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Naresh Dadhich

Publications and source records attributed to Naresh Dadhich.

At least 91 records · Page 5Linked to original sources
arXiv2013

Gravitational collapse in pure Lovelock gravity in higher dimensions

We study collapse of inhomogeneous dust and null dust (Vaidya radiation) in pure Lovelock gravity in higher dimensions. Since pure Lovelock gravity is kinematic in odd d=2N+1 dimension, hence pertinent dimension for the study is even d=2N+2, where N is degree of Lovelock polynomial. It turns out that pure Lovelock collapse favors naked singularity as against black hole for the Einstein case in the same dimension while strength of singularity as measured by divergence of Kretshmann scalar is interestingly the same in the two cases; i.e. the corresponding scalars have the same fall off behavior.

gr-qc↗
arXiv2013

On the static Lovelock black holes

We consider static spherically symmetric Lovelock black holes and generalize the dimensionally continued black holes in such a way that they asymptotically for large r go over to the d-dimensional Schwarzschild black hole in dS/AdS spacetime. This means that the master algebraic polynomial is not degenerate but instead its derivative is degenerate. This family of solutions contains an interesting class of pure Lovelock black holes which are the Nth order Lovelock Λ-vacuum solu- tions having the remarkable property that their thermodynamical parameters have the universal character in terms of the event horizon radius. This is in fact a characterizing property of pure Lovelock theories. We also demonstrate the universality of the asymptotic Einstein limit for the Lovelock black holes in general.

gr-qc↗
arXiv2012

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 $G^{(n)}_{ab} = -Λg_{ab} +κ_n T_{ab}$ for $d=2n+1, \, 2n+2$ dimensions with the single coupling constant $κ_n$, and $n=1$ is the usual Einstein equation. It turns out that gravitational behavior is essentially similar in the critical dimensions for all $n$. 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 $r_h^{d-2n}$ and so for the critical dimensions it always goes as $r_h, \, r_h^2$. In terms of the area, it would go as $A^{1/n}$. 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 $k_1=k_2$ and $k_1=-k_2$ respectively.

gr-qc↗
arXiv2012

Magnetic Penrose Process and Blanford-Zanejk mechanism: A clarification

The Penrose process (PP) is an ingenious mechanism of extracting rotational energy from a rotating black hole, however it was soon realized that it was not very efficient for its astrophysical applications for powering the central engine of quasars and AGNs. The situation however changed dramatically in the presence of magnetic field produced by the accretion disk surrounding the hole in the equatorial plane. In 1985, Wagh, Dhurandhar and Dadhich had for the first time considered the magnetic Penrose process (MPP) in which the magnetic field could now provide the energy required for a fragment to ride on negative energy orbit thereby overcoming the stringent velocity constraint of the original PP. Thus MPP turned very efficient and so much so that efficiency could now even exceed 100 percent. They had in principle established revival of PP for astrophysical applications in powering the high energy sources. MPP is however similar to the earlier discovered and well known Blandford-Znajeck (BZ) mechanism in which the rotational energy of the hole is extracted out through a purely electromagnetic process. Though both the processes use magnetic field as a device to extract rotational energy from the hole, yet their kernel is quite different in spirit. For the former magnetic field provides the threshold energy for particle to get onto negative energy orbit so that the other fragment goes out with enhanced energy while for the latter it generates an electric potential difference between the equatorial plane and the polar region, and it is the discharge of which that drives the energy flux out of the hole. In other words, MPP is still rooted in the spacetime geometry while BZ is essentially driven by electromagnetic interaction.

astro-ph.HE↗
arXiv2012

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 $~1/r^2$ in an AdS spacetime.

gr-qc↗
arXiv2012

On the equivalence of the Einstein-Hilbert and the Einstein-Palatini formulations of general relativity for an arbitrary connection

In the framework of the Einstein-Palatini formalism, even though the projective transformation connecting the arbitrary connection with the Levi Civita connection has been floating in the literature for a long time and perhaps the result was implicitly known in the affine gravity community, yet as far as we know Julia and Silva were the first to realise its gauge character. We rederive this result by using the Rosenfeld-Dirac-Bergmann approach to constrained Hamiltonian systems and do a comprehensive self contained analysis establishing the equivalence of the Einstein-Palatini and the metric formulations without having to impose the gauge choice that the connection is symmetric. We also make contact with the the Einstein-Cartan theory when the matter Lagrangian has fermions.

gr-qc↗
arXiv2012

Einstein is Newton with space curved

The two defining features of the Einsteinian gravity are that it is self interactive as well as it links universally to all particles including zero mass particles. In the process of obtaining the Schwarzshild solution for gravitational field of a mass point, we would demonstrate how are these features incorporated? We would also show, unlike the Newtonian gravity, why the gravitational potential in the Schwarzshild solution can have its zero only at infinity and nowhere else;i.e. it is determined absolutely. We also consider particle orbits to expose certain insightful and subtle points of concept and principle.

gr-qc↗
arXiv2012

The Lovelock gravity in the critical spacetime dimension

It is well known that the vacuum in the Einstein gravity, which is linear in the Riemann curvature, is trivial in the critical (2+1=3) dimension because vacuum solution is flat. It turns out that this is true in general for any odd critical $d=2n+1$ dimension where $n$ is the degree of homogeneous polynomial in Riemann defining its higher order analogue whose trace is the nth order Lovelock polynomial. This is the "curvature" for nth order pure Lovelock gravity as the trace of its Bianchi derivative gives the corresponding analogue of the Einstein tensor \cite{bianchi}. Thus the vacuum in the pure Lovelock gravity is always trivial in the odd critical (2n+1) dimension which means it is pure Lovelock flat but it is not Riemann flat unless $n=1$ and then it describes a field of a global monopole. Further by adding Lambda we obtain the Lovelock analogue of the BTZ black hole.

