arXiv subjects

Naresh Dadhich

Publications and source records attributed to Naresh Dadhich.

At least 19 recordsLinked to original sources

arXiv2026

On the stability of the objects of limiting compactness: Black hole and Buchdahl star

In General Relativity, there exist two objects of limiting compactness, one with a null boundary defining the horizon of a black hole and the other with a timelike boundary defining a Buchdahl star. The two are characterized by gravitational energy equal to or half the mass. Since non-gravitational mass-energy is the source of gravitational energy, both of these objects are manifestly stable. We demonstrate in this letter, in a simple and general way, that the equilibrium state defining the object is indeed stable, independent of the nature of the perturbation.

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arXiv2025

On the Limitations of a Generalized Vaidya Metric

We prove that there can not be a smooth matching of the Generalized Vaidya metric with an exterior Schwarzschild/Vaidya patch across a finite boundary hypersurface unless the mass function is a function of the null coordinate alone. By explicitly deriving the extrinsic curvature components, we show that for $\partial m / \partial r \neq 0$ one has a discontinuity in the curvature and induces a surface stress-energy tensor, corresponding to a thin shell of matter. This discontinuity also appears in the geometric invariant $\mathcal{K} = K_{ab}K^{ab}$ and in the Kodama current, indicating a mismatch in quasi-local energy flux across the boundary. The analysis of timelike geodesics leads to the same condition, reinforcing that the generalized Vaidya geometry with $\partial m / \partial r \neq 0$ cannot represent a consistent stellar interior bounded by a regular surface. We therefore note that the generalized Vaidya spacetime should be interpreted as an unbounded geometry with intrinsic heat flux rather than a viable bounded source.

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arXiv2025

The Third Law of Black Hole Dynamics in Lovelock Gravity

The third law of black hole dynamics states that it is impossible, through any classical perturbation of a stationary configuration, to reduce the surface gravity of a black hole to zero. In this work, we examine the validity of this law for static, spherically symmetric charged black holes in the Lovelock theory of gravity. By studying infinitesimal variations in mass and charge, we derive a set of inequalities that constrain these variations. Our analysis shows that as the surface gravity approaches zero ($\kappa \to 0$), the range of admissible perturbations gradually diminishes, thereby forbidding the attainment of extremality through any finite classical process. The saturation of the inequality is interpreted as the emergence of a dynamical barrier near extremality, which prevents further evolution toward the extremal configuration.

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arXiv2025

Buchdahl stars and bounds with cosmological constant

The Schwarzschild interior solution, when combined with the assumption of a finite central pressure, leads to the well-known Buchdahl bound. This bound establishes an upper limit on the mass-to-radius ratio of an object, which is equivalent to imposing an upper limit on the gravitational potential. Remarkably, this limit exhibits considerable universality, as it applies to a broader class of solutions beyond the original Schwarzschild interior metric. By reversing this argument, one can define the most compact horizonless object that satisfies this gravitational bound. Intriguingly, the same bound arises when applying the Virial theorem to an appropriately chosen combination of gravitational and potential energy. In this work, we explore the generalised Buchdahl compactness bound in the presence of a cosmological constant. We investigate its implications, define a suitable gravitational energy and an associated potential energy that incorporate the cosmological term, and demonstrate that the universality of the Buchdahl bound persists. However, we also observe that different bounds emerge depending on the chosen approach.

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arXiv2025

On electrogravity duality and black hole with global monopole

By resolving the Riemann curvature into electric and magnetic parts, Einstein's equation can accordingly be written in terms of electric (active and passive) and magnetic parts. The electrogravity duality is defined by the interchange of active and passive parts. It turns out that in static and stationary spacetimes, there is a subset of the equations (that identifies the effective vacuum equation) that is sufficient to yield the vacuum solution. In spherically symmetric spacetime, the electrograv dual of the effective equation solves to give the Schwarzschild black hole with a global monopole. Interestingly, this is not so for axial symmetry, where the Kerr vacuum solution turns out to be electrograv self-dual. However, in the asymptotic limit where the effect of rotation dies out, the situation reverts to the static case, admitting a global monopole. This is also what follows when we apply the Newman-Janis transformation to the static black hole with a global monopole.

