## 24 Citations

### Non-existence of time-periodic vacuum spacetimes

- Mathematics
- 2015

We prove that smooth asymptotically flat solutions to the Einstein vacuum equations which are assumed to be periodic in time, are in fact stationary in a neighborhood of infinity. Our result applies…

### Scattering from infinity for semilinear wave equations satisfying the null condition or the weak null condition

- Mathematics
- 2021

We show global existence backwards from scattering data at infinity for semilinear wave equations satisfying the null condition or the weak null condition. Semilinear terms satisfying the weak null…

### A VECTOR FIELD METHOD FOR NON-TRAPPING, RADIATING SPACETIMES

- Mathematics, Physics
- 2015

We study the global decay properties of solutions to the linear wave equation in 1+3 dimensions on time-dependent, weakly asymptotically flat spacetimes. Assuming non-trapping of null geodesics and a…

### A Vector Field Method for Non-Trapping, Radiating Spacetimes

- Mathematics, Physics
- 2014

We study the global decay properties of solutions to the linear wave equation in 1+3 dimensions on time-dependent, weakly asymptotically flat spacetimes. Assuming non-trapping of null geodesics and a…

### Carleman estimates with sharp weights and boundary observability for wave operators with critically singular potentials

- MathematicsJournal of the European Mathematical Society
- 2021

We establish a new family of Carleman inequalities for wave operators on cylindrical spacetime domains containing a potential that is critically singular, diverging as an inverse square on all the…

### A scattering theory for the wave equation on kerr black hole exteriors

- Mathematics
- 2018

We develop a definitive physical-space scattering theory for the scalar wave equation on Kerr exterior backgrounds in the general subextremal case |a|<M. In particular, we prove results corresponding…

### Stationarity of asymptotically flat non-radiating electrovacuum spacetimes

- Physics
- 2016

It is proven that a solution to the Einstein-Maxwell equations whose gravitational and electromagnetic radiation fields vanish at infinity is in fact stationary in a neighbourhood of spatial…

### A uniqueness theorem for 3D semilinear wave equations satisfying the null condition

- Mathematics
- 2021

. In this paper, we prove a uniqueness theorem for a system of semilinear wave equations satisfying the null condition in R 1+3 . Suppose that two global solutions with C ∞ c initial data have equal…

### On Schwarzschild causality in higher dimensions

- MathematicsClassical and Quantum Gravity
- 2020

We show that the causal properties of asymptotically flat spacetimes depend on their dimensionality: while the time-like future of any point in the past conformal infinity I− contains the whole of…

## References

SHOWING 1-10 OF 43 REFERENCES

### Non-existence of time-periodic vacuum spacetimes

- Mathematics
- 2015

We prove that smooth asymptotically flat solutions to the Einstein vacuum equations which are assumed to be periodic in time, are in fact stationary in a neighborhood of infinity. Our result applies…

### Uniqueness Results for Ill-Posed Characteristic Problems in Curved Space-Times

- Mathematics
- 2007

We prove two uniqueness theorems concerning linear wave equations; the first theorem is in Minkowski space-times, while the second is in the domain of outer communication of a Kerr black hole. Both…

### Hawking’s Local Rigidity Theorem Without Analyticity

- Mathematics
- 2009

We prove the existence of a Hawking Killing vector-field in a full neighborhood of a local, regular, bifurcate, non-expanding horizon embedded in a smooth vacuum Einstein manifold. The result extends…

### Radiation Fields on Schwarzschild Spacetime

- Mathematics
- 2014

In this paper we define the radiation field for the wave equation on the Schwarzschild black hole spacetime. In this context it has two components: the rescaled restriction of the time derivative of…

### On asymptotically flat solutions of Einstein's equations periodic in time: II. Spacetimes with scalar-field sources

- Mathematics, Physics
- 2010

We extend the work in our earlier paper (Bičák J et al 2010 Class. Quantum Grav. 27 055007) to show that time-periodic, asymptotically flat solutions of the Einstein equations analytic at , whose…

### On the local extension of Killing vector-fields in Ricci flat manifolds

- Mathematics
- 2011

We revisit the extension problem for Killing vector-fields in smooth Ricci flat manifolds, and its relevance to the black hole rigidity problem. We prove both a stronger version of the main local…

### Uniqueness properties of solutions to Schrödinger equations

- Mathematics
- 2011

nX j=1 ∂ 2 u ∂x 2 (x) = 0, (harmonic functions) in the unit ball {x ∈ R n : |x| 2, since harmonic functions are still real analytic in {x ∈ R n : |x| < 1}. In fact, it is well-known that if P(x,D) is…

### On ``Time-Periodic'' Black-Hole Solutions to Certain Spherically Symmetric Einstein-Matter Systems

- Physics
- 2003

AbstractThis paper explores black hole solutions of various Einstein-wave matter systems admitting a time-orientation preserving isometry of their domain of outer communications taking some point to…

### Nonexistence of time‐periodic solutions of the Dirac equation in an axisymmetric black hole geometry

- Physics
- 2000

We prove that in the non extreme Kerr Newman black hole geometry the Dirac equation has no normalizable time periodic solutions A key tool is Chandrasekhar s separation of the Dirac equation in this…

### Quasi-spherical light cones of the Kerr geometry

- Mathematics, Physics
- 1998

Quasi-spherical light cones are lightlike hypersurfaces of the Kerr geometry that are asymptotic to Minkowski light cones at infinity. We derive the equations of these surfaces and examine their…