arXiv subjects

Virinchi Rallabhandi

Publications and source records attributed to Virinchi Rallabhandi.

3 recordsLinked to original sources

arXiv2026

On toric self-dual Einstein gravitational instantons

We consider the classification of toric self-dual Einstein gravitational instantons with negative cosmological constant. As is well known, any Killing vector field on a self-dual Einstein manifold defines a local conformal K\"ahler structure. We prove that if the conformal K\"ahler structure associated to one of the torus Killing fields is global and extends to an ALE manifold with no additional fixed points, then the corresponding self-dual Einstein instanton is precisely given by the infinite class of multipole solutions constructed by Calderbank, Pedersen and Singer.

math.DG↗

arXiv2025

On energy bounds in asymptotically locally AdS spacetimes

This work considers positive energy theorems in asymptotically, locally AdS spacetimes. Particular attention is given to spacetimes where conformal infinity has compact, Einstein cross-sections admitting Killing or parallel spinors; a positive energy theorem is derived for such spacetimes in terms of geometric data intrinsic to the cross-section. This is followed by the first complete proofs of the BPS inequalities in (the bosonic sectors of) 4D and 5D minimal, gauged supergravity, including with magnetic fields, provided the Maxwell field is exact. The BPS inequalities are proven for asymptotically AdS spacetimes, but also generalised to the aforementioned class of asymptotically, locally AdS spacetimes.

gr-qc↗

arXiv2025

Spinorial quasilocal mass for spacetimes with negative cosmological constant

A new notion of quasilocal mass is defined for generic, compact, two dimensional, spacelike surfaces in four dimensional spacetimes with negative cosmological constant. The definition is spinorial and based on work for vanishing cosmological constant by Penrose and Dougan & Mason. Furthermore, this mass is non-negative, equal to the Misner-Sharp mass in spherical symmetry, equal to zero for every generic surface in AdS, has an appropriate form for gravity linearised about AdS and has an appropriate limit for large spheres in asymptotically AdS spacetimes.

gr-qc↗