Properties of generalized Schwarzschild spacetimes with extra dimensions

Abstract

We show that an ansatz for $1+3+n$ dimensional static spacetime with spherical symmetry in three dimensions and Euclidean symmetry in $n$ dimensions, parametrized by only one function of radial coordinate, leads to a limited set of vacuum solutions of the Einstein field equations. They can also be identified as Weyl solutions. We investigate properties of these spacetimes through the Kretschmann scalar, Newtonian mass defined through the Newtonian limit, Komar mass, Einstein, Landau--Lifshitz, and ADM mass. In addition to $1+3+n$ dimensional Minkowski spacetime, there are two classes of solutions. The first class is a trivial product of the Schwarzschild spacetime and Euclidean spaces in extra dimensions, while the second class is non-trivial. In the case with no horizon, there is a naked singularity, all masses are equal, and they are negative. In the case when there is a horizon, this horizon accommodates a physical singularity, which corresponds to Kaluza--Klein bubbles featuring exotic properties. Einstein, Landau--Lifshitz, and ADM masses are positive, while Newtonian and Komar masses are negative. This differentiates these solutions from trivial higher-dimensional extensions of the Schwarzschild solution.

12 pages, this version does not contain the graph and the table from the original version, but it contains new additions, including the Weyl form of the metric, and Einstein, Komar, and ADM masses

References in corpus (36)

• A Large Mass Hierarchy from a Small Extra Dimension
• First M87 Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole
• First Sagittarius A* Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole in the Center of the Milky Way
• Black Strings and p-Branes are Unstable
• A rotating black ring in five dimensions
• Strong Coupling Expansion Of Calabi-Yau Compactification
• Kaluza-Klein Gravity
• Black Holes in Higher Dimensions
• A Correspondence Principle for Black Holes and Strings
• Black Holes in Theories with Large Extra Dimensions: a Review
• Black Holes Radiate Mainly on the Brane
• The Instability of Charged Black Strings and p-Branes
• Generalized Weyl Solutions
• Black Hole Solutions in Heterotic String Theory on a Torus
• On the Unification Problem in Physics
• Solving the Hierarchy Problem with Noncompact Extra Dimensions
• General Static Spherically Symmetric Black Holes of Heterotic String on a Six Torus
• The Dark Side of String Theory: Black Holes and Black Strings
• Braneless Black Holes
• Brane factories
• Black Hole Evaporation and Compact Extra Dimensions
• Physical Properties of Four Dimensional Superstring Gravity Black Hole Solutions
• Sequences of Bubbles and Holes: New Phases of Kaluza-Klein Black Holes
• On the stability of naked singularities
• Cosmic p-branes
• Ricci-Flat Branes
• Stability of naked singularities and algebraically special modes
• More Ricci-flat branes
• Schwarzschild Black Branes and Strings in higher-dimensional Brane Worlds
• Naked shell singularities on the brane
• More on general $p$-brane solutions
• Schwarzschild generalized black hole horizon and the embedding space
• P-brane Black Holes and Post-Newtonian Approximation
• Static Ricci-flat 5-manifolds admitting the 2-sphere
• Charged seven-dimensional spacetimes with spherically symmetric extra-dimensions
• Post-Newtonian parameters for general black hole and spherically symmetric p-brane solutions