Fetching the paper…
Reading the bibliography…
We present a new vector field approach to almost-sharp decay for the wave equation on spherically symmetric, stationary and asymptotically flat spacetimes.
The limiting amplitude principle
Morawetz, C. S · 1962
Earlier work this paper cites.
10 exact gravitationally conserved quantities
Newman, E. T., and Penrose, R · 1965
Earlier work this paper cites.
New conservation laws for zero rest mass fields in asympotically flat space-time
Newman, E. T., and Penrose, R · 1968
Earlier work this paper cites.
Non-spherical perturbations of relativistic gravitational collapse. I. Scalar and gravitational perturbations
Price, R · 1972
Earlier work this paper cites.
Gravitation
Misner, C. W., Thorne, K. S., and Wheeler, J. A · 1973
Earlier work this paper cites.
Linear Partial Differential Operators
Hörmander, L · 1976
Earlier work this paper cites.
Long time behavior of solutions to nonlinear wave equations
Klainerman, S · 1983
Earlier work this paper cites.
Gaussian beams and the propagation of singularities
Ralston, J · 1983
Earlier work this paper cites.
Uniform decay estimates and the Lorentz invariance of the classical wave equation
Klainerman, S · 1985
Earlier work this paper cites.
Global solutions of nonlinear hyperbolic equations for small initial data
Christodoulou, D · 1986
Earlier work this paper cites.
On the existence of n n -geodesically complete or future complete solutions of Einstein’s field equations with smooth asympotic structure
Friedrich, H · 1986
Earlier work this paper cites.
The null condition and global existence to nonlinear wave equations
Klainerman, S · 1986
Earlier work this paper cites.
Nonlinear nature of gravitation and gravitational-wave experiments
Christodoulou, D · 1991
Earlier work this paper cites.
The Global Nonlinear Stability of the Minkowski Space
Christodoulou, D., and Klainerman, S · 1994
Earlier work this paper cites.
Late-time behavior of stellar collapse and explosions. II: Nonlinear evolution
Gundlach, C., Price, R., and Pullin, J · 1994
Earlier work this paper cites.
Instability results for the wave equation in the interior of Kerr black holes
Luk, J., and Sbierski, J · 1995
Earlier work this paper cites.
Partial Differential Equations
Evans, L. C · 1998
Earlier work this paper cites.
Stability and instability of the Cauchy horizon for the spherically symmetric Einstein–Maxwell–scalar field equations
Dafermos, M · 2003
Earlier work this paper cites.
The interior of charged black holes and the problem of uniqueness in general relativity
Dafermos, M · 2005
Earlier work this paper cites.
A proof of Price’s law for the collapse of a self-gravitating scalar field
Dafermos, M., and Rodnianski, I · 2005
Earlier work this paper cites.
Decay rates for spherical scalar waves in a Schwarzschild geometry
Kronthaler, J · 2007
Earlier work this paper cites.
Lectures on non-linear wave equations
Sogge, C. D · 2008
Earlier work this paper cites.
Phase space analysis on some black hole manifolds
Blue, P., and Soffer, A · 2009
Earlier work this paper cites.
The redshift effect and radiation decay on black hole spacetimes
Dafermos, M., and Rodnianski, I · 2009
Earlier work this paper cites.
A new physical-space approach to decay for the wave equation with applications to black hole spacetimes
Dafermos, M., and Rodnianski, I · 2010
Cited alongside, same era.
Improved decay for solutions to the linear wave equation on a Schwarzschild black hole
Luk, J · 2010
Cited alongside, same era.
Stability and instability of extreme Reissner–Nordström black hole spacetimes for linear scalar perturbations I
Aretakis, S · 2011
Cited alongside, same era.
Stability and instability of extreme Reissner–Nordström black hole spacetimes for linear scalar perturbations II
Aretakis, S · 2011
Cited alongside, same era.
Decay of axisymmetric solutions of the wave equation on extreme Kerr backgrounds
Aretakis, S · 2012
Cited alongside, same era.
On pointwise decay of linear waves on a Schwarzschild black hole background
On the global uniqueness for the Einstein-Maxwell-scalar field system with a cosmological constant: I. Well posedness and breakdown criterion
Costa, J. L., Girão, P. M., Natário, J., and Silva, J. D · 2015
Later among the works it cites.
