Abstract
The recently proposed effective equation of motion for the 4D-Einstein–Gauss–Bonnet gravity admits a static black hole solution that has, like the Rissner–Nordström charged black hole, two horizons instead of one for the Schwarzschild black hole. This means that the central singularity is timelike instead of spacelike. It should though be noted that in Dge 5, the solution always admits only one horizon like the Schwarzshild solution. In the equation defining the horizon, the rescaled Gauss–Bonnet coupling constant appears as a new ‘gravitational charge’ with a repulsive effect to cause in addition to event horizon a Cauchy horizon. Thus it radically alters the causal structure of the black hole.
Highlights
It is well known that the Lovelock theory [1], whose action is a homogeneous polynomial in Riemann curvature, is the most natural higher dimensional generalization of the Einstein gravity – general relativity (GR)
It is possible to make higher order terms contribute in the equation in 4D by dilaton coupling – a scalar field coupled to higher order term in the action, see for instance [2,3,4,5]
In that the GB coupling is scaled as α → α/(D−4) and thereby cancelling out (D −4) factor in the equation, and taking the limit D → 4. This results into an effective equation in 4D which is the Einstein–Gauss–Bonnet (EGB) equation written for D = 4.1 it could be solved in spacetime with some specific symmetries for different situations, black holes and cosmology
Summary
It is well known that the Lovelock theory [1], whose action is a homogeneous polynomial in Riemann curvature, is the most natural higher dimensional generalization of the Einstein gravity – general relativity (GR). In this letter we wish to take up the issue of the static black hole solution of the new proposed 4D-EGB equation that admits two horizons instead of the usual one for the Schwarzschild solution. On the other hand the EGB equation has only one horizon like the Schwarzschild in D ≥ 5 which is the natural rightful playground for it.
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