arXiv subjects

Sandipan Sengupta

Publications and source records attributed to Sandipan Sengupta.

At least 19 recordsLinked to original sources

arXiv2026

A Topological Origin of Black Hole Mass

We show that the notion of a black hole mass could be superceded by that of a topological charge in a spacetime without matter and curvature singularity. This feature emerges through a set new spacetime solutions of first order gravity in vacuum, named as bubble spacetimes, constructed here by weaving together the degenerate and nondegenerate metric phases. For a static bubble, the boundary surface connecting the two phases is characterized by a universal topological number. Notably, this surface coincides with the photon sphere of the conventional black hole irrespective of the presence of the cosmological constant. In contrast, a phase boundary located at the event horizon is shown to be topologically trivial. Thus, along with the black hole mass, the photon sphere also acquires a topological interpretation.

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arXiv2025

Galactic Spacetime Solutions with a Varying Newton's Coupling

We find a new family of galactic metrics corresponding to flat rotation curves at the outer radii. These are vacuum solutions to a gravity theory where the Newton's coupling varies mildly in space. The effective `mass', whose origin is purely geometric, receives a negative non-baryonic contribution. The angle of deflection of a light ray propagating in this geometry is found to be diminished rather than enhanced compared to the Einsteinian bending, the effect being highly suppressed though. Hence, these spacetimes are observationally dintinguishable from other geometric or `dark matter' based alternatives invoked to explain mass discrepancies in galaxies.

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arXiv2025

Cosmological Consequences of Varying Couplings in Gravity Action

We develop a Lagrangian formulation for gravity with matter where the gravitational couplings are universally treated as being field-dependent. The solutions for FLRW geometries and the associated time evolution of the Newton and cosmological couplings are found. The distance-redshift relations are shown to prefer a slowly growing Newton's coupling along with a negative equation of state ($w\geq -\frac{1}{3}$) for the matter fluid at the present epoch of accelerated expansion, while ruling out Dirac's large number hypothesis. We obtain an improved bound on $\dot{G}(t)$ as: $1.67\times 10^{-11} yr^{-1}<\frac{\dot{G}}{G}<3.34\times 10^{-11} yr^{-1}$ in the context of supernova cosmology, as well as a new constraint on $\dot{\Lambda}(t)$ as: $-0.67\times 10^{-11} yr^{-1}<\frac{\dot{\Lambda}}{\Lambda}<-1.34\times 10^{-11} yr^{-1}$. Based on this formulation, we also present a dynamical solution to the `cosmic coincidence' problem.

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arXiv2024

Exact Solutions with Asymptotically Flat Galactic Rotation Curves

We present a new set of spacetime solutions for spiral galaxies corresponding to flat rotation curves at large distances. These correspond to anisotropic pressure, which could be sourced by either matter or geometry. As examples, we elucidate the galactic metrics corresponding to the non-ideal generalizations of `dust' and `radiation', respectively. Further, we find a dynamical realization of the Einstein cluster when the spatially averaged equation of state (w) happens to be non-zero but small. The correction to the Einsteinian bending angle for a light ray penetrating a large galactic halo is predicted to be: $(2+3w)\pi v^2/(1+3w)c^2$, v being the limiting rotational velocity. We infer a mild decline of the rotation curves ($ v'(r) ~ 1/r^2 $) at large radii for sufficiently luminous galaxies, as also indicated by some specific observations.

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arXiv2023

A discrete discontinuity between the two phases of gravity

When tetrad (metric) fields are not invertible, the standard canonical formulation of gravity cannot be adopted as it is. Here we develop a Hamiltonian theory of gravity for non-invertible tetrad. In contrast to Einstein gravity, this phase is found to exhibit three local degrees of freedom. This reflects a discrete discontinuity in the limit of a vanishing tetrad determinant. For the particular case of vanishing lapse, the Hamiltonian constraint disappears from the classical theory upon fixing the torsional gauge-freedom. Any state functional invariant under the internal gauge rotations and spatial diffeomorphisms is a formal solution of the associated quantum theory. The formulation here provides a Hamiltonian basis to analyze gravity theory around a physical singularity, which corresponds to a zero of the tetrad determinant in curved spacetime.

