相关论文: Geometric inequalities in spherically symmetric sp…
Spherically symmetric spacetimes admit the so-called Kodama vector, which provides a locally conserved current and a preferred time even for dynamical spacetime without any time translation symmetry. A charge associated with this conserved…
In this study, we employ eth-operators and spin-weighted spherical harmonics to express the ADM mass of a static space-time based on the mean values of its components over a a radius-$r$ sphere. While initially derived for standard…
A recent generalization of the Hawking-Hayward quasilocal energy to scalar-tensor gravity is adapted to general spherically symmetric geometries. It is then applied to several black hole and other spherical solutions of scalar-tensor and…
We point out an association between anomalies in the Hawking quasilocal mass (or, in spherical symmetry, in its better known version, the Misner-Sharp-Hernandez mass) and unphysical properties of the spacetime geometry. While anomalous…
In the spherically symmetric case the requirements of regularity of density and pressures and finiteness of the ADM mass $m$, together with the weak energy condition, define the family of asymptotically flat globally regular solutions to…
The mathematical theory of isometric embedding is applied to study the notion of quasilocal mass in general relativity. In particular, I shall report some recent progress of quasilocal mass with reference to a cosmological spacetime, such…
We propose a new parametric framework to describe in generic metric theories of gravity the spacetime of spherically symmetric and slowly rotating black holes. In contrast to similar approaches proposed so far, we do not use a Taylor…
A new notion of quasilocal mass is defined for generic, compact, two dimensional, spacelike surfaces in four dimensional spacetimes with negative cosmological constant. The definition is spinorial and based on work for vanishing…
A geometric inequality in General Relativity relates quantities that have both a physical interpretation and a geometrical definition. It is well known that the parameters that characterize the Kerr-Newman black hole satisfy several…
A canonical formalism for spherical symmetry, originally developed by Kucha\v{r} to describe vacuum Schwarzschild black holes, is extended to include a spherically symmetric, massless, scalar field source. By introducing the ADM mass as a…
We investigate properties of a quasi-local mass in a higher-dimensional spacetime having symmetries corresponding to the isomertries of an $(n-2)$-dimensional maximally symmetric space in Einstein-Gauss-Bonnet gravity in the presence of a…
Recently symmetries of gravity and gauge fields in the asymptotic regions of spacetime have been shown to play vital role in their low energy scattering phenomena. Further, for the black hole spacetime, near horizon symmetry has been…
We summarize our work on spherically symmetric midi-superspaces in loop quantum gravity. Our approach is based on using inhomogeneous slicings that may penetrate the horizon in case there is one and on a redefinition of the constraints so…
While the quasi-local thermodynamics of spherically symmetric black holes is well described by pressure and volume, extending this framework to rotating spacetimes poses a significant challenge. Rotation induces an oblate deformation of the…
We extend the concept of the Kodama symmetry, a quasi-local time translation symmetry for dynamical spherically symmetric spacetimes, to a specific class of dynamical axisymmetric spacetimes, namely the families of Kerr-Vaidya and…
We elaborate on the anholonomic frame deformation method, AFDM, for constructing exact solutions with quasiperiodic structure in modified gravity theories, MGTs, and general relativity, GR. Such solutions are described by generic…
A quasi-local mass, typically defined as an integral over a spacelike $2$-surface $\Sigma$, should encode information about the gravitational field within a finite, extended region bounded by $\Sigma$. Therefore, in attempts to quantize…
We present a new vector field approach to almost-sharp decay for the wave equation on spherically symmetric, stationary and asymptotically flat spacetimes. Specifically, we derive a new hierarchy of higher-order weighted energy estimates by…
A new spinorial strategy for the construction of geometric inequalities involving the Arnowitt-Deser-Misner (ADM) mass of black hole systems in general relativity is presented. This approach is based on a second order elliptic equation (the…
A new inequality for a nonlinear surface layer integral is proved for minimizers of causal variational principles. This inequality is applied to obtain a new proof of the positive mass theorem with volume constraint. Next, a positive mass…