arXiv subjects

Naresh Dadhich

Publications and source records attributed to Naresh Dadhich.

180 records · Page 10Linked to original sources

arXiv1998

A duality relation for fluid spacetime

We consider the electromagnetic resolution of gravitational field. We show that under the duality transformation, in which active and passive electric parts of the Riemann curvature are interchanged, a fluid spacetime in comoving coordinates remains invariant in its character with density and pressure transforming, while energy flux and anisotropic pressure remaining unaltered. Further if fluid admits a barotropic equation of state, $p = (γ- 1) ρ$ where $1 \leq γ\leq 2$, which will transform to $p = (\frac{2 γ}{3 γ- 2} - 1) ρ$. Clearly the stiff fluid and dust are dual to each-other while $ρ+ 3 p =0$, will go to flat spacetime. However the n $(ρ- 3 p = 0)$ and the deSitter $(ρ+ p = 0$) universes ar e self-dual.

gr-qc↗

arXiv1997

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.

gr-qc↗

arXiv1997

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.

gr-qc↗

arXiv1997

Inhomogeneous imperfect fluid spherical models without Big-Bang singularity

So far all known singularity-free cosmological models are cylindrically symmetric. Here we present a new family of spherically symmetric non-singular models filled with imperfect fluid and radial heat flow, and satisfying the weak and strong energy conditions. For large $t$ anisotropy in pressure and heat flux tend to vanish leading to a perfect fluid. There is a free function of time in the model, which can be suitably chosen for non-singular behaviour and there exist multiplicity of such choices.

gr-qc↗

arXiv1997

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.

gr-qc↗

arXiv1997

An ansatz for spacetimes of zero gravitational mass : global monopoles and textures

We propose a geometric ansatz, a restriction on Euclidean / Minkowski distance in the embedding space being propotional to distance in the embedded space, to generate spacetimes with vanishing gravitational mass ($R_{ik} u^i u^k = 0, u_i u^i = 1 $). It turns out that these spacetimes can represent global monopoles and textures. Thus the ansatz is a prescription to generate zero mass spacetimes that could describe topological defects, global monopoles and textures.

gr-qc↗

arXiv1997

On the third law of black hole dynamics

The third law of black hole dynamics states that the surface gravity (temperature) of black hole cannot be reduced to zero in finite sequence of physical interactions. We argue that the same is true when surface gravity is replaced by gravitational charge. We demonstrate that the prescribed window for infalling energy and radiation pinches off as extremality ($M^2 = a^2 + Q^2 $) is approached.

gr-qc↗

arXiv1997

On the Schwarzschild field

General relativity is a non-linear theory with the distinguishing feature that gravitational field energy also acts as gravitational charge density. In the well-known Schwarzschild solution describing field of an isolated massive body at rest, the scalar function $ϕ$ characterising the field acts as a gravitational potential as well as it curves space part of spacetime. We demonstrate explicitly that it is the latter property that accounts for the non-linear (gravity as its own source) aspect which is not explicit in usual derivations. It is worth noting that the Einstein vacuum equations ultimately reduce to the Laplace equation and its first integral which fixes zero of $ϕ$ at infinity. Thus the Schwarzschild field alongwith its asymptotic flat character is completely determined without application of any boundary condition by the field equations themselves. That means non-zero constant value of $ϕ$ will have non-vacuous effect. It in fact produces stresses exactly of the form required to represent a global monopole. By retaining freedom of choosing zero of $ϕ$, which will break asymptotic flatness, we can obtain the Schwarzschild black hole with global monopole charge. It is the non-linear aspect responsible for ``curving'' space, which has no Newtonian analogue, survives even when $ϕ$ is constant but not zero.

gr-qc↗

arXiv1997

Schwarzschild black hole with global monopole charge

We derive the metric for a Schwarzschild black hole with global monopole charge by relaxing asymptotic flatness of the Schwarzschild field. We then study the effect of global monopole charge on particle orbits and the Hawking radiation. It turns out that existence, boundedness and stability of circular orbits scale up by $(1-8 πη^2)^{-1}$, and the perihelion shift and the light bending by $(1-8 πη^2)^{-3/2}$, while the Hawking temperature scales down by $(1 - 8 πη^2)^2$ the Schwarzschild values. Here $η$ is the global charge.