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arXiv2023

Canonical Gravity in Degenerate Limit

We construct a limit of Hamiltonian gravity as the determinant of the spatial triad (and hence of the four-metric) goes to zero. Within the Barbero-Immirzi SU (2) formulation, we present two possible realizations of this limit, with the consequence that the Hamiltonian constraint becomes simpler and spatial diffeomorphisms become trivial. In the first case, the Hamiltonian constraint exhibits a polynomial structure, being formally similar to the Euclidean Hamitonian constraint of Sen-Ashtekar self-dual formulation. In the latter, the constraints become free from ordering ambiguity. Further, we show that the Carrollian gravity emerges as a special case of this degenerate limit, thus providing it a new geometric interpretation independent of the speed of light or any dimensionful coupling constant (G).

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arXiv2023

Hamiltonian form of `Carroll' gravity

We develop a Hamiltonian description of the `Carroll' (Levy Leblond-Sen Gupta) limit of gravity theory in the first-order formalism. Through a constraint analysis, the number of local degrees of freedom are shown to be two in this singular limit. The associated Hamiltonian constraint depends only on the densitized triad fields and their space derivatives. We also provide a scaling prescription within the Hilbert-Palatini theory to obtain the first-order analogue of the `electric' limit of canonical metric gravity. The simplicity of both these limiting Hamiltonian forms in these variables make them interesting candidates for quantization.

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arXiv2022

4D Einstein-Gauss-Bonnet Gravity From Non-Einsteinian Phase

We set up an Einstein-Gauss-Bonnet theory in four dimensions, based on the recent formulation of pure gravity with extra dimensions of vanishing metrical length [1]. In absence of torsion, the effective field equations depend only on the four-metric, reflecting a quadratic curvature nonlinearity but no higher than second order derivatives. In contrast with recent proposals to obtain 4dEGB theories through a singular rescaling of the Gauss-Bonnet coupling, this formalism requires no (classical) regularization of divergences and is inequivalent to Horndeski gravity, while being generally covariant and independent of compactification. Notably, the vacuum field equations admit FLRW cosmologies containing nonsingular bounce and self-accelerating Universe, and spherically symmetric black holes more general than Schwarzschild. The quadratic theory of gravity emerging here is shown to be preserved against the inclusion of higher Lovelock densities in 5+2n dimensions.

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arXiv2021

Two-dimensional gravity from vanishing metrical dimensions

We obtain a dynamical formulation of two-dimensional gravity from a non-Einsteinian phase in higher dimensions $(D=3+2n)$. The formalism is associated with (at least) one extra dimension of vanishing proper length, thus being inequivalent to either a Kaluza-Klein compactification or the Mann-Ross dimensional reduction defined upon a singular limit. The emergent solutions admit any arbitrary curvature in contrast with Jackiw-Teitelboim constant curvature gravity. We present the static and homogeneous solutions as explicit examples. The effective field equations are shown to remain unaffected by the inclusion of higher Lovelock terms beyond Einstein.

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arXiv2021

The Life and Science of Thanu Padmanabhan

Thanu Padmanabhan was a renowned Indian theoretical physicist known for his research in general relativity, cosmology, and quantum gravity. In an extraordinary career spanning forty-two years, he published more than three hundred research articles, wrote ten highly successful technical and popular books, and mentored nearly thirty graduate students and post-doctoral fellows. He is best known for his deep work investigating gravitation as an emergent thermodynamic phenomenon. He was an outstanding teacher, and an indefatigable populariser of science, who travelled very widely to motivate and inspire young students. Paddy, as he was affectionately known, was also a close friend to his students and collaborators, treating them as part of his extended academic family. On September 17, 2021 Paddy passed away very unexpectedly, at the age of sixty-four and at the height of his research career, while serving as a Distinguished Professor at the Inter-University Centre for Astronomy and Astrophysics, Pune. His untimely demise has come as a shock to his family and friends and colleagues. In this article, several of them have come together to pay their tributes and share their fond memories of Paddy.

physics.hist-ph↗

arXiv2021

Finite model of an electric charge

We set up a model of an electric charge where the noninvertible metric phase of first order gravity supercedes the point charge singularity in a curved spacetime. A topological interpretation of the electric charge is provided in terms of an index defined for the degenerate spacetime solution, being closely related to the Euler characteristic. The gravitational equations of motion at this phase are found to be equivalent to the laws of electrostatics. The associated field energy is finite and the geometry sourcing the charge is regular.

