General theory of large D membranes consistent with second law of thermodynamics

We write down the most general membrane equations dual to black holes for a general class of gravity theories, up to sub-leading order in 1/D in large D limit. We derive a “minimal” entropy current which satisfies a local form of second law from these membrane equations. We find that consistency with second law requires the membrane equations to satisfy certain constraints. We find additional constraints on the membrane equations from the existence of membrane solutions dual to stationary black holes. Finally we observe a tension between second law and matching with Wald entropy for dual stationary black hole configurations, for the minimal entropy current. We propose a simple modification of the membrane entropy current so that it satisfies second law and also the stationary membrane entropy matches the Wald entropy.

Mimetic gravity in (2 + 1)-dimensions

One of the most important achievements in general relativity has been discovery of the (2 + 1)-dimensional black hole solutions of Einstein gravity in anti-de Sitter (AdS) spacetime [7]. In this paper, we construct, for the first time, the (2 + 1)-dimensional solutions of mimetic theory of gravity. These solutions may provide a powerful background to investigate the physical properties of mimetic gravity and examine its viability in lower spacetime dimensions. In particular, some physical properties of stationary black hole solutions of this theory in the presence of charge or angular momentum are investigated.

Hawking Radiation is Nothing: Developed Correlation of Entropy with Black Hole Area

Read is the first word and divine order in the Holy Quran. My lovely physics does not answer many mysteries in the universe including black holes. The observed ordinary matter in the universe is only ~5 %. The remaining is 27% dark matter and approximately 68% dark energy of. This paper introduces a developed model and concept to black hole anatomy and entropy-surface area correlation. It considers the stationary black hole a one entity of 4 concentric spheres around the singularity. They are the event horizon, photon sphere at 1.5Rs, unstable light sphere at 2.6Rs and innermost stable particle sphere at 3Rs. An equation (Sayed Ts formula) was derived excluded heuristics of Professor S. Hawking. This formula is based on different proportional constant between entropy and black hole surface area; not ¼ as He conjectured. In spite of my respect and humanity sympathy with Prof. Hawking, his tombstone equation should be corrected. There is neither radiation escape from black holes nor any signal detected due to micro black holes evaporation. Finally, it can be stated that Hawking radiation is Nothing.

Mass formulae and staticity condition for dark matter charged black holes

The Arnowitt–Deser–Misner formalism is used to derive variations of mass, angular momentum and canonical energy for Einstein–Maxwell dark matter gravity in which the auxiliary gauge field coupled via kinetic mixing term to the ordinary Maxwell one, which mimics properties of hidden sector. Inspection of the initial data for the manifold with an interior boundary, having topology of $$S^2$$ S 2 , enables us to find the generalised first law of black hole thermodynamics in the aforementioned theory. It has been revealed that the stationary black hole solution being subject to the condition of encompassing a bifurcate Killing horizon with a bifurcation sphere, which is non-rotating, must be static and has vanishing magnetic Maxwell and dark matter sector fields, on static slices of the spacetime under consideration.

Further selected solutions

In previous chapters we presented the key notions associated with stationary black-hole spacetimes, as well as the minimal set of metrics needed to illustrate the basic features of the world of black holes. In this chapter we present some further black holes, selected because of their physical and mathematical interest. We start, in Section 5.1, with the Kerr–de Sitter/anti-de Sitter metrics, the cosmological counterparts of the Kerr metrics. Section 5.2 contains a description of the Kerr–Newman–de Sitter/anti-de Sitter metrics, which are the charged relatives of the metrics presented in Section 5.1. In Section 5.3 we analyse in detail the global structure of the Emparan–Reall ‘black rings’: these are five-dimensional black-hole spacetimes with R × S 1 × S 2-horizon topology. The Rasheed metrics of Section 5.4 provide an example of black holes arising in Kaluza–Klein theories. The Birmingham family of metrics, presented in Section 5.5, forms the most general class known of explicit static vacuum metrics with cosmological constant in all dimensions, with a wide range of horizon topologies.

An introduction to black holes

In this chapter the basics of the geometry of stationary black-hole spacetimes are presented. We start in Section 4.1 with a brief review of astrophysical black holes. We continue in Section 4.2 with the presentation of the flagship black hole, the Schwarzschild solution: we construct there its various extensions, and analyse some of its properties. The general notions arising in the context of black-hole geometries are presented in Section 4.3. A systematic discussion of extensions of spacetimes is carried out in Section 4.4. The charged counterparts of the Schwarzchild metric, namely the Reissner–Nordström metrics, are analysed in Section 4.5. The Kerr metric, expected to describe the most general vacuum, stationary, and rotating black holes, is presented in Section 4.6. The electrovacuum Majumdar–Papapetrou spacetimes, containing two or more disconnected black-hole regions, are described in Section 4.7.

A spherically topological analysis of stationary black holes

A black hole with zero angular momentum is said to be stationary and under certain conditions such a black hole can represented as a sphere. This review examines Hawking’s topology theorem, the Schwarzschild metric, novel solutions to Einstein’s equations, resonances of hyperbolic orbits around the event horizon for spherical, stationary black holes, and analyzes their importance. It is suggested, that in the spherical stationary black hole case, the Fourier analysis can be used to find the resonances due to Geometric scattering of hyperbolic orbits and thus the outgoing energy fields from the event horizon can be found more precisely; allowing for the adequate signal processing analysis to be found for such a field.

Thermodynamics of a Non-Stationary Black Hole Based on Generalized Uncertainty Principle

In the general theory of relativity (GTR), black holes are defined as objects with very strong gravitational fields even light can not escape. Therefore, according to GTR black hole can be viewed as a non-thermodynamic object. The worldview of a black hole began to change since Hawking involves quantum field theory to study black holes and found that black holes have temperatures that analogous to black body radiation. In the theory of quantum gravity there is a term of the minimum length of an object known as the Planck length that demands a revision of Heisenberg's uncertainty principle into a Generalized Uncertainty Principle (GUP). Based on the relationship between the momentum uncertainty and the characteristic energy of the photons emitted by a black hole, the temperature and entropy of the non-stationary black hole (Vaidya-Bonner black hole) were calculated. The non-stationary black hole was chosen because it more realistic than static black holes to describe radiation phenomena. Because the black hole is dynamic then thermodynamics studies are conducted on both black hole horizons: the apparent horizon and its event horizon. The results showed that the dominant correction term of the temperature and entropy of the Vaidya-Bonner black hole are logarithmic.