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…