Related papers: Vanishing conditions on Weyl tensor for Einstein-t…
It is well-known that the Einstein condition on warpedgeometries requires the fibres to be necessarily Einstein. However, exact warped solutions have often been obtained using one- and two-dimensional bases. In this paper, keeping the…
We derive a Weyl invariant equation for Gravity by gauging the global Weyl invariance of vacuum Einstein equations. The equation is linear in the curvature and a natural generalization of Einstein equations to Weyl geometry. The system has…
We explicitly construct static black hole solutions to the fully non-linear, D=4, Einstein-Maxwell-AdS equations that have no continuous spatial symmetries. These black holes have a smooth, topologically spherical horizon (section), but…
In [P. Kanti, B. Kleihaus, J. Kunz, Phys. Rev. Lett. 107, 271101 (2011)] it was shown that the four-dimensional Einstein-dilaton-Gauss-Bonnet theory allows for wormholes without introducing any exotic matter. The numerical solution for the…
We show that in any spacetime dimension $D\ge 4$, degenerate components of the event horizon do not exist in static vacuum configurations with positive cosmological constant. We also show that without a cosmological constant asymptotically…
We show that the static tidal Love number of Schwarzschild black holes in four dimensions and in the vacuum vanishes at any order in the external tidal force. We also identify the underlying non-linear symmetry which is responsible for this…
We prove that there are no restrictions on the spatial topology of asymptotically flat solutions of the vacuum Einstein equations in (n+1)-dimensions. We do this by gluing a solution of the vacuum constraint equations on an arbitrary…
As Einstein's gravity is a non-renormalizable theory, it can be a good description of physics only at the scales of energy or spacetime curvature below the Planck mass. Moreover, it requires the presence of an infinite tower of…
Using Bochner techniques, we prove that a compact Einstein manifold of dimension $n \ge 4$ has constant curvature provided that the curvature operator of the second kind satisfies a cone condition that is strictly weaker than nonnegativity.…
We show that a spacetime satisfying the linearized vacuum Einstein equations around a type D background is generically of type I, and that the splittings of the Principal Null Directions (PNDs) and of the degenerate eigenvalue of the Weyl…
Recently, a no inner (Cauchy) horizon theorem for static black holes with non-trivial scalar hairs has been proved in Einstein-Maxwell-scalar theories. In this paper, we extend the theorem to the static black holes in…
One says that a Riemannian four-manifold is \emph{weakly Einstein} if the three-index contraction of its curvature tensor against itself equals a function times the metric. Since this includes all four-manifolds that are Einstein, or…
In a recent paper[1], it has been shown that, there cannot be any rotating (Kerr) Black Hole (BH) with finite mass in order that the generic properties associated with the symmetries of stationary axisymmetric Einstein equations are obeyed,…
We study compactness for nonnegative solutions of the fourth order constant $Q$-curvature equations on smooth compact Riemannian manifolds of dimension $\ge 5$. If the $Q$-curvature equals $-1$, we prove that all solutions are universally…
We review results on the spherically symmetric, asymptotically flat Einstein-Vlasov system. We focus on a recent result where we found explicit conditions on the initial data which guarantee the formation of a black hole in the evolution.…
We present, in an explicit form, the metric for all spherically symmetric Schwarzschild-Bach black holes in Einstein-Weyl theory. In addition to the black hole mass, this complete family of spacetimes involves a parameter that encodes the…
Einstein spacetimes (that is vacuum spacetimes possibly with a non-zero cosmological constant {\Lambda}) with constant non-zero Weyl eigenvalus are considered. For type Petrov II & D this assumption allows one to prove that the non-repeated…
Adopting noncommutative spacetime coordinates, we determined a new solution of Einstein equations for a static, spherically symmetric matter source. The limitations of the conventional Schwarzschild solution, due to curvature singularities,…
This paper is motivated by the non-linear stability problem for the expanding region of Kerr de Sitter cosmologies in the context of Einstein's equations with positive cosmological constant. We show that under dynamically realistic…
We prove that an n($\geq$ 4)-dimensional compact Bach-flat manifold with positive constant $\sigma_2$ is an Einstein manifold, provided that its Weyl curvature satisfies a suitable pinching condition.