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arXiv2025

Relativistic Virial Theorem, Limiting Compactness, and the end state of gravitational collapse

It is noteworthy that limiting compactness of a static bounded configuration is characterized by a general principle: \textit{one, by equipartition of mass between inside and outside, and the other by vanishing of energy inside.} The former implies gravitational energy being half of mass leading to limiting compactness $M/R = 4/9$ of Buchdahl star while for the latter, the two are equal giving $M/R = 1/2$ of black hole with horizon. \emph{This is the relativistic Virial theorem respectively for massive and massless particles.} It is remarkable that it prescribes that there can exist only two equilibrium states which also define limiting compactness of the object. Consequently, it leads to a profound prediction that the ultimate endproduct of gravitational collapse could only be one of the two, Buchdahl star or black hole.

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arXiv2024

Accreting Black Holes radiate classical Vaidya radiation to pave way for Hawking radiation

It is well known that locally defined marginally outer trapped surface (MOTS) is null and coincident with the event horizon of an unperturbed static Schwarzschild black hole. This is however not true for an accreting black hole for which MOTS separates out and turns spacelike. In this letter, we obtain the necessary and sufficient condition for MOTS to remain null and coincident with the event horizon even when matter is continuously accreting on. This also has an important bearing on the quantum Hawking radiation which is supposed to emanate from the MOTS, and it cannot propagate out to infinity unless MOTS is null. The condition is, infalling timelike Type I fluid should turn null or Type II, as it falls on the horizon. This transition from timelike to null is caused by the tidal deformation of the infalling fluid, and that produces an outward directed heat flux giving rise to Vaidya radiation emanating out of the boundary of accreting zone. We thus predict a remarkable new phenomena that accreting black hole radiates classical Vaidya radiation that paves the way for the Hawking radiation.

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arXiv2024

Energetics of Buchdahl stars and the magnetic Penrose process

Buchdahl star is the most compact object without an event horizon and is an excellent candidate for a black hole mimicker. Unlike black holes, rotating Buchdahl star can be over-extremal with respect to the black hole, sustaining a larger spin. We show that it can also develop an ergosphere above the threshold spin $\beta > 1/\sqrt{2}$, which allows extraction of its rotational energy. Electromagnetic field around Buchdahl star is also expected to differ from that of black hole in both strength and topology. In this paper, we explore the energetics of Buchdahl star focusing on the magnetic Penrose process in the two magnetic field configurations, i.e., uniform and dipole. Below the threshold spin, Buchdahl star is expected to be quiet, while above the threshold it can be much more efficient than the black hole if a dipolar magnetic field is developed on its surface.

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arXiv2024

C. V. Vishveshwara (Vishu) On The Black Hole Trek

With his seminal and pioneering work on the stability of the Schwarzschild black hole and its interaction with gravitational radiation, Vishu had opened a new window on black hole astrophysics. One of the interesting results that soon followed was that "a black hole has no hair", it is entirely specified by the three parameters, mass, spin and charge, and nothing more. The discovery of gravitational waves in 2016 produced by merger of two black holes, and observed by the Ligo-Virgo collaboration, carried the definitive signature of quasi-normal modes, the phenomenon of black hole ringdown, exactly what Vishu had predicted in his 1970 Nature paper~(See Isaacson's commentary) 46 years ago. This was the crowning glory.

