Related papers: Hyperboloidal framework for the Kerr spacetime
The perturbations of the Kerr metric and the miracle of their exact solutions play a critical role in the comparison of predictions of general relativity with astrophysical observations of compact massive objects. The differential equations…
We investigate the solution of the continued fraction equation by which we determine "the renormalized angular momentum parameter", $\nu$, in the formalism developed by Leaver and Mano, Suzuki, and Takasugi. In this formalism, we describe…
General relativity's prediction that all black holes are described by the Kerr metric, irrespective of their size, can now be empirically tested using electromagnetic observations of supermassive black holes and gravitational waves from…
Post-adiabatic models of extreme- and intermediate-mass-ratio inspirals will require calculations of second-order gravitational self-force effects in the spacetime of a spinning, Kerr black hole. We take a step toward such calculations by…
As a first step towards the calculation of waveform of Extreme Mass Ratio Inspirals for Modified Gravity theories, we calculate the orbital frequencies of a Small Compact Object inspiralling into a super massive blackhole for a Nonlocal…
One of the primary aims of upcoming space-borne gravitational wave detectors is to measure radiation in the mHz range from extreme-mass-ratio inspirals. Such a detection would place strong constraints on hypothetical departures from a Kerr…
We analyze the stationary, uncharged, rotating, vacuum solution to Weyl conformal gravity. We elucidate the causal and ergoregion structure of the spacetimes found in the parameter space of the metric for positive mass. These are then…
In linear perturbation theory for Kerr black holes, there are two equivalent formalisms, namely the Teukolsky and the Sasaki-Nakamura (SN) formalism. Typically, one defaults to the Teukolsky formalism, especially when calculating extreme…
We use the continued fraction method to determine the eigenfrequencies associated with a scalar field around a Kerr-like black hole. The Kerr-like metric considered in this article is a subclass of the general parametrization of…
We explicitly solve the equations for the propagation of an electromagnetic wave up to the subleading order geometric optics expansion in the Kerr spacetime. This is done in two nontrivial steps. We first construct a set of parallel…
This is a short review of a series of papers which, in collaboration with Yue Ma, establish several novel existence results for systems of coupled wave-Klein-Gordon equation. Our method, the Hyperbolic Hyperboloidal Method, has allowed us…
The excitation of quadratic quasinormal modes is an important nonlinear phenomenon for a Kerr black hole ringing at a specific linear mode. The amplitude of this second-order effect is proportional to the square of the linear mode…
The differential equations governing the late-time ring-down of the perturbations of the Kerr metric, the Teukolsky Angular Equation and the Teukolsky Radial Equation, can be solved analytically in terms of confluent Heun functions. In this…
According to the holographic principle, the description of a volume of space can be thought of as encoded on its boundary. Holographic principle establishes equivalence, or duality, between theoretical description of volume physics, which…
This paper is a part of a series devoted to the Euclidean-hyperboloidal foliation method introduced by the authors for investigating the global existence problem associated with nonlinear systems of coupled wave-Klein-Gordon equations with…
Recent strong-field regime tests of gravity are so far in agreement with general relativity. In particular, astrophysical black holes appear all to be consistent with the Kerr spacetime, but the statistical error on current observations…
The radiation gauges used by Chrzanowski (his IRG/ORG) for metric reconstruction in the Kerr spacetime seem to be over-specified. Their specification consists of five conditions: four, which we treat here as valid gauge conditions, plus an…
We derive the analytical solutions of the bound timelike geodesic orbits in Kerr spacetime. The analytical solutions are expressed in terms of the elliptic integrals using Mino time $\lambda$ as the independent variable. Mino time decouples…
Recent theoretical results show the existence of arbitrary speeds (0 <= v < \infty) solutions of all relativistic wave equations. Some recent experiments confirm the results for sound waves. The question arises naturally: What is the…
The future LISA detector will constitute the prime instrument for high-precision gravitational wave observations.LISA is expected to provide information for the properties of spacetime in the vicinity of massive black holes which reside in…