Related papers: A note on a third order curvature invariant in sta…
We have investigated the behavior of three curvature invariants for Schwarzschild, Reissner-Nordstr{\o}m, Kerr, and Kerr-Newman black holes. We have also studied these invariants for a Schwarzschild-de Sitter space-time, the $\gamma$…
We construct a scalar polynomial curvature invariant that transforms covariantly under a conformal transformation from any spherically symmetric metric. This invariant has the additional property that it vanishes on the event horizon of any…
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…
Inspired by the example of Abdelqader and Lake for the Kerr metric, we construct local scalar polynomial curvature invariants that vanish on the horizon of any stationary black hole: the squared norms of the wedge products of n linearly…
We introduce three approaches to generate curvature invariants that transform covariantly under a conformal transformation of a four dimensional spacetime. For any black hole conformally related to a stationary black hole, we show how a set…
It is well known that all curvature invariants of the order zero vanish for type-III and type-N vacuum spacetimes. We briefly summarize properties of higher order curvature invariants for these spacetimes.
We compute analytically differential invariants for accelerating, rotating and charged black holes with a cosmological constant $\Lambda$. In particular, we compute in closed form novel explicit algebraic expressions for curvature…
The divergence of curvature invariants at a given point signals the impossibility of extending the spacetime to that point, with the derivative order of these diverging invariants determining the differentiability class of the considered…
Some judiciously chosen local curvature scalars can be used to invariantly characterize event horizons of black holes in $D > 3$ dimensions, but they fail for the three dimensional Ba\~nados-Teitelboim-Zanelli (BTZ) black hole since all…
We investigate static, spherically symmetric solutions in gravitational theories which have limited curvature invariants, aiming to remove the singularity in the Schwarzschild space-time. We find that if we only limit the Gauss-Bonnet term…
Although black holes are eminent manifestations of very strong gravity, the geometry of space-time around and even inside them can be significantly affected by additional bodies present in their surroundings. We study such an influence…
The results of paper [1] are generalized for vacuum type-III solutions with, in general, a non-vanishing cosmological constant Lambda. It is shown that all curvature invariants containing derivatives of the Weyl tensor vanish if a type-III…
We prove that the only asymptotically flat spacetimes with a suitably regular event horizon, in a generalised Majumdar-Papapetrou class of solutions to higher-dimensional Einstein-Maxwell theory, are the standard multi-black holes. The…
Static spherically symmetric solutions for conformal gravity in three dimensions are found. Black holes and wormholes are included within this class. Asymptotically the black holes are spacetimes of arbitrary constant curvature, and they…
The behaviour of stationary gravitational perturbations is studied for generalised static black holes in spacetimes of greater than three dimensions, using the formulation developed by the present author and Ishibashi. For the case in which…
We present an asymptotically flat and stationary multi-black lens solution with bi-axisymmetry of $U(1)\times U(1)$ as a supersymmetric solution in the five-dimensional minimal ungauged supergravity. We show that the spatial cross section…
Scalar curvature invariants are studied in type N solutions of vacuum Einstein's equations with in general non-vanishing cosmological constant Lambda. Zero-order invariants which include only the metric and Weyl (Riemann) tensor either…
We present a new family of multi-centered rotating black hole solutions in 5D vacuum Einstein gravity, providing explicit examples of cohomogeneity-three spacetimes. It is well known that, in the presence of two commuting Killing vector…
We derive a stationary and axisymmetric black hole solution to quadratic order in the spin angular momentum. The previously found, linear-in-spin terms modify the odd-parity sector of the metric, while the new corrections appear in the…
We present a review on Lagrangian models admitting spherically symmetric regular black holes, and cosmological bounce solutions. Non-linear electrodynamics, non-polynomial gravity, and fluid approaches are explained in details. They consist…