arXiv subjects

Dawood Kothawala

Publications and source records attributed to Dawood Kothawala.

At least 19 recordsLinked to original sources

arXiv2026

Dynamical friction on black holes in scalar field environment

Astrophysical black holes exist within non-vacuum environments, and their motion through these environments generically result in a force on these black holes through processes such as dynamical friction and Bondi accretion. We explore these forces numerically for black holes moving through a complex scalar field of mass $m$ with constant acceleration $a$, while also revisiting the constant velocity case considered in the existing literature. The former is modeled by the C-metric, while we use Painlevé-Gullstrand metric with an additional divergence and vorticity free velocity field to mimic the constant velocity motion. Our simulations reveal several novel and interesting aspects of the drag force in both cases. For the constant velocity case, the force saturates at late times, with a value that depends on velocity in a manner distinct from known dependence. For the constant acceleration case, the force increases to a maximum value $F_\star$ and then reduces drastically, with $F_\star \approx 0.3~ m a$. Moreover, the density wake in this case shows revivals separated by decreasing time intervals.

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arXiv2026

Quantum nature of gravity and spacetime: Fundamental insights from the Hoyle-Narlikar theory

The Hoyle-Narlikar action-at-a-distance formulation for gravity remains one of the most mathematically rigorous attempts to incorporate Mach principle into physics. A lesser known, but no less significant, is the fact that it is also one of the first in which two point functions play a key role in determining spacetime structure, and hence, are more fundamental than the metric. We argue that these ingredients have direct relevance for modern attempts to understand fundamental, emergent, and informational aspects of quantum spacetime. The non-local description of quantum spacetime, with Planck scale $\ell_0$ as a zero-point length, provides a mechanism through which the entire universe can inform local causal structure, `a la Mach, Hoyle, and Narlikar. In this chapter, we highlight certain key aspects of the HN theory and then discuss case studies from modern research that illustrate how the quantum spacetime might realize a version of the quantum gravitational Mach principle.

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arXiv2026

When the Ringing Stops: Purely Imaginary Modes in the Ringdown Spectrum of Dynamical Black Holes

We extend the frequency-domain analysis of quasinormal modes in a dynamical, spherically symmetric black hole spacetime undergoing constant-rate mass evolution. In particular, we report a novel feature of the spectrum: the presence of purely imaginary eigenvalues in addition to the usual light-ring modes. We study the frequencies of these modes both analytically and numerically. The analytical calculation uses a novel formalism based on recent advances in connection coefficients of Heun functions. We then compute the frequencies numerically using a spectral method on hyperboloidal slices and find excellent agreement between the two approaches. Finally, we validate the frequency-domain results against an independent set of time-domain simulations. Our analysis shows that the purely imaginary modes govern the late-time signal through exponentially decaying tails. In the Schwarzschild limit, both frequency- and time-domain studies consistently show that the purely imaginary modes give rise to the familiar Schwarzschild power-law tail.

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arXiv2026

Geodesic structure of spacetime near singularities

Geodesic flows emanating from an arbitrary point $\mathscr{P}$ in a manifold $\mathscr{M}$ carry important information about the geometric properties of $\mathscr{M}$. These flows are characterized by Synge's world function and van Vleck determinant - important bi-scalars that also characterize quantum description of physical systems in $\mathscr{M}$. If $\mathscr{P}$ is a regular point, these bi-scalars have well known expansions around their flat space expressions, quantifying \textit{local flatness} and equivalence principle. We show that, if $\mathscr{P}$ is a singular point, the scaling behavior of these bi-scalars changes drastically, capturing the non-trivial structure of geodesic flows near singularities. This yields remarkable insights into classical structure of spacetime singularities and provides useful tool to study their quantum structure.

