7 citations · 33 across the 14 of their papers we have counts for
14 papers
On Axially Symmetric Perturbations of Kerr Black Hole Spacetimes
Nishanth Gudapati
The lack of a positive-definite and conserved energy is a serious obstacle in the black hole stability problem. In this work, we will show that there exists a positive-definite and…
Curvature Propagation for the 3+1 Dimensional U(1) Symmetric Einstein Spacetimes
Nishanth Gudapati
As it is well known, the global structure of the Einstein equations for general relativity in the context of the initial value problem, is a difficult and intricate mathematical pr…
Scattering for the Equivariant U(1) Problem
Nishanth Gudapati
Extending our previous works on the Cauchy problem for the equivariant Einstein-wave map system, we prove that the linear part dominates the nonlinear part of the wave maps e…
Energy Extraction, or Lack Thereof
Nishanth Gudapati
The problem of stability of rotating black holes is the subject of a long standing research program since the 1960s and remains an unresolved problem in general relativity. A major…
Axially Symmetric Perturbations of Kerr Black Holes II: Boundary Behaviour of the Dynamics in the Orbit Space
Nishanth Gudapati
In a previous work, we constructed a positive-definite total energy functional for the axially symmetric linear perturbative theory of Kerr black hole spacetimes. That work is base…
Quasi-Local Mass near the Singularity, the Event Horizon and the Null Infinity of Black Hole Spacetimes
Nishanth Gudapati, Shing-Tung Yau
The behaviour of geometric quantities close to geometric pathologies of a spacetime is relevant to deduce the physical behaviour of the system. In this work, we compute the quasi-l…
Axially Symmetric Perturbations of Kerr Black Holes I: A gauge-invariant construction of ADM Energy
Nishanth Gudapati
Based on the Hamiltonian dimensional reduction of axially symmetric, Ricci-flat Lorentzian spacetimes to a Einstein-wave map system with the (negatively curved) hyperbo…
A Conserved Energy for Axially Symmetric Newman-Penrose-Maxwell Scalars on Kerr Black Holes
Nishanth Gudapati
We show that there exists a 1-parameter family of positive-definite and conserved energy functionals for axially symmetric Newman-Penrose-Maxwell scalars on the maximal spacelike h…
A Positive-Definite Energy Functional for Axially Symmetric Maxwell's Equations on Kerr-de Sitter Black Hole Spacetimes
Nishanth Gudapati
We prove that there exists a phase space of canonical variables for the initial value problem for axially symmetric Maxwell fields propagating in Kerr-de Sitter black hole spacetim…
On 3+1 Lorentzian Einstein Manifolds with One Rotational Isometry
Nishanth Gudapati
We consider 3+1 rotationally symmetric Lorentzian Einstein spacetime manifolds with and reduce the equations to 2+1 Einstein equations coupled to `shifted' wave maps. Subsequ…
A Note on the Dimensional Reduction of Axisymmetric Spacetimes
Nishanth Gudapati
We investigate the dimensional reduction of 3+1 vacuum axisymmetric Einstein's equations to 2+1 dimensional Einstein-wave map system and observe that the resulting system is 1) not…
On Scattering for Small Data of 2+1 Dimensional Equivariant Einstein-Wave Map System
Benjamin Dodson, Nishanth Gudapati
We consider the Cauchy problem of 2+1 equivariant wave maps coupled to Einstein's equations of general relativity and prove that two separate (nonlinear) subclasses of the system d…
Global Regularity for the 2+1 Dimensional Equivariant Einstein-Wave Map System
Lars Andersson, Nishanth Gudapati, Jeremie Szeftel
In this paper we consider the equivariant 2+1 dimensional Einstein-wave map system and show that if the target satisfies the so called Grillakis condition, then global existence ho…
On the Cauchy Problem for Energy Critical Self-Gravitating Wave Maps
Nishanth Gudapati
This work is on the Cauchy problem for critical wave maps coupled to Einstein's equations of general relativity. The main result of this work is the proof that the energy of the Ei…