相关论文: Isoperimetric inequality for higher-dimensional bl…

Recent results of Trudinger on Isoperimetric Inequalities for non-convex bodies are applied to the gravitational collapse of a lightlike shell of matter to form a black hole. Using some integral identities for co-dimension two surfaces in…

For static black holes in Einstein gravity, if matter fields satisfy a few general conditions, we conjecture that three characteristic parameters about the spatial size of black holes, namely the outermost photon sphere area…

We consider $n$-dimensional spacetimes which are axisymmetric--but not necessarily stationary (!)--in the sense of having isometry group $U(1)^{n-3}$, and which satisfy the Einstein equations with a non-negative cosmological constant. We…

In this work, we investigate the $n$-dimensional charged static black hole solutions in the Einstein-\ae ther theory. By taking the metric parameter $k$ to be $1,0$, and $-1$, we obtain the spherical, planar, and hyperbolic spacetimes…

We present a proof of the reverse isoperimetric inequality - a central conjecture in extended black hole thermodynamics - for black holes in Einstein gravity with $D \geq 4$, employing a two-pronged geometric-analytic method. Our analysis…

In a paper \cite{P} in 1973, R. Penrose made a physical argument that the total mass of a spacetime which contains black holes with event horizons of total area $A$ should be at least $\sqrt{A/16\pi}$. An important special case of this…

We construct the spacetime in the vicinity of a general isolated, rotating, charged black hole. The black hole is modeled as a weakly isolated horizon, and we use the characteristic initial value formulation of the Einstein equations with…

We construct a regular black hole solution on the orbifold ${\mathbb C}^{n}/{\mathbb Z}_{n}$ in the ($2n+1$)-dimensional Einstein-Maxwell theory. The event horizon is $S^{2n-1}/{\mathbb Z}_{n}$.

Four-dimensional magnetic black holes including dilaton and abelian gauge fields which are solutions of supergravity can also be obtained by dimensional reduction of the Einstein-Maxwell gravity in five dimensions. In the extremal case the…

Exact vacuum solutions with a nontrivial torsion for the Einstein-Gauss-Bonnet theory in five dimensions are constructed. We consider a class of static metrics whose spacelike section is a warped product of the real line with a nontrivial…

Using a recently developed generalized Weyl formalism, we construct an asymptotically flat, static vacuum Einstein solution that describes a superposition of multiple five-dimensional Schwarzschild black holes. The spacetime exhibits a…

Consider a compact, orientable, three dimensional Riemannian manifold with boundary with nonnegative scalar curvature. Suppose its boundary is the disjoint union of two pieces: the horizon boundary and the outer boundary, where the horizon…

The vacuum Einstein equations in five dimensions are shown to admit a solution describing an asymptotically flat spacetime regular on and outside an event horizon of topology S^1 x S^2. It describes a rotating ``black ring''. This is the…

We consider static black holes in Einstein gravity and study parameters characterizing the black hole size, namely the radii of the horizon $R_+$, photon sphere $R_{\rm ph}$ and black hole shadow $R_{\rm sh}$. We find a sequence of…

We obtain higher dimensional analogues of the results of Mantoulidis and Schoen in [8]. More precisely, we show that (i) any metric $g$ with positive scalar curvature on the $3$-sphere $S^3$ can be realized as the induced metric on the…

In this paper, we present a new solution of the vacuum Einstein equations in five dimensions which is a static black hole with hyperscaling violation and with a three-dimensional horizon modeled by one the eight Thurston geometries, namely…

The Penrose inequality estimates the lower bound of the mass of a black hole in terms of the area of its horizon. This bound is relatively loose for extremal or near extremal black holes. We propose a new Penrose-like inequality for static…

We prove that in Einstein-Maxwell theory the inequality $(8\pi J)^2+(4\pi Q^2)^2 < A^2$ holds for any sub-extremal axisymmetric and stationary black hole with arbitrary surrounding matter. Here $J, Q$, and $A$ are angular momentum, electric…

Stationary black holes in 5-dimensional Einstein-Maxwell-Chern-Simons theory possess surprising properties. When considering the Chern-Simons coefficient $\lambda$ as a parameter, two critical values of $\lambda$ appear: the supergravity…

The set of all metrics that can be placed on a given manifold defines an infinite-dimensional `superspace' that can itself be imbued with the structure of a Riemannian manifold. Geodesic distances between points on Met$(M)$ measure how…