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arXiv2026

Microcanonical Phase Space and Entropy in Curved Spacetime

We discuss the structure of microcanonical ensembles in inertial and non-inertial frames attached to a confined system of positive energy particles in curved spacetime. Under certain physically reasonable assumptions that ensure the existence of such ensembles, we obtain, for microcanonical ensembles, exact analytical results in certain stationary spacetimes such as Rindler, Schwarzschild, and de Sitter along with leading curvature corrections in arbitrary curved spacetimes. For de Sitter, the exact results have interesting limits when the size of the system is comparable to $Λ^{-1/2}$. We further highlight two generic characteristics of the leading curvature corrections for a point particle system confined to a spherical or cubical box: (1) they are characterized by Ricci and Einstein tensors, and (2) their contribution is proportional to the bounding area. We argue that the area scaling in (2) does not hold for arbitrary box geometries. We also present a general argument to highlight two distinct sources of divergences in the phase space volume, coming from redshift and spatial geometry, and illustrate this by comparing and contrasting the results for (i) geodesic box in de Sitter, (ii) geodesic box in Schwarzschild, and (iii) uniformly accelerated box in Minkowski. Finally, we extend these results to $N$ particle systems in the restricted case of massless (ultra-relativistic) limit for static spacetimes, for which the results follow very simply from single particle results. Furthermore, we show that the ultra-relativistic expression for equipartition of energy in flat spacetimes continues to hold in static spacetimes.

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arXiv2025

Twin-paradox and Entanglement

We study the quantum version of the classical twin paradox in special relativity by replacing the twins with quantum detectors, and studying the transitions and entanglement induced by coupling them to a quantum field. We show that the \textit{changes} in direction of acceleration leave imprints on detector responses and entanglement, inducing novel features which might have relevance in black hole spacetimes.

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arXiv2025

Worldline EFT treatment of quadratic and cubic gravity theories

This paper explores modifications to General Relativity (GR) by considering higher-order curvature terms in the gravitational action, specifically focusing on the quadratic Ricci scalar and a particular cubic contraction of the Riemann tensor. These modifications introduce new interactions at short distances, potentially altering the dynamics of compact objects. We calculate the effective two-body binding potential energy for these modified theories to quantify these effects using the worldline effective field theory (WEFT) formalism. This approach allows us to systematically integrate out short-distance gravitational effects, capturing the modifications to the binding potential. Our results demonstrate how the quadratic Ricci scalar and cubic Riemann tensor terms contribute to the two-body interaction at the leading order, highlighting deviations from classical GR predictions. These findings offer insight into the potential observational signatures of modified gravity theories in binary systems and other astrophysical settings.

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arXiv2025

Entanglement between accelerated probes in a de Sitter spacetime

We initiate an investigation into features of vacuum entanglement as probed by accelerated quantum probes in curved spacetime. Focussing specifically on de Sitter (dS) spacetime with curvature $Λ$, we obtain several exact results corresponding to different kinematical set-up of the probes. The interaction with the quantum field creates a non-local correlation between initially uncorrelated probes accelerating in different directions. It is well known that a single quantum probe in dS spacetime with uniform acceleration $a$ responds exactly as a quantum probe in Minkowski spacetime with "effective" acceleration $q \equiv\sqrt{a^2+Λ}$. However, no such mapping generically exists for the entanglement between probes. Our results suggest that entanglement exhibits independent variations with changes in acceleration and curvature depending on different configurations of detector motion.

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arXiv2024

Non-inertial frames that can mimic gravitational fields

One version of the principle of equivalence, as originally formulated by Einstein, states that ``gravity" can be mimicked locally by going to an ``accelerated frame of reference". As highlighted by Synge, the physical content of this principle remains obscure in so far as it does not refer to the Riemann tensor $R_{abcd}$, which encodes the true effects of gravity. We here give the acceleration profile of a $Born$ rigid, Rindler$esque$, frame that can mimic a gravitational field corresponding to a given $R_{abcd}$. The generalised deviation equation that yields this result also has Centrifugal and Coriolis terms appearing in a purely relational context, yielding a similar connection between angular velocity of rotating, rigid inertial frames and the Riemann tensor. We comment briefly on implications for Mach principle.

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arXiv2024

Rotating detectors in dS/AdS spacetimes

We analyse several aspects of detectors with uniform acceleration $a$ and uniform rotation $Ω$ in de Sitter ($Λ>0$) and anti-de Sitter ($Λ<0$) spacetimes, focusing particularly on the periodicity, in (Euclidean) proper time $τ_{\rm traj}$, of geodesic interval $τ_{\rm geod}$ between two events on the trajectory. For $Λ<0$, $τ_{\rm geod}$ is periodic in ${\rm i} τ_{\rm traj}$ for specific values of $a$ and $Ω$. These results are used to obtain numerical plots for the response rate $\dot{\mathcal{F}}$ of Unruh-de Witt detectors, which display non-trivial combined effects of rotation and curvature through the dimensionless parameter $Λc^2/Ω^2$. In particular, periodicity does not imply thermality due to additional poles in the Wightman function away from the imaginary axis. We then present some results for stationary rotational motion in arbitrary curved spacetime, as a perturbative expansion in curvature.