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arXiv2023

Gravitational Collapse in pure Gauss-Bonnet gravity

We study the process of gravitational collapse in pure Gauss-Bonnet gravity. In the homogeneous dust collapse, we show that the $D=7$ pure Gauss-Bonnet theory has gravitational dynamics indistinguishable from Einstein's theory in $D=4$, meaning that collapsing particle feel the same potential as in the classical 4-dimensional general relativistic case. In $D<7$ pure Gauss-Bonnet gravity becomes weaker, while in $D>7$ it becomes stronger, with respect to General Relativity. In the inhomogeneous dust collapse we find the mass modes in the expansion of the energy density in any dimensions that lead to either naked singularities or black holes as final states of collapse.

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arXiv2023

The Buchdahl Bound Denotes The Geometrical Virial Theorem

In this paper, we geometrically establish yet another correspondence between Newtonian mechanics and general relativity by connecting the Buchdahl bound and the Virial theorem. Buchdahl stars are defined by the saturation of the Buchdahl bound, $\Phi(R) \leq 4/9$ where $\Phi(R)$ is the gravitational potential felt by a radially falling particle. An interesting alternative characterization is given by gravitational energy being half of non-gravitational energy. With insightful identification of the former with kinetic and the latter with potential energy, it has been recently argued that the equilibrium of a Buchdahl star may be governed by the Virial theorem. In this paper, we provide a purely geometric version of this theorem and thereby of the Buchdahl star characterization. We show that the condition for an accreting Buchdahl star to remain in the state of Virial equilibrium is that it must expel energy via heat flux, appearing in the exterior as Vaidya radiation. If that happens then a Buchdahl star continues in the Virial equilibrium state without ever turning into a black hole.

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arXiv2022

On the equilibrium of the Buchdahl star

The Buchdahl star is the limiting compactness (which is indicated by sturation of the Buchdahl bound) object without horizon. It is in general defined by the potential felt by radially falling timelike particle, $\Phi(R) = 4/9$, in the field of a static object. On the other hand black hole is similarly characterized by $\Phi(R)=1/2$ which defines the horizon. Further it is remarkable that in terms of gravitational and non-gravitational energy, the Buchdahl star is alternatively defined when gravitational energy is half of non-gravitational energy while the black hole when the two are equal. When an infinitely dispersed system of bare mass $M$ collapses under its own gravity to radius $R$, total energy encompassed inside $R$ would be $E_{tot}(R)=M-E_{grav}(R)$. That is, energy inside the object is increased by the amount equivalent to gravitational energy lying outside and which manifests as internal energy in the interior. If the interior consists of free particles in motion interacting only through gravity as is the case for the Vlasov kinetic matter, internal (gravitational) energy could be thought of as kinetic energy and the defining condition for the Buchdahl star would then be kinetic (gravitational) energy equal to half of non-gravitational (potential) energy. Consequently it could be envisaged that equilibrium of the Buchdahl star interior is governed by the celebrated Virial theorem like relation (average kinetic energy equal to half of average potential energy). On the same count the black hole equilibrium is governed by equality of gravitational and non-gravitational energy !

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arXiv2022

Strong cosmic censorship conjecture for a charged AdS black hole

The strong cosmic censorship conjecture states (SCCC) that one cannot extend spacetime beyond the Cauchy horizon with a square-integrable connection. This conjecture was postulated to save the deterministic nature of the most successful theory of gravitation, general relativity. In order to explore the validation/violation of the SCCC for the charged anti-de Sitter black hole spacetime, we compute the ratio of the imaginary part of the quasinormal mode frequencies and the surface gravity at the Cauchy horizon both analytically and numerically. The lowest value of which defines the key parameter $β$ determining the fate of SCCC where $β< 1/2$ indicates validation and else violation. We show that $β> 1/2$ for a charged AdS black hole with the dissipative boundary conditions in the near extremal region. Thus the SCCC is violated for this spacetime.