gr-qc↗
arXiv2011

FLRW cosmology in Weyl-Integrable Space-Time

We investigate the Weyl space-time extension of general relativity (GR) for studying the FLRW cosmology through focusing and defocusing of the geodesic congruences. We have derived the equations of evolution for expansion, shear and rotation in the Weyl space-time. In particular we consider the Starobinsky modification, $f(R)=R+βR^2-2Λ$, of gravity in the Einstein-Palatini formalism, which turns out to reduce to the Weyl integrable space-time (WIST) with the Weyl vector being a gradient. The modified Raychaudhuri equation takes the form of the Hill-type equation which is then analysed for studying formation of the caustics. In this model, it is possible to have a Big Bang singularity free cyclic Universe but unfortunately the periodicity turns out to be extremely short.

gr-qc↗
arXiv2011

Thermodynamical universality of the Lovelock black holes

The necessary and sufficient condition for the thermodynamical universality of the static spherically symmetric Lovelock black hole is that it is the pure Lovelock Λ-vacuum solution. By universality we mean the thermodynamical parameters: temperature and entropy always bear the same relationship to the horizon radius irrespective of the Lovelock order and the spacetime dimension. For instance, the entropy always goes in terms of the horizon radius as rh and r^2 respectively for h odd and even dimensions. This universality uniquely identifies the pure Lovelock black hole with Λ.

gr-qc↗
arXiv2011

On the measure of spacetime and gravity

By following the general guiding principle that nothing should be prescribed or imposed on the universal entity, spacetime, we establish that it is the homogeneity (by which we mean homogeneity and isotropy of space and homogeneity of time) that requires not only a universally constant invariant velocity but also an invariant length given by its constant curvature, $Λ$ and spacetime is completely free of dynamics. Thus $c$ and $Λ$ are the only two true constants of the spacetime structure and no other physical constant could claim this degree of fundamentalness. When matter is introduced, the spacetime becomes inhomogeneous and dynamic, and its curvature then determines by the Bianchi differential identity the equation of motion for the Einstein gravity. The homogeneity thus demands that the natural state of \textit{free spacetime} is of constant curvature and the cosmological constant thus emerges as a clear prediction which seems to be borne out by the observations of accelerating expansion of the Universe. However it has no relation to the vacuum energy and it could be envisioned that in terms of the Planck area the Universe measures $10^{120}$ units!

gr-qc↗
arXiv2011

Universal features of gravity and higher dimensions

We study some universal features of gravity in higher dimensions and by universal we mean a feature that remains true in all dimensions $\geq4$. They include: (a) the gravitational dynamics always follows from the Bianchi derivative of a homogeneous polynomial in Riemann curvature and it thereby characterizes the Lovelock polynomial action, (b) all the $Λ$-vacuum solutions of the Einstein-Lovelock as well as pure Lovelock equation have the same asymptotic limit agreeing with the $d$ dimensional Einstein solution and (c) gravity inside a uniform density sphere is independent of the spacetime dimension and it is always given by the Schwarzschild interior solution.

gr-qc↗
arXiv2011

On the enigmatic $Λ$ - a true constant of spacetime

Had Einstein followed the Bianchi differential identity for the derivation of his equation of motion for gravitation, $Λ$ would have emerged as a true new constant of spacetime on the same footing as the velocity of light? It is then conceivable that he could have perhaps made the most profound prediction that the Universe may suffer accelerated expansion some time in the future! Further we argue that its identification with the quantum vacuum energy is not valid as it should have to be accounted for like the gravitational field energy by enlarging the basic framework of spacetime and not through a stress tensor. The acceleration of the expansion of the Universe may indeed be measuring its value for the first time observationally.

gr-qc↗
arXiv2010

On Lovelock vacuum solution

We show that the asymptotic large $r$ limit of all Lovelock vacuum and electrovac solutions with $Λ$ is always the Einstein solution in $d \geq 2n+1$ dimensions. It is completely free of the order $n$ of the Lovelock polynomial indicating universal asymptotic behaviour.

hep-th↗
arXiv2010

Radiating black holes in Einstein-Yang-Mills theory and cosmic censorship

Exact nonstatic spherically symmetric black-hole solution of the higher dimensional Einstein-Yang-Mills equations for a null dust with Yang-Mills gauge charge are obtained by employing Wu-Yang \textit{ansatz}, namely, HD-EYM Vaidya solution. It is interesting to note that gravitational contribution of YM gauge charge for this ansatz is indeed opposite (attractive rather than repulsive) that of Maxwell charge. It turns out that the gravitational collapse of null dust with YM gauge charge admit strong curvature shell focusing naked singularities violating cosmic censorship. However, there is significant shrinkage of the initial data space for a naked singularity of the HD-Vaidya collapse due to presence of YM gauge charge. The effect of YM gauge charge on structure and location of the apparent and event horizons is also discussed.

gr-qc↗
arXiv2010

Characterization of the Lovelock gravity by Bianchi derivative

We prove the theorem: The second order quasi-linear differential operator as a second rank divergence free tensor in the equation of motion for gravitation could always be derived from the trace of the Bianchi derivative of the fourth rank tensor, which is a homogeneous polynomial in curvatures. The existence of such a tensor for each term in the polynomial Lagrangian is a new characterization of the Lovelock gravity.

gr-qc↗
arXiv2010

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.

physics.gen-ph↗