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arXiv2024

Universal role of curvature in vacuum entanglement

We highlight some universal features concerning the role of spacetime curvature in the entanglement induced between quantum probes coupled to a quantum field in a suitable vacuum state. The probes are initially causally disconnected and non-entangled. We explore the parameter space $\{ω, d_0, \boldsymbol{v}_0\}$ spanned by the energy gap $ω$ of the detectors, and the initial values of separation distance $d_0$ and relative velocity $\boldsymbol{v}_0$, both covariantly defined in arbitrary curved spacetime. We also obtain numerical results in de Sitter spacetimes and use these to explore strong curvature regime, while also corroborating our perturbative results in arbitrary curved spacetime. Our analysis shows that curvature can induce entanglement features in certain regions of the above parameter space, in a manner which facilitates using entanglement as a probe of spacetime curvature.

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arXiv2024

Workshop on the limiting compactness objects: Black holes and Buchdahl stars

The workshop was organized at IUCAA on Oct 30 - Nov 3, 2023 as a compact discussion and discourse meeting with a threadbare exposition and discussion of the various aspects and the questions arising. It was occasioned by the visit of Professor Hakan Andreasson of the Gothenburg Technical University, Sweden. He has been exploring with his collaborators the Einstein - Vlasov system for over a decade and a half as a possible matter source for compact objects. This system characterizes itself by free particles in motion and interacting only through gravity. For a limiting compactness, this may be the most appropriate state. The main thrust of the workshop was to understand this new object, Buchdahl Star (BS), of limiting compactness without a horizon. It is almost as compact as a black hole (BH) and yet has no horizon and hence is open for interaction with the outside world. Ever since the proposal of the membrane paradigm envisaging a timelike fiducial surface near BH horizon, BS offers an excellent possibility of the existence of such a real astrophysical object. It could very well compete with BH as a mimicker for various physical and astrophysical phenomena. Thus, it opens up a new vista of study and investigation of all the questions that one asks for BH, for this new creature, BS. The workshop was intended to identify certain interesting questions as well as the people interested in studying them. On this count, the workshop has been a huge success as several interesting questions have been identified, a few groups have been formed to take up different problems, and the work has already started. Nothing more could one have asked from such an exercise. A brief summary of some of the talks is included, followed by a brief discussion of the projects identified as a result of the discussions during the workshop.

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arXiv2023

Limits of a non-local quantum spacetime

A generic implication of incorporating gravitational effects in the analysis of quantum measurements is the existence of a zero-point length of spacetime. This requires an inherently non-local description of spacetime, beyond the usual one based on metric $g_{ab}(x)$ etc. The quantum spacetime should instead be reconstructed from non-local bi-tensors of the form $\mathscr{G}_{ab \ldots i'j' \ldots}(x,x')$. A deeper look then reveals a subtle interplay interplay between non-locality and the limit $G\hbar/c^3 \to 0$. In particular, the so called emergent gravity paradigm -- in which gravitational dynamics/action/spacetime are emergent and characterised by an *entropy functional* -- arises as the Cheshire grin of a fundamentally non-local quantum spacetime. This essay describes the flow of metric with respect to Planck length, and proposes a novel action for the same.

