Related papers: On uniqueness of static spacetime with conformal s…
The infinite cosmological "constant" limit of the de Sitter solutions to Einstein's equation is studied. The corresponding spacetime is a singular, four-dimensional cone-space, transitive under proper conformal transformations, which…
There are a number of publications on relativistic objects dealing either with black holes or naked singularities in the center. Here we show that there exist static spherically symmetric solutions of Einstein equations with a strongly…
We consider $d$-dimensional static spacetimes in Einstein gravity with a cosmological constant in the presence of a minimally coupled massless scalar field. The spacetimes have a $(d-2)$-dimensional base manifold given by an Einstein space…
We reexamine the Israel-type proof of the uniqueness theorem of the static spacetime outside the photon surface in the Einstein-conformal scalar system. We derive in a systematic fashion a new divergence identity which plays a key role in…
We discuss the uniqueness of the static black hole in the Einstein gravity with a conformally coupled scalar field. In particular, we prove the uniqueness of the region outside of the photon surface, not event horizon.
In the present paper we prove a uniqueness theorem for the static and asymptotically flat solutions to the Einstein-scalar field equations which possess a photon sphere. We show that such solutions are uniquely specified by their mass $M$…
We discuss the uniqueness of the static spacetimes with non-trivial conformal scalar field. Then, we can show that the spacetime is unique to be the Bocharova-Bronnikov-Melnikov-Bekenstein solution outside the surface composed of the…
In the present paper we consider the Einstein-multiple-scalar field theory. When the target space of the scalar fields is a complete, simply connected Riemannian manifold with non-positive sectional curvature we prove that the static and…
We study global aspects of complete, non-singular asymptotically locally AdS spacetimes solving the vacuum Einstein equations whose conformal infinity is an arbitrary globally stationary spacetime. It is proved that any such solution which…
In this paper, we establish that a four-dimensional static vacuum asymptotically flat spacetime containing a massive particle sphere is isometric to the Schwarzschild spacetime. Our results expand upon existing uniqueness theorems for…
We consider the problem of uniqueness of static and asymptotically flat Einstein-Maxwell spacetimes with a photon sphere $P^3$. We are using a naturally modified definition of a photon sphere for electrically charged spacetimes with the…
We consider plane-symmetric spacetimes satisfying Einstein's field equations with positive cosmological constant, when the matter is a fluid whose pressure is equal to its mass-energy density (i.e. a so-called stiff fluid). We study the…
In many cases a scalar field can lead to accelerated expansion in cosmological models. This paper contains mathematical results on this subject particularly on type I Bianchi space-time. In this paper, global existence to the coupled…
In this paper, we combine and generalize to higher dimensions the approaches to proving the uniqueness of connected (3+1)-dimensional static vacuum asymptotically flat black hole spacetimes by M\"uller zum Hagen--Robinson--Seifert and by…
We analyse spacetimes with a conformal scalar field source, a cosmological constant and a quartic self-interaction term for the scalar field. We also consider additional matter contents in the form of Maxwell and Yang-Mills fields or…
We review recent results concerning the spherically symmetric Einstein-scalar field system with positive cosmological constant. We do so by comparing with the classical results of Christodoulou concerning the asymptotically flat case…
We investigate self-similar scalar field solutions to the Einstein equations in whole cylinder symmetry. Imposing self-similarity on the spacetime gives rise to a set of single variable functions describing the metric. Furthermore, it is…
In many cases a massive nonlinear scalar field can lead to accelerated expansion in cosmological models. This paper contains mathematical results on this subject for flat Robertson-Walker space-time. Global existence to the coupled…
The scalar invariant, I, constructed from the "square" of the first covariant derivative of the curvature tensor is used to probe the local geometry of static spacetimes which are also Einstein spaces. We obtain an explicit form of this…
Uniqueness of the four-dimensional static, asymptotically flat, Einstein-Maxwell spacetime with both electric and magnetic charges, containing non-extremal massive particle sphere, being an inner boundary in it, has been proved. It is…