Related papers: Sufficient Conditions for Apparent Horizons in Sph…
Horizons and bound photon orbits are defining features of black holes that translate into key features of black hole images. We present a purely geometric proof that spherically symmetric, isolated objects with horizons in gravity theories…
We give a geometric criterion for the breakdown of an Einstein vacuum space-time foliated by a constant mean curvature, or maximal, foliation. More precisely we show that the foliated space-time can be extended as long as the the second…
We have investigated the thermodynamical properties of the universe with dark energy. It is demonstrated that in a universe with spacial curvature the natural choice for IR cutoff could be the apparent horizon radius. We shown that any…
We analyse the necessary and sufficient conditions for the occurrence of superradiance. Starting with a wave equation we examine the possibility of superradiance in terms of an effective potential and boundary conditions. In particular, we…
We give an alternate proof of one of the results given in [16] showing that initial data sets with boundary for the Einstein equations $(M, g, k)$ satisfying the dominant energy condition can be conformally deformed to the strict dominant…
This paper proves a theorem about the existence of an apparent horizon in general relativity, which applies equally well to vacuum configurations and matter configurations. The theorem uses the reciprocal of the surface-to-volume ratio of a…
Our current picture of black hole gravitational collapse relies on two assumptions: i) the resulting singularity is hidden behind an event horizon -- weak cosmic censorship conjecture -- and ii) spacetime eventually settles down to a…
We discuss the particle horizon problem in the framework of spatially homogeneous and isotropic scalar cosmologies. To this purpose we consider a Friedmann-Lemaitre-Robertson-Walker (FLRW) spacetime with possibly non-zero spatial sectional…
We investigate the validity of Thorne's hoop conjecture in non-axisymmetric spacetimes by examining the formation of apparent horizons numerically. If spaces have a discrete symmetry about one axis, we can specify the boundary conditions to…
The necessary and sufficient condition for the existence of $\alpha$-surfaces in complex space-time manifolds with nonvanishing torsion is derived. For these manifolds, Lie brackets of vector fields and spinor Ricci identities contain…
We prove the global in time existence of spherically symmetric solutions to an initial-boundary value problem for a system of partial differential equations, which consists of the equations of linear elasticity and a nonlinear,…
To observe the dynamic formation of black holes in general relativity, one essentially needs to prove that closed trapped surfaces form during evolution from initial data that do not already contain trapped surfaces. We discuss the recent…
It is known that spherically symmetric spacetimes admit flat spacelike foliations. We point out a simple method of seeing this result via the Hamiltonian constraints of general relativity. The method yields explicit formulas for the…
In this paper we consider the positive mass theorem for general initial data sets satisfying the dominant energy condition which are singular across a piecewise smooth surface. We find jump conditions on the metric and second fundamental…
We provide simple necessary and sufficient conditions under which a path constitutes a solution to an infinite-horizon, continuous-time optimal control problem. We prove transversality conditions under standard assumptions. We also present…
We prove that the area of sections of future event horizons in space-times satisfying the null energy condition is non-decreasing towards the future under any one of the following circumstances: 1) the horizon is future geodesically…
We prove that the maximal development of any spherically symmetric spacetime with collisionless matter (obeying the Vlasov equation) or a massless scalar field (obeying the massless wave equation) and possessing a constant mean curvature…
The problem of obtaining necessary and sufficient conditions for local existence of non-negative solutions in Lebesgue spaces for semilinear heat equations having monotonically increasing source term $f$ has only recently been resolved…
We numerically construct time-symmetric initial data sets of a black hole in the Randall-Sundrum brane world model, assuming that the black hole is spherical on the brane. We find that the apparent horizon is cigar-shaped in the 5D…
Within the framework of an eternal inflationary scenario, a natural question regarding the production of eternal bubbles is the essential condition requires to have a universe capable of generating life. In either an open or a closed…