Tabasum Rahnuma
Theoretical physicist · Gravitational waves & quantum gravity

The sky is the boundary.

The theory behind what LIGO and LISA hear: the asymptotic structure of spacetime, the symmetries and memories carried by gravitational waves, and the multipolar post-Minkowskian construction of the metrics behind the signal.

QUC Research Fellow, Korea Institute for Advanced Study (KIAS), Seoul

Explore the research Curriculum Vitae
Live: binary inspiral · merger · ringdown — and the strain it radiates
About

Dr. Tabasum Rahnuma

Portrait of Dr. Tabasum Rahnuma

I am a theoretical physicist working on gravitational waves — the theory underlying what detectors like LIGO and LISA observe. My research spans the asymptotic structure of spacetime: the infinite-dimensional symmetries at its boundaries, the permanent memories that passing waves imprint on detectors, and the soft theorems that tie both to quantum scattering.

The formalism I am most fond of these days is the multipolar post-Minkowskian expansion — describing a compact object, whether a star or a black hole, by its infinite tower of mass and current multipoles, and constructing its exterior metric recursively, order by order in Newton's constant.

I am a QUC Research Fellow at the Quantum Universe Center, Korea Institute for Advanced Study (KIAS), Seoul; previously a postdoctoral researcher at APCTP, Pohang. I completed my PhD in 2024 at IISER Bhopal, India, under the supervision of Dr. Nabamita Banerjee.

Away from the blackboard, I play the keyboard and spend my solitary hours reading.

Gravitational-wave physics · Quantum gravity · Asymptotic symmetries · Scattering amplitudes · Post-Minkowskian formalisms · Celestial & flat-space holography · General relativity

Research interests

Two routes into gravity's structure

Multipolar post-Minkowskian formalism · current focus

How does one compute the spacetime metric outside a real star? In Newtonian gravity the answer is the multipole expansion: the mass distribution is encoded in moments of increasing order ℓ, each falling off one power of 1/r faster than the last. An observer outside the smallest sphere enclosing the source can reconstruct the field from these moments alone.

re Source R x′ x |x| > R r = |x| |x − x′| ℓ = 0 ℓ = 1 ℓ = 2 ℓ = 3 ℓ = 4 1/r 1/r² 1/r³ 1/r⁴ 1/r⁵
The setting of the multipole expansion. A stationary source of size R sits at the origin; for any observer at |x| > R, the field 1/|x − x′| Taylor-expands into multipole moments, the order-ℓ moment falling off as 1/rℓ+1.

General relativity complicates this beautifully. Einstein's equations are nonlinear, so beyond leading order in Newton's constant G the multipoles do not stay separate: gravity itself gravitates, and the moments mix. The expansion becomes multipolar post-Minkowskian (MPM) — a double expansion in ℓ and in powers of G — and each higher order in G is built recursively by gluing products of lower-order moments:

ℓ Gⁿ G¹ G² G³ M M/r Sᵃ Sᵃ/r² Mᵃᵇ Mᵃᵇ/r³ Sᵃᵇ Sᵃᵇ/r⁴ Mᵃᵇᶜ Mᵃᵇᶜ/r⁵ M² M²/r² MSᵃ MSᵃ/r³ MMᵃᵇ, SᵃSᵇ MMᵃᵇ/r⁴ MᵃᵇSᶜ MᵃᵇSᶜ/r⁵ MᵃᵇMᶜᵈ M²ᵃᵇ/r⁶ GR mixes multipoles M³, M·M²ᵃᵇ, M·S², M·Mᵃᵇᶜ, Sᵃᵇᶜ, … recursive — rapidly growing ℓ = 0 ℓ = 1 ℓ = 2 ℓ = 3 ℓ = 4 Linear in multipole (1PM) Bilinear in multipole (2PM)
The multipolar post-Minkowskian (MPM) expansion. At order G the field is linear in the mass multipoles ML and current multipoles SL (blue). At G² Einstein's nonlinearity glues pairs of moments together (warm) — the monopole couples to the quadrupole, spins couple to spins — and from G³ onward the recursion compounds rapidly. Redrawn from my talk slides.