On the Global Uniqueness for the Einstein-Maxwell-Scalar Field System with a Cosmological Constant. Part 2: Structure of the Solutions and Stability of the Cauchy Horizon
Costa, J. L., Girão, P. M., Natário, J., and Silva, J. D · 2015
Later among the works it cites.
Linear waves in the interior of extremal black holes II
Gajic, D · 2015
Later among the works it cites.
Boundedness and decay of scalar waves at the Cauchy horizon of the Kerr spacetime
Hintz, P · 2015
Later among the works it cites.
Analysis of linear waves near the Cauchy horizon of cosmological black holes
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
Donninger, R., Schlag, W., and Soffer, A · 2012
Cited alongside, same era.
A vector field method approach to improved decay for solutions to the wave equation on a slowly rotating kerr black hole
Luk, J · 2012
Cited alongside, same era.
Price’s law on nonstationary spacetimes
Metcalfe, J., Tataru, D., and Tohaneanu, M · 2012
Cited alongside, same era.
The characteristic gluing problem and conservation laws for the wave equation on null hypersurfaces
Aretakis, S · 2013
Cited alongside, same era.
A note on instabilities of extremal black holes from afar
Aretakis, S · 2013
Cited alongside, same era.
On a non-linear instability of extremal black holes
Aretakis, S · 2013
Cited alongside, same era.
Lectures on black holes and linear waves
Dafermos, M., and Rodnianski, I · 2013
Cited alongside, same era.
Hintz, P., and Vasy, A · 2015
Later among the works it cites.
On the global stability of the wave-map equation in Kerr spaces with small angular momentum
Ionescu, A. D., and Klainerman, S · 2015
Later among the works it cites.
Proof of linear instability of the Reissner-Nordström Cauchy horizon under scalar perturbations
Luk, J., and Oh, S.-J · 2015
Later among the works it cites.
Characterisation of the energy of Gaussian beams on Lorentzian manifolds with applications to black hole spacetimes
Sbierski, J · 2015
Later among the works it cites.
Global spherically symmetric solutions of non-linear wave equations with null condition on extremal Reissner-Nordström spacetimes
Angelopoulos, Y · 2016
Closest in time.
Asymptotic blow-up for a class of semi-linear wave equations on extremal Reissner-Nordström
Angelopoulos, Y., Aretakis, S., and Gajic, D · 2016
Closest in time.
Late-time asymptotics for the wave equation on spherically symmetric, stationary backgrounds
Angelopoulos, Y., Aretakis, S., and Gajic, D · 2016
Closest in time.
Horizon instability of extremal Kerr black holes: Nonaxisymmetric modes and enhanced growth rate
Casals, M., Gralla, S. E., and Zimmerman, P · 2016
Closest in time.
Bounded energy waves on the black hole interior of Reissner-Nordström-de Sitter
Costa, J. L., and Franzen, A · 2016
Closest in time.
The linear stability of the Schwarzschild solution to gravitational perturbations
Dafermos, M., Holzegel, G., and Rodnianski, I · 2016
Closest in time.
Time-translation invariance of scattering maps and blue-shift instabilities on Kerr black hole spacetimes
Dafermos, M., Rodnianski, I., and Shlapentokh-Rothman, Y · 2016
Closest in time.
Linear waves in the interior of extremal black holes I
Gajic, D · 2016
Closest in time.
Transient instability of rapidly rotating black holes
Gralla, S. E., Zimmerman, A., and Zimmerman, P · 2016
Closest in time.
The global non-linear stability of the Kerr-de Sitter family of black holes
Hintz, P., and Vasy, A · 2016
Closest in time.
Slowly Decaying Waves on Spherically Symmetric Spacetimes and an Instability of Ultracompact Neutron Stars
Keir, J · 2016
Closest in time.
Logarithmic local energy decay for scalar waves on a general class of asymptotically flat spacetimes
Moschidis, G · 2016
Closest in time.
A proof of Friedman’s ergosphere instability for scalar waves
Moschidis, G · 2016
Closest in time.
The r p r^{p} -weighted energy method of Dafermos and Rodnianski in general asymptotically flat spacetimes and applications
Moschidis, G · 2016
Closest in time.
Late-time decay of perturbations outside extremal charged black hole
Sela, O · 2016
Closest in time.