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arXiv2021

Magnetic monopole as a spacetime defect

We propose that the only possible realization of a magnetic pole is emergent, it being an artefact of a torsion defect in a curved spacetime. This special phase is characterized by a class of degenerate metric spacetime solutions of first order gravity in vacuum. The (apparent) magnetic charge is shown to have a topological origin, given by a lower dimensional counterpart of the Nieh-Yan index. At the invertible metric phase at a distance, this topological charge gets reflected as the (magnetic) Reissner-Nordstrom charge to an asymptotic observer, even though the defect itself remains hidden.

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arXiv2020

Gravity theory with a dark extra dimension

We set up a vacuum theory of gravity with an extra dimension of vanishing proper length. The most general solution to the field equations are presented. This formulation is free of Kaluza-Klein modes and does not allow the propagation of gravitons along the invisible fifth direction. Apart from a vacuum energy and radiation, the associated emergent theory exhibits a nonpropagating vector-tensor multiplet which has no analogue in standard Einstein gravity. It is naturally inert, obeys a bounded equation of state and has coupling properties radically different from ordinary matter. Based on these distinctive features, we propose that this geometric multiplet could supercede the hypothetical ``dark matter''. As further evidence in support of this possibility, we show that the galactic rotation curves are predicted to be asymptotically flat.

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arXiv2019

Schwarzschild phase without a black hole

We present a smooth extension of the Schwarzschild exterior geometry, where the singular interior is superceded by a vacuum phase with vanishing metric determinant. Unlike the Kruskal-Szekeres continuation, this solution to the first-order field equations in vacuum has no singularity in the curvature two-form fields, no horizon and no global time. The underlying non-analytic structure provides a distinct geometric realization of `mass' in classical gravity. We also find that the negative mass Schwarzschild solution does not admit a similar extension within the first-order theory. This is consistent with the general expectation that degenerate metric solutions associated with the Hilbert-Palatini Lagrangian formulation should satisfy the energy conditions.

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arXiv2019

Taming Dirac strings and timelike loops in vacuum gravity

The problem of singularities associated with Dirac strings and closed timelike curves in classical solutions of pure gravity is analyzed here. A method to eliminate these is introduced and established first for the Taub-NUT geometry. This is superceded by a smooth solution of first order field equations, which is defined to be a unique extension of the Taub Universe to a degenerate metric phase. As an additional feature, this framework naturally provides a geometric interpretation of the magnetic charge in the context of gravity theory without matter. Finally, exploiting the two phases of the metric determinant, we find a (smooth and unique) continuation of the Misner geometry as well, ridding it of closed timelike worldlines which exist in its otherwise Einsteinian manifestation.

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arXiv2018

Geometry of Two-Sheeted Spacetime Solutions

In contrast to Einstein's theory, the first order formulation of gravity turns out to be a natural habitat for double-sheeted spacetime solutions which satisfy the vacuum field equations everywhere. These bridge-like geometries exhibit degenerate tetrads at their core that separates the two sheets. Here we study the geodesics of these solutions and elucidate their causal structure. These spacetimes emerge as a classical realization of a two-universe solution in pure gravity. We also find the angle of deflection of light propagating in a bridge geometry. From this, we conclude that this spacetime would be indistinguishable from the Schwarzschild exterior when observed from asymptotia.

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arXiv2018

Time travel in vacuum spacetimes

The possibility of time travel through the geodesics of vacuum solutions in first order gravity is explored. We present explicit examples of such geometries, which contain degenerate as well as nondegenerate tetrad fields that are sewn together continuously over different regions of the spacetime. These classical solutions to the field equations satisfy the energy conditions.

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arXiv2017

Spacetime-bridge solutions in vacuum gravity

Spacetimes, which are representations of a bridge-like geometry in gravity theory, are constructed as vacuum solutions to the first order equations of motion. Each such configuration consists of two copies of an asymptotically flat sheet, connected by a bridge of finite extension where tetrad is noninvertible. These solutions can be classified into static and non-static spacetimes. The associated SO(3,1) invariant fields, namely the metric, affine connection and field-strength tensor, are all continuous across the hypersurfaces connecting the invertible and noninvertible phases of tetrad and are finite everywhere. These regular spacetime-bridge solutions do not have any analogue in Einsteinian gravity in vacuum.

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