With P. H. Damgaard, Hojin Lee, and Kanghoon Lee, I develop recursive methods that organize exactly this structure and solve Einstein's equations directly — no scattering amplitudes, no worldlines. We have constructed the metric of a star of general composition to second post-Minkowskian order, and solved the Kerr black hole iteratively to fourth order in G and all orders in spin. One striking corollary: tweak a star's multipoles slightly away from the Kerr values and you obtain a horizonless object that mimics a black hole until probed very close to where the horizon would be. These constructions feed directly into precision modeling for gravitational-wave observables.

Asymptotic symmetries & the infrared structure of gravity

This program — beginning in my PhD work and continuing today — studies the symmetries living at the boundaries of spacetime and the physics they constrain. Using celestial conformal field theory techniques, my collaborators and I derived asymptotic symmetry algebras of Einstein–Yang–Mills, Einstein–Maxwell, and maximally supersymmetric 𝒩 = 8 supergravity, the latter via double copy methods. More recently we constructed a perturbative S-matrix for massive vector fields in anti-de Sitter space.

Asymptotic symmetries Memory effect Soft theorems
The infrared triangle (Strominger, 2017): three equivalent descriptions of the low-energy physics of gravity and gauge theory. Each edge is a precise mathematical equivalence.

The glossary below explains the key concepts; each entry stands on its own.

Post-Minkowskian expansion

The weak-field expansion of general relativity in powers of Newton's constant G, without assuming slow motion. A central open question is whether the series converges — which matters directly for the two-body problem behind gravitational-wave predictions.

Multipole expansion & black-hole mimickers

A star's exterior gravitational field is encoded in its infinite set of mass and current multipole moments. The Kerr black hole occupies one degenerate corner of this multipole space; tweaking the moments slightly away from the Kerr values yields a compact object with no horizon that is observationally Kerr-like until probed very close in — a black-hole mimicker.

Recursive metric construction

Instead of computing scattering amplitudes and extracting classical pieces, one solves the Einstein equations themselves iteratively: in harmonic gauge and Landau–Lifshitz variables, the field equations become recursion relations in momentum space, where each order is assembled from convolutions — the classical analogue of loop integrals — of all lower orders.

Gravitational memory effect

The passage of gravitational waves produces a permanent shift in the relative positions of a pair of inertial detectors. The peak sensitivities of LIGO and LISA may capture the memory's rise during a binary black hole merger — the inspiral, merger, and ringdown animated at the top of this page.

Asymptotic (BMS) symmetries

Symmetries are transformations of fields that leave physical observables invariant; asymptotic symmetries are those that survive far from the gravitational system. In four-dimensional asymptotically flat spacetime they form the infinite-dimensional BMS group, whose supertranslations relate the spacetime geometries before and after gravitational radiation passes.

Soft theorems

Symmetry constraints on scattering amplitudes in the low-energy regime. When one external particle — a photon or graviton "messenger" — is taken to zero energy, the amplitude factorizes into a lower-point amplitude times a universal soft factor, independent of the theory considered. Via Ward identities on the celestial sphere, the asymptotic symmetries reproduce exactly these theorems — closing the infrared triangle above.

Celestial holography & CCFT

Celestial Holography describes the physics of four-dimensional asymptotically flat Minkowski spacetime in terms of a quantum field theory on its boundary. In the compactified Penrose diagram below, the boundaries are the null surfaces ℐ⁺ and ℐ⁻, with a sphere at every point — so, in effect, we look at the sky to learn what happens inside the four-dimensional world. The field theory on that sphere is the Celestial Conformal Field Theory (CCFT).

i⁺ i⁻ i⁰ i⁰ ℐ⁺ ℐ⁻ Minkowski spacetime
Penrose diagram of flat spacetime. Radiation leaves through future null infinity ℐ⁺ — the "sky" where the celestial CFT lives. The dashed line is a light ray at 45°.
Double copy

A correspondence expressing gravity amplitudes as a "square" of gauge theory amplitudes. We used it to study soft and collinear limits in 𝒩 = 8 supergravity, importing gauge-theory technology into gravitational calculations.

For a non-specialist account of how symmetries probe the holographic universe, I recommend this Quanta Magazine article; its references are a good entry point to the literature.

Research notes

Notes & thesis

Self-contained notes that may assist researchers entering these areas.

Suggestions for modifications and corrections to the notes are highly appreciated.

Publications

Papers

Complete record on iNSPIRE-HEP →

Selected talks

Recent invited talks

A full list of talks, conferences, and research visits is in the CV.

Contact

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