Minimum Retraction of a Topological Black Hole

Andreas Wagner^*
*Correspondence: Andreas Wagner, Department of Mathematics, University of New Mexico, Albuquerque, USA, Email:

Editorial Note

We characterize the spherical topology of black holes in a special case of spherical symmetry. For this purpose, we carefully consider the metrics space of topological black holes B4. By adjusting some of the parameters, we infer the appropriate components and the equatorial geodesics on the line element of the topological black holes. We also construct the minimum retraction ρ2:B4→ C 3 2. As a result, the minimum deformation retract has also been inferred to explain the effects on their center of mass in binary system. This would help us to better understand some of possible applications in astrophysics and the Cosmology, such as the natural phenomena of merging two black holes and curved the space-time in general relativity. In addition, we find the relation between limit folding and limit minimum retraction on the n-dimension. The folding on connected sum of essential sub-manifolds of the topological black hole have constructed for different types and characteristics.

Topological Black Hole

In astrophysics, the stellar Black holes are formed when very massive stars collapse at the end of their life cycle. According to the Einstein’s theory of general relativity, the compact objects (Black holes, Neutron stars and White dwarfs) caused the deformation (or wrapping) of space-time due to their hypergravity. This action will also revent anything including the light to escape from the region of their space-time. However, studying the Black hole in a binary system gives rise to various interesting research fields on both theory and observation, because he event horizons of two objects get deformed by the gravitational presence of one another. As a result, four dimensional static vacuum black holes in anti-de Sitter (Ads) space-time can have horizons of various shape. It is noteworthy to mention here that, the sources of gravitational waves produced by mergers of stellar Black holes have been detected, as the first time, with LIGO-Virgo Scientific Collaboration in 2015, as an observational evidence for their existence (see Abbott et al. 2016 and references there).

The role of Einstein-Maxwell equations in Ads space-time

In order to better understand the black hole physics, we need to describe black holes by using some topological transformations. The topological black holes may be created by starting with Ads space-time. This would then prudently force a certain identification, which has the effect of generating event horizons in the resultant quotient space-time.

We consider a class of dark opening answers for Einstein's conditions in d measurements with a negative cosmological steady. These arrangements have the property that the skyline is a (d-2) dimensional Einstein complex of positive, zero, or negative arch. The mass, temperature, and entropy are determined. Utilizing the correspondence with conformal field hypothesis, the stage construction of the arrangements is analyzed, and used to decide the right mass reliance of the Bekenstein-Hawking entropy.

We investigate the traditional dependability of topological dark openings in d-dimensional enemy of de Sitter space-time, where the skyline is an Einstein complex of negative bend. As indicated by the check invariant formalism of Ishibashi and Kodama, gravitational irritations are delegated being of scalar, vector, or tensor sort, contingent upon their change properties regarding the skyline complex. For the massless dark opening, we show that the irritation conditions for everything modes can be diminished to a basic scalar field condition. This condition is by and large reasonable as far as hyper geometric capacities, along these lines permitting a careful logical assurance of possible gravitational dangers. We build up a vital and adequate condition for soundness, as far as the eigenvalues λ of the Lichnerowicz administrator not too far off complex, specifically λ≥−4 (d-2). For the instance of negative mass dark openings, we show that an adequate condition for strength is given by λ≥−2 (d-3).