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arXiv2022

Like Black holes, Buchdahl stars cannot be extremalized

It was shown long back in \cite{Dadhich97} that a non-extremal black hole cannot be converted into an extremal one by test particle adiabatic accretion. The Buchdahl star is the most compact object without horizon and is defined by $\Phi(R) = 4/9$, while black hole by $\Phi(R) = 1/2$. Here $\Phi(R)$ is the gravitational potential experienced by a particle, radially falling for static and axially for the rotating object. In this short note we examine the question of extremalization of the Buchdhal star and show that the same result holds good as for the black hole. That is, a non-extremal Buchdahl star cannot be extremalized by test particle accretion. Further since extremal limit for BS is $>1$, it could facilitate formation of extremal black holes by neutral and spinless accretion. That is perhaps the only way they could be formed.

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arXiv2022

Fundamental forces and their dynamics

In this essay, we wish to propose a general principle: \it{the equation of motion or dynamics of a fundamental force should not be prescribed but instead be entirely driven by geometry of the appropriate spacetime manifold, and the equation is then obtained by employing only the geometric property without appeal to an action.} The motivation for this pronouncement comes from the fact that the equation of motion of general relativity follows from the geometry of Riemannian spacetime manifold without appeal to anything else from outside. The driving differential geometric property is the Bianchi identity satisfied by the Riemann curvature tensor. Similarly it is geometry of the principal tangent bundle of fibre spacetime manifold that may account for dynamics of the gauge vector fields. It is the classical electric force for the Abelian gauge symmetry group while the non-Abelian symmetry leads to the non-Abelian forces, the weak and the strong. We shall also reflect on a unified picture of the basic forces, and the duality correspondences it may inspire.

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arXiv2022

Weak cosmic censorship conjecture in the pure Lovelock gravity

It is well known that a rotating black hole in four dimension could be overspun by linear order test particle accretion which however always gets overturned when non-linear perturbations are included. It turns out that in the Einstein gravity, repulsion due to rotation dominates over attraction due to mass in dimensions, $D>5$, and consequently black hole cannot be overspun even for linear order accretion. For the pure Lovelock rotating black hole, this dimensional threshold is $D>4N+1$ where $N$ is degree of single $N$th order term in the Lovelock polynomial in the action. Thus the pure Lovelock rotating black holes always obey the weak cosmic censorship conjecture (WCCC) in all dimensions greater than $4N+1$. Since overall gravity being repulsive beyond this dimensional threshold, how is rotating black hole then formed there?

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arXiv2022

Novel way to the metric of higher dimensional rotating black holes

We wish to carry forward to higher dimensions the insightful and novel method of obtaining the Kerr metric proposed by one of us [Gen. Relativ. Gravit. 45, 2383 (2013)] for deriving the Myers-Perry rotating black hole metric. We begin with a flat spacetime metric written in oblate spheroidal coordinates (ellipsoidal geometry) appropriate for the inclusion of rotation, and then introduce arbitrary functions to introduce a gravitational potential due to mass, which are then determined by requiring that a massless particle experiences no acceleration, while a massive particle feels Newtonian acceleration at large r. We further generalize the method to include the cosmological constant Λ to obtain the MyersPerry de Sitter/antide Sitter black hole metric.

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arXiv2022

Strong cosmic censorship conjecture for a charged BTZ black hole

The strong cosmic censorship conjecture, whose validation asserts the deterministic nature of general relativity, has been studied for charged BTZ black holes in three dimensional general relativity, as well as for Nth order pure Lovelock gravity in d=2N+1 spacetime dimensions. Through both analytical and numerical routes, we have computed the ratio of the imaginary part of the quasi-normal mode frequencies with the surface gravity at the Cauchy horizon. The lowest of which corresponds to the key parameter associated with violation of strong cosmic censorship conjecture. Our results demonstrate that this parameter is always less than the critical value $(1/2)$, thereby respecting the strong cosmic censorship conjecture. This is in complete contrast to the four or, higher dimensional black holes, as well as for rotating BTZ black hole, where the violation of strong cosmic censorship conjecture exists. Implications and possible connection with the stability of the photon orbits have been discussed.

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