I work on a variety of mathematical problems arising in general relativity. These problems have intersections with hyperbolic partial differential equations and geometric analysis. Some of the directions that I have been actively pursuing are mentioned below.  

Publications

1. Deformations of the Kerr-(A)dS near horizon geometry (with Eric Bahuaud, Hari Kunduri and Eric Woolgar) Class.Quant.Grav. 41 (2024) 6, 065001

2. Rigidity of quasi-Einstein metrics: the incompressible case (with Eric Bahuaud, Hari Kunduri and Eric Woolgar) Lett.Math.Phys. 114 (2024) 1, 8

3. Static near horizon geometries and rigidity of quasi-Einstein manifolds (with Eric Bahuaud, Hari Kunduri and Eric Woolgar) Lett.Math.Phys. 112 (2022) 6, 116

4. Slow decay of waves in gravitational solitons (with Hari Kunduri) Annales Henri Poincare 22 (2021) 3, 821-872

5. Horizons as boundary conditions in spherical symmetry (with Ivan Booth) Phys.Rev.D 100 (2019) 6, 064019

6. Soliton mechanics (with , Uzair Hussain and Hari Kunduri) Phys.Rev.D 94 (2016) 12, 124029

7. Extended phase space thermodynamics for charged and rotating black holes and Born-Infeld vacuum polarization ( with Robert B. Mann and David Kubiznak) JHEP 11 (2012) 110