Constant Curvature Black Hole Research Articles

Black hole solutions to Einstein-Bel-Robinson gravity

In this paper, we study the physical properties of black holes in the framework of the recently proposed Einstien-Bel-Robinson gravity. We show that interestingly the theory propagates a transverse and massless graviton on a maximally symmetric background with positive energy. There is also a single ghost-free branch that returns to the Einstein case when β → 0. We find new black hole solutions to the equations, both approximate and exact, the latter being a constant curvature black hole solution, and discuss inconsistencies with metrics that were previously claimed to be approximate solutions to the equations. We obtain the conserved charges of the theory and briefly study the thermodynamics of the black hole solutions.

Constant curvature black holes in Einstein AdS gravity: Euclidean action and thermodynamics

We compute the Euclidean action for constant curvature black holes (CCBHs), as an attempt to associate thermodynamic quantities to these solutions of Einstein anti-de Sitter (AdS) gravity. CCBHs are gravitational configurations obtained by identifications along isometries of a $D$-dimensional globally AdS space, such that the Riemann tensor remains constant. Here, these solutions are interpreted as extended objects, which contain a $(D-2)$-dimensional de-Sitter brane as a subspace. Nevertheless, the computation of the free energy for these solutions shows that they do not obey standard thermodynamic relations.

Action growth for black holes in modified gravity

The general form of the action growth for a large class of static black hole solutions in modified gravity which includes $F(R)$-gravity models is computed. The cases of black hole solutions with non vanishing Ricci curvature are also considered, generalizing the results previously found and valid only for constant curvature black holes. An argument is put forward to provide a physical interpretation of the results.

Constant curvature black holes in Einstein-AdS gravity: Conserved quantities

We study physical properties of constant curvature black holes (CCBHs) in Einstein anti-de Sitter (AdS) gravity. These objects, which are locally AdS throughout the space, are constructed from identifications of global AdS spacetime, in a similar fashion as Banados-Teitelboim-Zanelli (BTZ) black hole in three dimensions. We find that, in dimensions equal or greater than four, CCBHs have zero mass and angular momentum. Only in odd dimensions we are able to associate a nonvanishing conserved quantity to these solutions, which corresponds to the vacuum (Casimir) energy of the spacetime.

Hawking temperature of constant curvature black holes

The constant curvature (CC) black holes are higher dimensional generalizations of Banados-Teitelboim-Zanelli black holes. It is known that these black holes have the unusual topology of ${\mathcal{M}}_{D\ensuremath{-}1}\ifmmode\times\else\texttimes\fi{}{S}^{1}$, where $D$ is the spacetime dimension and ${\mathcal{M}}_{D\ensuremath{-}1}$ stands for a conformal Minkowski spacetime in $D\ensuremath{-}1$ dimensions. The unusual topology and time-dependence for the exterior of these black holes cause some difficulties to derive their thermodynamic quantities. In this work, by using a globally embedding approach, we obtain the Hawking temperature of the CC black holes. We find that the Hawking temperature takes the same form when using both the static and global coordinates. Also, it is identical to the Gibbons-Hawking temperature of the boundary de Sitter spaces of these CC black holes.

THERMODYNAMICS OF CONSTANT CURVATURE BLACK HOLES THROUGH SEMICLASSICAL TUNNELING

We study the semiclassical tunneling of scalar and fermion fields from the horizon of a Constant Curvature Black Hole, which is locally AdS and whose five-dimensional analogue is dual to [Formula: see text] super-Yang–Mills. In particular, we highlight the strong reliance of the tunneling method for Hawking radiation on near-horizon symmetries, a fact often hidden behind the algorithmic procedure with which the tunneling approach tends to be used. We ultimately calculate the emission rate of scalars and fermions, and hence the black hole's Hawking temperature.

Separation of the Dirac equation in the (3 + 1)-dimensional constant curvature black hole background and its solution

The behavior of spin-half particles is discussed in the (3 + 1)-dimensional constant curvature black hole (CCBH) spacetime. We use Schwarzschild-like coordinates, valid outside the black hole event horizon. The constant time surfaces corresponding to the timelike Killing vector are degenerate at the black hole event horizon and also along an axis. We write down the Dirac equation in this spacetime using the Newman–Penrose formalism which is not easily separable unlike that in the Kerr metric. However, with a particular choice of basis system the equation is separable and we obtain the solutions. We discuss the structural difference in the Dirac equation in the CCBH spacetime with that in the Kerr geometry, due to a difference in the corresponding spacetime metrices the resulting complexity arose in separation in the earlier case.

Constant curvature black hole and dual field theory

We consider a five-dimensional constant curvature black hole, which is constructed by identifying some points along a Killing vector in a five-dimensional AdS space. The black hole has the topology M4×S1, its exterior is time-dependent and its boundary metric is of the form of a three-dimensional de Sitter space times a circle, which means that the dual conformal field theory resides on a dynamical spacetime. We calculate the quasilocal stress-energy tensor of the gravitational background and then the stress-energy tenor of the dual conformal field theory. It is found that the trace of the tensor does indeed vanish, as expected. Further we find that the constant curvature black hole spacetime is just the “bubble of nothing” resulting from Schwarzschild-AdS black holes when the mass parameter of the latter vanishes.

Entropy of a scalar field in a(3+1)-dimensional constant curvature black hole background

We consider the thermodynamics of a minimally coupled massive scalar field in a $(3+1)$-dimensional constant curvature black hole background. The brick wall model of 't Hooft is used. When Scharzschild-like coordinates are used it is found that, apart from the usual radial brick wall cutoff parameter, an angular cutoff parameter is required to regularize the solution. The free energy of the scalar field is obtained through a counting of the states using the WKB approximation. It is found that the free energy and the entropy are logarithmically divergent in both cutoff parameters.

Gravity from topological field theory

We construct a topological field theory which, on the one hand, generalizes BF theories in that there is a non-trivial coupling to ``topological matter fields;'' and, on the other, generalizes the three-dimensional model of Carlip and Gegenberg to arbitrary dimensional manifolds. Like the three dimensional model, the theory can be considered to describe a gravitational field interacting with topological matter. In particular, in two dimensions, the model is that of gravity on a torus. In four dimensions, the model is shown to admit constant curvature black hole solutions.

Entropy of constant curvature black holes in general relativity

We consider the thermodynamic properties of the constant curvature black hole solution recently found by Banados. We show that it is possible to compute the entropy and the quasilocal thermodynamics of the spacetime using the Einstein-Hilbert action of General Relativity. The constant curvature black hole has some unusual properties which have not been seen in other black hole spacetimes. The entropy of the black hole is not associated with the event horizon; rather it is associated with the region between the event horizon and the observer. Further, surfaces of constant internal energy are not isotherms so the first law of thermodynamics exists only in an integral form. These properties arise from the unusual topology of the Euclidean black hole instanton.

Constant curvature black holes

Constant curvature black holes are constructed by identifying points in anti-de Sitter space. In n dimensions, the resulting topology is R^{n-1} * S_1, as opposed to the usual R^2 * S_{n-2} Schwarzschild black hole, and the corresponding causal structure is displayed by a (n-1)-dimensional picture, as opposed to the usual 2-dimensional Kruskal diagram. The five dimensional case, which can be embedded in a Chern-Simons supergravity theory, is analyzed in detail.