Comment: 6 pages, LaTeX versio
On ``minimally curved spacetimes'' in general relativity
We consider a spacetime corresponding to uniform relativistic potential
analogus to Newtonian potential as an example of ``minimally curved
spacetime''. We also consider a radially symmetric analogue of the Rindler
spacetime of uniform proper acceleration relative to infinity.Comment: 7 pages, LaTeX versio
A curious spacetime entirely free of centrifugal acceleration
In the Einstein gravity, besides the usual gravitational and centrifugal
potential there is an additional attractive term that couples these two
together. It is fun to enquire whether the latter could fully counteract the
centrifugal repulsion everywhere making the spacetime completely free of the
centrifugal acceleration. We present here such a curious spacetime metric and
it produces a global monopole like stresses going as in an AdS
spacetime.Comment: 3 pages, late
A duality relation : global monopole and texture
We resolve the entire gravitational field;i.e. the Riemann curvature into its
electric and magnetic parts. In general, the vacuum Einstein equation is
symmetric in active and passive electric parts. However it turns out that the
Schwarzschild solution, which is the unique spherically symmetric vacuum
solutions can be characterised by a slightly more general equation which is not
symmetric. Then the duality transformation, implying interchange of active and
passive parts will relate the Schwarzschlid particle with the one with global
monopole charge. That is the two are dual of each-other. It further turns out
that flat spacetime is dual to massless global monopole and global texture
spacetimes.Comment: 10 pages, LaTeX versio
Isothermal spherical perfect fluid model: Uniqueness and Conformal mapping
We prove the theorem: The necessary and sufficient condition for a
spherically symmetric spacetime to represent an isothermal perfect fluid
(barotropic equation of state with density falling off as inverse square of the
curvature radius) distribution without boundary is that it is conformal to the
``minimally'' curved (gravitation only manifesting in tidal acceleration and
being absent in particle trajectory) spacetime.Comment: 7 pages, TeX versio
General Relativity in Post Independence India
The most outstanding contribution to general relativity in this era came in
1953 (published in 1955 \cite{akr}) in the form of the Raychaudhri equation. It
is in 1960s that the observations began to confront the eupherial theory and
thus began exploration of GR as a legitimate physical theory in right earnest.
The remarkable discoveries of cosmic microwave background radiation, quasars,
rotating Kerr black hole and the powerful singularity theorems heralded a new
canvas of relativistic astrophysics and cosmology. I would attempt to give a
brief account of Indian participation in these exciting times.Comment: 27 pages, latex, Published in Current Science: Special Issue on 100
Years of General Relativity edited by Banibrata Mukhopadhya and T P Sing
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