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arXiv2023

Synge's World function and the quantum spacetime

All our observations that characterise space and time are expressed in terms of non-local, bi-tensorial objects such as geodesic intervals between events and two-point (Green) functions. In this contribution, I highlight the importance of characterising spacetime geometry in terms of such non-local objects, focusing particularly on two important bi-tensors that play a particular fundamental role -- Synge's World function and the van Vleck determinant. I will first discuss how these bi-tensors help capture information about spacetime geometry, and then describe their role in characterising quantum spacetime endowed with a lower bound, say $\ell_0$, on spacetime intervals. Incorporating such a length scale in a Lorentz covariant manner necessitates a description of spacetime geometry in terms of above bi-tensors, and naturally replaces the conventional description based on the metric tensor $g_{ab}(x)$ with a description in terms of a non-local bi-tensor $q_{ab}(x, y)$. The non-analytic structure of $q_{ab}(x, y)$ which renders a perturbative expansion in $\ell_0$ meaningless, also generically leaves a non-trivial ``relic" in the limit $\ell_0 \to 0$. I present some results where such a relic term is manifest; specifically, I will discuss how this: (i) suggests a description of gravitational dynamics different from the one based on Einstein-Hilbert lagrangian, (ii) implies dimensional reduction to $2$ at small scales, (iii) connects with the notion of cosmological constant itself being a non-local vestige of the small scale structure of spacetime, (iv) helps address the issues of spacetime singularities. I will conclude by discussing the ramifications of these ideas for quantum gravity.

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arXiv2023

Decoherence due to Spacetime Curvature

There has been considerable interest over the past years in investigating the role of gravity in quantum phenomenon such as entanglement and decoherence. In particular, gravitational time dilation is believed to decohere superpositions of center of mass of composite quantum systems. Since true effects of gravity are encoded in the curvature of spacetime, the universality of such decoherence must be characterized through components of Riemann tensor $R_{abcd}$, with a clear separation from non-inertial kinematic effects. We obtain the reduced density matrix of a composite system in a generic curved spacetime and express the decoherence time scale explicitly in terms of curvature. The decoherence in an inertial frame is caused by tidal acceleration. We also analyze the effects of self-gravity and show that the coupling of gravitational interaction with external curvature can not be captured by the replacement $m \to m + H_{\rm int}/c^2$.

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arXiv2022

Covariant formulation of Generalised Uncertainty Principle

We present a formulation of the generalised uncertainty principle based on commutator $\left[ {\hat x}^i, {\hat p}_j \right]$ between position and momentum operators defined in a covariant manner using normal coordinates. We show how any such commutator can acquire corrections if the momentum space is curved. The correction is completely determined by the extrinsic curvature of the surface $p^2=$ constant in the momentum space, and results in non-commutativity of normal position coordinates $\left[ {\hat x}^i, {\hat x}^j \right] \neq 0$. We then provide a construction for the momentum space geometry as a suitable four dimensional extension of a geometry conformal to the three dimensional relativistic velocity space - the Lobachevsky space - whose curvature is determined by the dispersion relation $F(p^2)=-m^2$, with $F(x)=x$ yielding the standard Heisenberg algebra.

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arXiv2021

Effect of tidal curvature on dynamics of accelerated probes

We obtain a remarkable semi-analytic expression concerning the role of purely tidal curvature on accelerated probes, revealing some novel insights into the role of absolute vs. tidal acceleration in the response of such probes. The key quantity we evaluate is the relation between geodesic ($τ_{\rm geod}$) and proper time ($τ_{\rm acc}$) intervals between events on the probe trajectory. This is obtained as a covariant power series in curvature using a combination of analytical and numerical tools. A serendipitous observation then reveals that one can $exactly$ sum all terms involving the $purely\;tidal$ component ${\mathscr E}_n= R_{abcd} \varepsilon^{ab} \varepsilon^{cd}$ of curvature, with $\varepsilon^{ab}$ the bi-normal to the plane of motion: $$ τ_{\rm geod} = \frac{2}{\sqrt{{-\mathscr E}_n}} \sinh ^{-1}\Biggl[\sqrt{\frac{-{\mathscr E}_n}{a^2-{\mathscr E}_n}} \sinh \left(\frac{1}{2} \sqrt{a^2-{\mathscr E}_n} \; τ_{\rm acc} \right) \Biggl] $$ For classical clocks, the above result represents an interesting closed form contribution of tidal curvature to the differential ageing of twins in the classic $Twin\;paradox$. For quantum probes, it gives a thermal contribution to the $detector\;response$ with a modified $Unruh\;temperature$ $$ [k_{\rm B} T]_{{\mathscr E}_n} = \frac{\hbar \sqrt{a^2- {\mathscr E}_n }}{2 π} $$ As an operational tool, the computational framework we present and the corresponding results should find applications to a wide range of physical problems that involve measurements and observations by use of accelerated probes in curved spacetimes.

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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.

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