gr-qc↗

arXiv1996

A Conformal Mapping and Isothermal Perfect Fluid Model

Instead of conformal to flat spacetime, we take the metric conformal to a spacetime which can be thought of as ``minimally'' curved in the sense that free particles experience no gravitational force yet it has non-zero curvature. The base spacetime can be written in the Kerr-Schild form in spherical polar coordinates. The conformal metric then admits the unique three parameter family of perfect fluid solution which is static and inhomogeneous. The density and pressure fall off in the curvature radial coordinates as $R^{-2}, $ for unbounded cosmological model with a barotropic equation of state. This is the characteristic of isothermal fluid. We thus have an ansatz for isothermal perfect fluid model. The solution can also represent bounded fluid spheres.

gr-qc↗

arXiv1996

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.

gr-qc↗

arXiv1995

A Class of Stationary Rotating String Cosmological Models

We obtain a one parameter class of stationary rotating string cosmological models of which the well-known G$\ddot o $del Universe is a particular case. By suitably choosing the free parameter function, it is always possible to satisfy the energy conditions. The rotation of the model hinges on the cosmological constant which turns out to be negative.

gr-qc↗

arXiv1994

The General Self-dual solution of the Einstein Equations

We obtain the most general explicit (anti)self-dual solution of the Einstein equations. We find that any (anti)self-dual solution can be characterised by three free functions of which one is harmonic. Any stationary (anti)self-dual solution can be characterised by a harmonic function. It turns out that the form of the Gibbons and Hawking multi-center metrics is the most general stationary (anti)self-dual solution. We further note that the stationary (anti)self-dual Einstein equations can be reinterpreted as the (anti)self-dual Maxwell equations on the Euclidean background metric.

gr-qc↗

arXiv1994

Uniqueness of the non-singular family and characterisation of cosmological models

We prove that for an orthogonal spacetime metric separable in space and time in comoving coordinates, the requirements of perfect fluid and non-singularity single out the unique family of singularity free cosmological models. Further homogeneous models could only be Bianchi I or FLRW while inhomogeneous ones can be with or without a singularity.

gr-qc↗

arXiv1994

Characterisation of orthogonal perfect fluid cosmological spacetimes

We consider the general orthogonal metric separable in space and time variables in comoving coordinates. We then characterise perfect fluid models admitted by such a metric. It turns out that the homogeneous models can only be either FLRW or Bianchi I while the inhomogeneous ones can only admit $G_2 $ (two mutually as well as hypersurface orthogonal spacelike Killing vectors) isometry. The latter can possess singularities of various kinds or none. The non-singular family is however unique and cylindrically symmetric.

gr-qc↗

arXiv1993

On Singularity Free Spacetimes--II : mid Geodesic Completeness

We study the geodesics of the singularity free metric considered in the preceding Paper I and show that they are complete. This once again demonstrates the absence of singularity. The geodesic completeness is established in general without reference to any particular matter distribution. The metric is globally hyperbolic and causally stable. The question of inapplicability of the powerful singularity theorems in this case is discussed.

gr-qc↗

arXiv1993

Singularity Free Spacetimes -- I :Metric and Fluid Models

We show that the metric for the singularity free family of fluid models [3] can be obtained by a simple and natural inhomogenisation and anisotropisation procedure from Friedman--Robertson--Walker metric with negative curvature. The metric is unique for cylindrically symmetric spacetime with metric potentials being separable functions of radial and time coordinates. It turns out that fluid models separate out into two classes, with $ρ\not= μp$ in general but $ρ= 3p$ in particular and $ρ= p$. It is shown that in both the cases radial heat flow can be incorporated without disturbing the singularity free character of the spacetime. Further by introducing massless scalar field it is possible to open out a narrow window for $μ, 4 \geq μ\geq 3$.

gr-qc↗

arXiv1993

Singularity Free Inhomogeneous Models with Heat Flow

We present a class of singularity free exact cosmological solutions of Einstein's equations describing a perfect fluid with heat flow. It is obtained as generalization of the Senovilla class [1] corresponding to incoherent radiation field. The spacetime is cylindrically symmetric and globally regular.

gr-qc↗